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# Solutions to the Mock Aptitude Test - I

1. If the angles of a quadrilateral form an arithmetic progression and the third angle measures three times the first, then the smallest angle is:

90 degrees

72 degrees

54 degrees

36 degrees (Answer)

2. The cocktail Bloody Mary contains 70% tomato juice, 20% lime juice and the rest liquor. The cocktail Go Bonkers is a mixture of Bloody Mary and ScrewDriver in the ratio 2:1. If GoBonkers contains 60% fruit juice, 15% lime juice and the rest liquor, then what is the percentage of lime juice in ScrewDriver?

20%

5% (Answer)

10%

15%

3. Alex bought a carpet to cover his drawing room completely. He found that its area was 2% less than that required. He tried to shift the carpet to his bedroom, but found that the carpet area was 5% more than the bedroom area. The length to breadth ratio of the carpet was 3:2, and he could not fit it in the kitchen either. In frustration, he cut the largest circle possible out of the carpet. The area of the waste material was 140 sq.ft. The area of the circular piece of the carpet was:

160 sq.ft.

140 sq.ft.

154 sq.ft (Answer)

194 sq.ft

4. Queen and Express are two trains of the same length. They cross each other in time T when traveling in the opposite directions. Queen over-takes Express in time t when both are moving in the same direction. Find the time taken by Queen to overtake Express when the latter is at rest, if Queen is faster than Express.

2Tt

t+T (Answer)

T+t

Tt

2T(T-t)

2(T+t)

Tt

5. X's age after 6 years will be three-seventh of his father's age. 10 years ago, the ratio of their ages was 1:5. What is X's father's age at present?

40

45

50 (Answer)

49

6. A hound takes 4 leaps to every 5 leaps of a hare, but 3 leaps of the hound are equal to 4 leaps of the hare. What is the ratio of the speed of the hound to the speed of the hare?

5 : 3

3 : 5

15 : 16

16 : 15 (Answer)

7. If the price of sugar increases by 40%, then by what maximum percentage can a family increase its sugar consumption, in order to avoid increase in its expenditure beyond 82% of the previous value?

60%

30% (Answer)

40%

50

8. A garrison of 1500 men has provisions for 48 days. At the end of 13 days, a reinforcement arrives and it is found that now the provisions would last for only 25 more days. What is the strength of the reinforcement?

575

600 (Answer)

625

400

9. On Republic Day, 66 kg of fruits (bananas, oranges, apples) were brought from the market. The ratio of the weights of bananas and oranges was 4 : 5. The ratio of the weights of oranges and apples was 2 : 3. Find the weight of the apples that were brought from the market.

16 kg

20 kg

24 kg

30 kg (Answer)

10. A manufacturer sells his goods to a wholesaler at 10% gain; the wholesaler to the retailer at 20% gain and the retailer to the customer at 30% gain. The percent that the customer has to pay more on the price charged by the manufacturer is:

72%

71 2/3%

71 3/5% (Answer)

73%

11. The average speed of a train including stoppages was 27 kmph and excluding stoppages was 41 kmph. How many minutes did the train stop per hour?

20.5 minutes (Answer)

15 minutes

25 minutes

30 minutes

12. A certain sum of money when deposited in a post office becomes 7/5 times in 8 years. An equal sum deposited in a fixed deposit in a bank doubles in 12 & 1/2 years. Which of the two agencies, the post office or the bank, gives a better rate of interest?

The Bank (Answer)

The Post Office

Both give equal interest

Can't be determined

13. A cylindrical vessel of base area 154 sq.cm. and height 1.2 cm is filled with sand. The sand is emptied to form a conical heap of the same height on the ground. What is the base radius of the cone?

15.4 cm

14.0 cm

12.1 cm (Answer)

17.5 cm

14. The sum of two numbers is 126 and their L.C.M. is 405. The H.C.F of the numbers is equal to

5

9 (Answer)

14

12

15. A student was asked to find the product of two 2-digit numbers but instead he reversed the position of the digits in both the numbers and calculated the answer and still managed to get the correct answer. Then, the number are:

31, 39

31, 26

23, 96

all of the above (Answer)

16. A boat going upstream takes 20 minutes while it takes 10 minutes for going downstream for the same distance. If speed of the boat in still water is 7.5 kmph, then find speed of the stream in kmph.

5

2.5 (Answer)

2

3

17. If a clock takes 10 seconds to strike 11, then how many seconds does it take to strike 6?

6

5 (Answer)

60/11

50/11

18. Two squirrels A & B are climbing up two separate 100 feet poles. Squirrel A climbs up 3 feet in 1 minute but slips back 1 foot for every 2 feet climbed. Squirrel B climbs up 4 feet in 1 minute but slips down 1.5 feet for every 2 feet climbed. Squirrel A stops for a minute after every 2 minutes, while Squirrel B stops for 1 minute after every 3 minutes. Assume that the slippage occurs continuously.

Which squirrel reaches the top first and in how many minutes?

Squirrel A in 101 minutes

Squirrel B in 132 minutes

Squirrel in 100 minutes (Answer)

Squirrel B in 133 minutes

19. A person borrowed a sum of Rs. 34,000 from his provident fund account on the condition to repay 22 monthly installments of Rs. 1500 and the last installment of Rs. 1000. What will be the simple interest at the rate of 4.5% per annum, which he pays as 24th installment.

Rs. 1510 (Answer)

Rs. 1250

Rs. 1400

Rs. 1600

20. A student has to match 3 historical events 'Dandi March', 'Quit India Movement' and 'Mahatma Gandhi Assassination' with years 1948, 1930 and 1942. The student has no knowledge of the correct answers and decides to match the events and the years randomly. The probability that the student gets exactly 2 answers correct is:

(Assume that the student knows that no two events occurred in the same year.)

0 (Answer)

1

2/3

0.5

21. In the next 3 questions, a related pair of words is followed by pairs of words. Choose the pair that best expresses a relationship similar to that of the given pair.

WEAR : JERKIN ::

eat : manumit

blow : longhorn

read : makimono (Answer)

scare : hecatomb

22. HERMETIC : AIR ::

watertight : moisture (Answer)

claustrophobic : closeness

combatant : strife

somnolent : boredom

23. FLURRY : BLIZZARD::

grass : dew

wind : air

shore : waves

drizzle : cloudburst (Answer)

24. Choose a set of words for each pair of blanks that best fits the meaning of the sentence as a whole.

Held up only by a ________ steel cable, the chair lift was _________ to carry only two people.

slender, instructed

single, intended (Answer)

sturdy, obliged

massive, designed

25. The _______ of the early morning light _______ the room, making it larger and cozier at once.

brilliance, shattered

softness, transformed (Answer)

harshness, transfigured

warmth, disfigured

26. As 'daring' goes with 'temerity', same way 'clear-sighted' goes with

Perspicacity (Answer)

Impulsiveness

Energy

Clemency

27. He walked to the garden.

Present

Future

Past (Answer)

None of these

28. Which of the following word is wrongly spelled?

possession

ocassion (Answer)

profession

procession

29. Give the word which is most opposite in the meaning of the word 'evident'.

doubtful (Answer)

unimportant

disagreed

understood

30. If ALONE is written as YKMMC, then CLASS is written as

BKVQQ

BKYRR (Answer)

AKYQQ

None of these

31. The missing number in the series 5 13 ? 71 133 is

33 (Answer)

63

26

49

32. What is the missing number in the following series:

2 6 3 4 20 5 6 ? 7

35

30

49

42 (Answer)

33. Which letter will be seventh to the left of the fourteenth letter from the right end of the English alphabet series?

F (Answer)

T

S

E

34. A is mother of B. C is father of B and C has 3 children. On the basis of this information, find out which of the following relations is correct.

C has 3 daughters.

C has 3 sons.

B is the son.

None of the above. (Answer)

35. Vinod is the brother of Bhaskar. Manu is the sister of Vinod. Biswal is the brother of Preetam and Preetam is the daughter of Bhaskar. Who is the uncle of Biswal?

Bhaskar

Manu

Vinod (Answer)

Information is incomplete

36. The total number of factors of 12! is

802

796

792 (Answer)

768

37. The angle between the hands of a clock when the time is 3:40 is

130 (Answer)

135

120

145

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM)

0

10

11 (Answer)

12

39. The number of ways in which 5 letters can be placed in 5 addressed envelopes so that no letter goes to the correct envelope is?

44 (Answer)

47

50

40

40. Refer to the following information to answer the questions that follow.

Two Countries, Aryavarta and Syria, have agreed to submit any disputes that might arise between them to arbitration panels drawn from a pool of arbitrators.

The pool consists of the following: three Aryan representatives- K, L and M; three Syrian representatives- P, Q and R and three neutral arbitrators- S, T and U.

Each arbitration panel must be formed according to the following conditions:

• A panel can have three, four, five or six members.

• At least one member of each panel must be neutral.

• Neither Aryan nor Syrian representatives can make up more than half the number of members on a panel.

• S cannot be on a panel with L, with M or with U.

• R cannot be on a panel with L or with T.

If both S and T are to be members of a three-member panel, then which of the following can be the third member of that panel?

L

M

P (Answer)

R

41. If R and S are both selected as members of a four-member panel, then which of the following must also be selected as a member of that panel?

K (Answer)

L

P

Q

42. If K, M, Q and R are all selected as members of a five-member panel, then which of the following must be selected as the fifth member of that panel?

L

U (Answer)

S

T

43. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

MLON

VCXE

OJQL

JQPK (Answer)

44. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

JPL

SGU

TGH (Answer)

BXD

45. Read the passage below and answer the questions following it on the basis of what is stated or implied in the passage.

Currently, the paramount problem in the field of biomaterials, the science of replacing diseased tissue with human-made implants, is control over the interface or surface, between implanted biomaterials and living tissues. The physical properties of most tissues can be matched by careful selection of raw materials: metals, ceramics, or several varieties of polymer materials. Even the requirement that biomaterials processed from these materials be or several varieties of polymer materials. Even the requirement that biomaterials processed from these materials be nontoxic to host tissue can be met by techniques derived from studying the reactions of tissue cultures to biomaterials or from short-term implants. But achieving necessary matches in physical properties across interfaces between living and non-living matter requires knowledge of which molecules control the bonding of cells to each other—an area that we have not yet explored thoroughly. Although recent research has allowed us to stabilize the tissue-biomaterial

interface by controlling either the chemical reactions or the microstructure of the biomaterials, our fundamental understanding of how implant devices adhere to tissues remains woefully incomplete.

According to the passage, the major problem currently scientists are facing in the field of biomaterials is:

assessing and regulating the bonding between host tissue and implants (Answer)

controlling the transfer of potentially toxic materials across the interface of tissue and implant

discovering new materials from which to construct implant devices

deciding in what situations implants are needed

46. The author’s primary purpose is to

answer a theoretical question in the field of biomaterials

discuss the current state of technology in the field of biomaterials (Answer)

resolve a research dispute in the field of biomaterials

predict an ethical crisis for biomaterials researchers

47. Read the information given below and answer the questions that follow:

1. Eleven students Anwar, Baham, Chetan, Dayal, Eshwar, Farooq, Gajendra, Hariom, Inayat, Jatin and Kishore are sitting on a bench in a lecture room facing towards the teacher.

2. Dayal is towards the left of Farooq and second to the right of Chetan.

3. Eshwar is second to the left of Anwar and is sitting on one end.

4. Jatin is the neighbourer of Anwar and Baham is third to the left of Gajendra.

5. Hariom is next to left of Dayal and is third to the right of Inayat.

Which two students are sitting on two ends?

Kishore and Dayal

Eshwar and Dayal

Eshwar and Farooq (Answer)

Kishore and Farooq

48. Which group of students is sitting just next to the right of Gajendra?

Chetan, Hariom, Dayal, Eshwar

Chetan, Hariom, Inayat, Baham

Chetan, Hariom, Dayal, Inayat

None of the above (Answer)

49. Who is sitting just in the middle?

Inayat (Answer)

Chetan

Baham

Jatin

50. Which of the given 5 statements is unnecessary?

(1) and (3)

(1)

(3)

All are necessary. (Answer)

90 degrees

72 degrees

54 degrees

36 degrees (Answer)

2. The cocktail Bloody Mary contains 70% tomato juice, 20% lime juice and the rest liquor. The cocktail Go Bonkers is a mixture of Bloody Mary and ScrewDriver in the ratio 2:1. If GoBonkers contains 60% fruit juice, 15% lime juice and the rest liquor, then what is the percentage of lime juice in ScrewDriver?

20%

5% (Answer)

10%

15%

3. Alex bought a carpet to cover his drawing room completely. He found that its area was 2% less than that required. He tried to shift the carpet to his bedroom, but found that the carpet area was 5% more than the bedroom area. The length to breadth ratio of the carpet was 3:2, and he could not fit it in the kitchen either. In frustration, he cut the largest circle possible out of the carpet. The area of the waste material was 140 sq.ft. The area of the circular piece of the carpet was:

160 sq.ft.

140 sq.ft.

154 sq.ft (Answer)

194 sq.ft

4. Queen and Express are two trains of the same length. They cross each other in time T when traveling in the opposite directions. Queen over-takes Express in time t when both are moving in the same direction. Find the time taken by Queen to overtake Express when the latter is at rest, if Queen is faster than Express.

2Tt

t+T (Answer)

T+t

Tt

2T(T-t)

2(T+t)

Tt

5. X's age after 6 years will be three-seventh of his father's age. 10 years ago, the ratio of their ages was 1:5. What is X's father's age at present?

40

45

50 (Answer)

49

6. A hound takes 4 leaps to every 5 leaps of a hare, but 3 leaps of the hound are equal to 4 leaps of the hare. What is the ratio of the speed of the hound to the speed of the hare?

5 : 3

3 : 5

15 : 16

16 : 15 (Answer)

7. If the price of sugar increases by 40%, then by what maximum percentage can a family increase its sugar consumption, in order to avoid increase in its expenditure beyond 82% of the previous value?

60%

30% (Answer)

40%

50

8. A garrison of 1500 men has provisions for 48 days. At the end of 13 days, a reinforcement arrives and it is found that now the provisions would last for only 25 more days. What is the strength of the reinforcement?

575

600 (Answer)

625

400

9. On Republic Day, 66 kg of fruits (bananas, oranges, apples) were brought from the market. The ratio of the weights of bananas and oranges was 4 : 5. The ratio of the weights of oranges and apples was 2 : 3. Find the weight of the apples that were brought from the market.

16 kg

20 kg

24 kg

30 kg (Answer)

10. A manufacturer sells his goods to a wholesaler at 10% gain; the wholesaler to the retailer at 20% gain and the retailer to the customer at 30% gain. The percent that the customer has to pay more on the price charged by the manufacturer is:

72%

71 2/3%

71 3/5% (Answer)

73%

11. The average speed of a train including stoppages was 27 kmph and excluding stoppages was 41 kmph. How many minutes did the train stop per hour?

20.5 minutes (Answer)

15 minutes

25 minutes

30 minutes

12. A certain sum of money when deposited in a post office becomes 7/5 times in 8 years. An equal sum deposited in a fixed deposit in a bank doubles in 12 & 1/2 years. Which of the two agencies, the post office or the bank, gives a better rate of interest?

The Bank (Answer)

The Post Office

Both give equal interest

Can't be determined

13. A cylindrical vessel of base area 154 sq.cm. and height 1.2 cm is filled with sand. The sand is emptied to form a conical heap of the same height on the ground. What is the base radius of the cone?

15.4 cm

14.0 cm

12.1 cm (Answer)

17.5 cm

14. The sum of two numbers is 126 and their L.C.M. is 405. The H.C.F of the numbers is equal to

5

9 (Answer)

14

12

15. A student was asked to find the product of two 2-digit numbers but instead he reversed the position of the digits in both the numbers and calculated the answer and still managed to get the correct answer. Then, the number are:

31, 39

31, 26

23, 96

all of the above (Answer)

16. A boat going upstream takes 20 minutes while it takes 10 minutes for going downstream for the same distance. If speed of the boat in still water is 7.5 kmph, then find speed of the stream in kmph.

5

2.5 (Answer)

2

3

17. If a clock takes 10 seconds to strike 11, then how many seconds does it take to strike 6?

6

5 (Answer)

60/11

50/11

18. Two squirrels A & B are climbing up two separate 100 feet poles. Squirrel A climbs up 3 feet in 1 minute but slips back 1 foot for every 2 feet climbed. Squirrel B climbs up 4 feet in 1 minute but slips down 1.5 feet for every 2 feet climbed. Squirrel A stops for a minute after every 2 minutes, while Squirrel B stops for 1 minute after every 3 minutes. Assume that the slippage occurs continuously.

Which squirrel reaches the top first and in how many minutes?

Squirrel A in 101 minutes

Squirrel B in 132 minutes

Squirrel in 100 minutes (Answer)

Squirrel B in 133 minutes

19. A person borrowed a sum of Rs. 34,000 from his provident fund account on the condition to repay 22 monthly installments of Rs. 1500 and the last installment of Rs. 1000. What will be the simple interest at the rate of 4.5% per annum, which he pays as 24th installment.

Rs. 1510 (Answer)

Rs. 1250

Rs. 1400

Rs. 1600

20. A student has to match 3 historical events 'Dandi March', 'Quit India Movement' and 'Mahatma Gandhi Assassination' with years 1948, 1930 and 1942. The student has no knowledge of the correct answers and decides to match the events and the years randomly. The probability that the student gets exactly 2 answers correct is:

(Assume that the student knows that no two events occurred in the same year.)

0 (Answer)

1

2/3

0.5

21. In the next 3 questions, a related pair of words is followed by pairs of words. Choose the pair that best expresses a relationship similar to that of the given pair.

WEAR : JERKIN ::

eat : manumit

blow : longhorn

read : makimono (Answer)

scare : hecatomb

22. HERMETIC : AIR ::

watertight : moisture (Answer)

claustrophobic : closeness

combatant : strife

somnolent : boredom

23. FLURRY : BLIZZARD::

grass : dew

wind : air

shore : waves

drizzle : cloudburst (Answer)

24. Choose a set of words for each pair of blanks that best fits the meaning of the sentence as a whole.

Held up only by a ________ steel cable, the chair lift was _________ to carry only two people.

slender, instructed

single, intended (Answer)

sturdy, obliged

massive, designed

25. The _______ of the early morning light _______ the room, making it larger and cozier at once.

brilliance, shattered

softness, transformed (Answer)

harshness, transfigured

warmth, disfigured

26. As 'daring' goes with 'temerity', same way 'clear-sighted' goes with

Perspicacity (Answer)

Impulsiveness

Energy

Clemency

27. He walked to the garden.

Present

Future

Past (Answer)

None of these

28. Which of the following word is wrongly spelled?

possession

ocassion (Answer)

profession

procession

29. Give the word which is most opposite in the meaning of the word 'evident'.

doubtful (Answer)

unimportant

disagreed

understood

30. If ALONE is written as YKMMC, then CLASS is written as

BKVQQ

BKYRR (Answer)

AKYQQ

None of these

31. The missing number in the series 5 13 ? 71 133 is

33 (Answer)

63

26

49

32. What is the missing number in the following series:

2 6 3 4 20 5 6 ? 7

35

30

49

42 (Answer)

33. Which letter will be seventh to the left of the fourteenth letter from the right end of the English alphabet series?

F (Answer)

T

S

E

34. A is mother of B. C is father of B and C has 3 children. On the basis of this information, find out which of the following relations is correct.

C has 3 daughters.

C has 3 sons.

B is the son.

None of the above. (Answer)

35. Vinod is the brother of Bhaskar. Manu is the sister of Vinod. Biswal is the brother of Preetam and Preetam is the daughter of Bhaskar. Who is the uncle of Biswal?

Bhaskar

Manu

Vinod (Answer)

Information is incomplete

36. The total number of factors of 12! is

802

796

792 (Answer)

768

37. The angle between the hands of a clock when the time is 3:40 is

130 (Answer)

135

120

145

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM)

0

10

11 (Answer)

12

39. The number of ways in which 5 letters can be placed in 5 addressed envelopes so that no letter goes to the correct envelope is?

44 (Answer)

47

50

40

40. Refer to the following information to answer the questions that follow.

Two Countries, Aryavarta and Syria, have agreed to submit any disputes that might arise between them to arbitration panels drawn from a pool of arbitrators.

The pool consists of the following: three Aryan representatives- K, L and M; three Syrian representatives- P, Q and R and three neutral arbitrators- S, T and U.

Each arbitration panel must be formed according to the following conditions:

• A panel can have three, four, five or six members.

• At least one member of each panel must be neutral.

• Neither Aryan nor Syrian representatives can make up more than half the number of members on a panel.

• S cannot be on a panel with L, with M or with U.

• R cannot be on a panel with L or with T.

If both S and T are to be members of a three-member panel, then which of the following can be the third member of that panel?

L

M

P (Answer)

R

41. If R and S are both selected as members of a four-member panel, then which of the following must also be selected as a member of that panel?

K (Answer)

L

P

Q

42. If K, M, Q and R are all selected as members of a five-member panel, then which of the following must be selected as the fifth member of that panel?

L

U (Answer)

S

T

43. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

MLON

VCXE

OJQL

JQPK (Answer)

44. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

JPL

SGU

TGH (Answer)

BXD

45. Read the passage below and answer the questions following it on the basis of what is stated or implied in the passage.

Currently, the paramount problem in the field of biomaterials, the science of replacing diseased tissue with human-made implants, is control over the interface or surface, between implanted biomaterials and living tissues. The physical properties of most tissues can be matched by careful selection of raw materials: metals, ceramics, or several varieties of polymer materials. Even the requirement that biomaterials processed from these materials be or several varieties of polymer materials. Even the requirement that biomaterials processed from these materials be nontoxic to host tissue can be met by techniques derived from studying the reactions of tissue cultures to biomaterials or from short-term implants. But achieving necessary matches in physical properties across interfaces between living and non-living matter requires knowledge of which molecules control the bonding of cells to each other—an area that we have not yet explored thoroughly. Although recent research has allowed us to stabilize the tissue-biomaterial

interface by controlling either the chemical reactions or the microstructure of the biomaterials, our fundamental understanding of how implant devices adhere to tissues remains woefully incomplete.

According to the passage, the major problem currently scientists are facing in the field of biomaterials is:

assessing and regulating the bonding between host tissue and implants (Answer)

controlling the transfer of potentially toxic materials across the interface of tissue and implant

discovering new materials from which to construct implant devices

deciding in what situations implants are needed

46. The author’s primary purpose is to

answer a theoretical question in the field of biomaterials

discuss the current state of technology in the field of biomaterials (Answer)

resolve a research dispute in the field of biomaterials

predict an ethical crisis for biomaterials researchers

47. Read the information given below and answer the questions that follow:

1. Eleven students Anwar, Baham, Chetan, Dayal, Eshwar, Farooq, Gajendra, Hariom, Inayat, Jatin and Kishore are sitting on a bench in a lecture room facing towards the teacher.

2. Dayal is towards the left of Farooq and second to the right of Chetan.

3. Eshwar is second to the left of Anwar and is sitting on one end.

4. Jatin is the neighbourer of Anwar and Baham is third to the left of Gajendra.

5. Hariom is next to left of Dayal and is third to the right of Inayat.

Which two students are sitting on two ends?

Kishore and Dayal

Eshwar and Dayal

Eshwar and Farooq (Answer)

Kishore and Farooq

48. Which group of students is sitting just next to the right of Gajendra?

Chetan, Hariom, Dayal, Eshwar

Chetan, Hariom, Inayat, Baham

Chetan, Hariom, Dayal, Inayat

None of the above (Answer)

49. Who is sitting just in the middle?

Inayat (Answer)

Chetan

Baham

Jatin

50. Which of the given 5 statements is unnecessary?

(1) and (3)

(1)

(3)

All are necessary. (Answer)

**If explanation regarding any solutions is needed, please post here.**

Yeah. Needed for the questions:

30. If ALONE is written as YKMMC, then CLASS is written as

31. The missing number in the series 5 13 ? 71 133 is

32. What is the missing number in the following series:

33. Which letter will be seventh to the left of the fourteenth letter from the right end of the English alphabet series? (I calculated as E)

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM) (Excluding right? So only 10?)

43. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

30. If ALONE is written as YKMMC, then CLASS is written as

31. The missing number in the series 5 13 ? 71 133 is

32. What is the missing number in the following series:

33. Which letter will be seventh to the left of the fourteenth letter from the right end of the English alphabet series? (I calculated as E)

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM) (Excluding right? So only 10?)

43. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

i didn't get the solution for these question. someone knows the method 😀

2. The cocktail Bloody Mary contains 70% tomato juice, 20% lime juice and the rest liquor. The cocktail Go Bonkers is a mixture of Bloody Mary and ScrewDriver in the ratio 2:1. If GoBonkers contains 60% fruit juice, 15% lime juice and the rest liquor, then what is the percentage of lime juice in ScrewDriver?

20%

5% (Answer)

10%

15%

11. The average speed of a train including stoppages was 27 kmph and excluding stoppages was 41 kmph. How many minutes did the train stop per hour?

20.5 minutes (Answer)

15 minutes

25 minutes

30 minutes

17. If a clock takes 10 seconds to strike 11, then how many seconds does it take to strike 6?

6

5 (Answer)

60/11

50/11

36. The total number of factors of 12! is

802

796

792 (Answer)

768

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM)

0

10

11 (Answer)

12

2. The cocktail Bloody Mary contains 70% tomato juice, 20% lime juice and the rest liquor. The cocktail Go Bonkers is a mixture of Bloody Mary and ScrewDriver in the ratio 2:1. If GoBonkers contains 60% fruit juice, 15% lime juice and the rest liquor, then what is the percentage of lime juice in ScrewDriver?

20%

5% (Answer)

10%

15%

11. The average speed of a train including stoppages was 27 kmph and excluding stoppages was 41 kmph. How many minutes did the train stop per hour?

20.5 minutes (Answer)

15 minutes

25 minutes

30 minutes

17. If a clock takes 10 seconds to strike 11, then how many seconds does it take to strike 6?

6

5 (Answer)

60/11

50/11

36. The total number of factors of 12! is

802

796

792 (Answer)

768

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM)

0

10

11 (Answer)

12

**11. The average speed of a train including stoppages was 27 kmph and excluding stoppages was 41 kmph. How many minutes did the train stop per hour?**

20.5 minutes (Answer)

15 minutes

25 minutes

30 minutes

41 km / 1 hr = 27 km / x hr

Ans: 1 hr - x hr

x = 0.658

hrs = x = 39.48

so ans = 60 - 39.48 = 20.52

32. What is the missing number in the following series:

the 6, 20 are all the product of the two numbers on either sides of it.. so the missing number is 42. 😀

33. Which letter will be seventh to the left of the fourteenth letter from the right end of the English alphabet series? (I calculated as E)

it is E it will be 7+14th from the z. i.e.6th from A. therfore it is F. 😀

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM) (Excluding right? So only 10?)

even i got oly 10. 😔

43. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

the last alone doesn't have vowel 😀

the 6, 20 are all the product of the two numbers on either sides of it.. so the missing number is 42. 😀

33. Which letter will be seventh to the left of the fourteenth letter from the right end of the English alphabet series? (I calculated as E)

it is E it will be 7+14th from the z. i.e.6th from A. therfore it is F. 😀

38. Between 6 AM and 6 PM, how many times does the hands of the clock form a straight line (i.e. 180 degrees? (Note: Excluding 6 AM and 6 PM) (Excluding right? So only 10?)

even i got oly 10. 😔

43. Check the four group of words given below. Three of these groups are alike in some way while one is different. Find the one which differs & mark it as your answer.

the last alone doesn't have vowel 😀

for this question i didn't work out.. guessed. its like only the first and second option can refer to some time. the third will have no unit and the last one's unit will be /hr. so went with option 1 😉 😛AbraKaDabra4. Queen and Express are two trains of the same length. They cross each other in time T when traveling in the opposite directions. Queen over-takes Express in time t when both are moving in the same direction. Find the time taken by Queen to overtake Express when the latter is at rest, if Queen is faster than Express.

2Tt

t+T (Answer)

T+t

Tt

2T(T-t)

2(T+t)

Tt

anyone knows the proper method 😀

30. If ALONE is written as YKMMC, then CLASS is written asIn the code, vowels are represented by two preceding alphabets whereas consonants are represented by the preceding alphabet.

ok... i thought it was like the first third had two preceeding alphabets and the rest the preceeding and so marked the option none of these 😉AbraKaDabraIn the code, vowels are represented by two preceding alphabets whereas consonants are represented by the preceding alphabet.

2. The cocktail Bloody Mary contains 70% tomato juice, 20% lime juice and the rest liquor. The cocktail Go Bonkers is a mixture of Bloody Mary and ScrewDriver in the ratio 2:1. If GoBonkers contains 60% fruit juice, 15% lime juice and the rest liquor, then what is the percentage of lime juice in ScrewDriver?Consider only the total percentage of lime juice in the constituents and in the final mix. If screwdrvier contains x% lime juice,

2(20) + 1(x) = 15(2+1)

Hence, x = 5%

The paper was I think simple. alphabets were 25 apart which will again start the cycle. So the option was third one. Solutions were simple that the quiz CAT by Praveena. 😀AbraKaDabraIn the code, vowels are represented by two preceding alphabets whereas consonants are represented by the preceding alphabet.

If a clock takes 10 seconds to strike 11, then how many seconds does it take to strike 6?There are 10 intervals between 11 strikings, which take 10 sec.

So 5 intervals between 6 strikings will take 5 sec.

Ok, can we discuss answers for all questions or can i post the solution for only those in which people have doubts??

@ss: I guess we should discuss all solutions. This would help many.

Ok then.. here goes..

1) The sum of all angles of a quadrilateral forms 360 degrees. And since it's an AP and the third term is thrice the first, the angles can be written as

x, 2x. 3x and 4x.

So, x+2x+3x+4x = 360

solving for x gives x=36

1) The sum of all angles of a quadrilateral forms 360 degrees. And since it's an AP and the third term is thrice the first, the angles can be written as

x, 2x. 3x and 4x.

So, x+2x+3x+4x = 360

solving for x gives x=36

@SS: But I solved it in this way... You know about the trial and error right... So, first I took the 54 and coming to the sum, it doesn't work out, as the total angle is not more than 180. 😔

Coming to the 36, I got this... 36 + 36 + 108 = 180! 😀 Bingo!!! 😁

Coming to the 36, I got this... 36 + 36 + 108 = 180! 😀 Bingo!!! 😁

For questions 47 to 50:

Using the given data, the order will be as follows:

Eshwar, Kishore, Anwar, Jatin, Baham, Inayat, Gajendra, Chetan, Hariom, Dayal, Farooq

Using the given data, the order will be as follows:

Eshwar, Kishore, Anwar, Jatin, Baham, Inayat, Gajendra, Chetan, Hariom, Dayal, Farooq

2) For this, there might be more elegant solutions.. But the way I did it was thus:

The ratio is 2:1. So, assume that the total amount of drink available is 300 ml.

In that 300 ml, the mixup is as follows: 180 ml of fruit juice, 45 ml of lime juice, 75 ml of liquor.

In this 300 ml, 200 ml of bloody mary and 100 ml of screwdriver is present.

Getting the composition of 200 ml of bloody mary, we get 140 ml of tomato juice, 40 ml of lime juice and 20 ml of liquor.

Now, it's straight forward to get the mixup of screwdriver, which is 40 ml of fruit juice, 5 ml of lime juice and 55 ml of liquor..

So the answer is 5%.

The ratio is 2:1. So, assume that the total amount of drink available is 300 ml.

In that 300 ml, the mixup is as follows: 180 ml of fruit juice, 45 ml of lime juice, 75 ml of liquor.

In this 300 ml, 200 ml of bloody mary and 100 ml of screwdriver is present.

Getting the composition of 200 ml of bloody mary, we get 140 ml of tomato juice, 40 ml of lime juice and 20 ml of liquor.

Now, it's straight forward to get the mixup of screwdriver, which is 40 ml of fruit juice, 5 ml of lime juice and 55 ml of liquor..

So the answer is 5%.

Let's go in order, please, if it's ok.. 😀

3. Assuming the length and breadth of the carpet to be 3x and 2x,

area of the carpet = 6*X[sup]2[/sup]

area of the largest circle from the carpet = pi*X[sup]2[/sup] (since circle with 2x as diameter is the largest circle possible)

So, area of the waste material = 140 = (6 - pi)*X[sup]2[/sup]

which gives x = 7

So, area of the circle is pi*7*7 which is 154

area of the carpet = 6*X[sup]2[/sup]

area of the largest circle from the carpet = pi*X[sup]2[/sup] (since circle with 2x as diameter is the largest circle possible)

So, area of the waste material = 140 = (6 - pi)*X[sup]2[/sup]

which gives x = 7

So, area of the circle is pi*7*7 which is 154

4. Hmm.. Time distance speed is really not my forte.. So, I'm skipping it for now. maybe someone can solve it for me 😛

5. In questions like these, all it takes is to form the equations correct. once you get the equations correct, you get the sum correct..

Assume X's present age is x and father's age is f. From the given conditions, two equations can be formed. They are,

(x+6) = (3/7)*(f+6)

(x-10) = (1/5)*(f-10)

Solving these equations, we get x as 18 and f as 50. So, father's present age is 50.

(P.S The answer is given to be 45, but as far as I checked, 50 seems to be the correct answer.. AKD, please confirm.)

5. In questions like these, all it takes is to form the equations correct. once you get the equations correct, you get the sum correct..

Assume X's present age is x and father's age is f. From the given conditions, two equations can be formed. They are,

(x+6) = (3/7)*(f+6)

(x-10) = (1/5)*(f-10)

Solving these equations, we get x as 18 and f as 50. So, father's present age is 50.

(P.S The answer is given to be 45, but as far as I checked, 50 seems to be the correct answer.. AKD, please confirm.)

Yeah, even I got the answer as 50... 😔

6. Here also, there might be more insightful ways to solve it, but what I found quick and easy was to assign numbers to the distance covered by the leaps of the hound and the hare.

Let's assume that the hound covers 20 feet in a leap, and the hare covers 15 feet. (Note here that this assumption should hold true for the values given in the question.0

ie., 3 leaps of hound = 4 leaps of hare = 60 feet

From here, it's a very simple speed distance problem.

The question is to find out the ratio of speeds. In a given time, a hound makes 4 leaps and a hare makes 5 leaps. Since the time is constant, ratio of speeds is same as ratio of distances.

So, ratio is, (4*20/3*15) which is 80/75 or 16/15

Let's assume that the hound covers 20 feet in a leap, and the hare covers 15 feet. (Note here that this assumption should hold true for the values given in the question.0

ie., 3 leaps of hound = 4 leaps of hare = 60 feet

From here, it's a very simple speed distance problem.

The question is to find out the ratio of speeds. In a given time, a hound makes 4 leaps and a hare makes 5 leaps. Since the time is constant, ratio of speeds is same as ratio of distances.

So, ratio is, (4*20/3*15) which is 80/75 or 16/15

7. Assume 100g of sugar costs Rs.100

Now, after the price rise, 100g of sugar costs Rs.140

We have to find how much sugar we can buy for Rs.182

So, with Rs.140, if we can buy 100g of sugar, with Rs.182, we can buy 130g of sugar.

So, there can be a maximum of 30% increase in the sugar consumption.

Now, after the price rise, 100g of sugar costs Rs.140

We have to find how much sugar we can buy for Rs.182

So, with Rs.140, if we can buy 100g of sugar, with Rs.182, we can buy 130g of sugar.

So, there can be a maximum of 30% increase in the sugar consumption.

8. Assume one soldier uses 1 unit of food per day. Since there are provisions for 1500 men for 48 days, the total amount of food available is

1500*48 = 72000 units of food.

Now, in 13 days, 1500*13 = 19500 units of food would have been used. The total remaining food is, 72000-19500 = 52500 units.

Given that this remaining food is enough only for 25 more days. So, the total number of men in the garrison now is,

52500/25 = 2100

Hence, the additional number of men in the reinforcement was 2100 - 1500 = 600

1500*48 = 72000 units of food.

Now, in 13 days, 1500*13 = 19500 units of food would have been used. The total remaining food is, 72000-19500 = 52500 units.

Given that this remaining food is enough only for 25 more days. So, the total number of men in the garrison now is,

52500/25 = 2100

Hence, the additional number of men in the reinforcement was 2100 - 1500 = 600

9. Let the weights of bananas, oranges and apples be x, y and z.

So, (x+y+z) = 66

Given, x/y = 4/5 ==> x = (4/5)*y

Also, y/z = 2/3 ==> y = (2/3)*z

Substituting for x and y in the main equation, we get z = 30, which is the weight of apples.

So, (x+y+z) = 66

Given, x/y = 4/5 ==> x = (4/5)*y

Also, y/z = 2/3 ==> y = (2/3)*z

Substituting for x and y in the main equation, we get z = 30, which is the weight of apples.

10. It can be done by assuming Rs.100 to be the cost price for the manufacturer..

So, the manufacturer charges Rs.110, the wholesaler charges Rs.132, the retailer charges Rs.171.6, which the customer should pay.

So, there's a 71.6% increase in price from the manufacturer's cost price.

If anyone knows any easier method, let me know. I think there's a better method which doesn't involve calculating the exact prices at each stage...

So, the manufacturer charges Rs.110, the wholesaler charges Rs.132, the retailer charges Rs.171.6, which the customer should pay.

So, there's a 71.6% increase in price from the manufacturer's cost price.

If anyone knows any easier method, let me know. I think there's a better method which doesn't involve calculating the exact prices at each stage...

even i got 50 as answerpraveenscienceYeah, even I got the answer as 50... 😔

**11. The average speed of a train including stoppages was 27 kmph and excluding stoppages was 41 kmph. How many minutes did the train stop per hour?**

20.5 minutes (Answer)

15 minutes

25 minutes

30 minutes

41 km / 1 hr = 27 km / x hr

Ans: 1 hr - x hr

x = 0.658

hrs = x = 39.48

so ans = 60 - 39.48 = 20.52

Someone could format my answer! 😀

**12. A certain sum of moneywhen deposited in a post office becomes 7/5 times in 8 years. An equal sum deposited in a fixed deposit in a bank doubles in 12 & 1/2 years. Which of the two agencies, the post office or the bank, gives a better rate of interest?**

Post Office: 1.4 times in 8 years. » 4.375 times in 25 years.

Bank: 2 times in 12.5 years. » 4 times in 25 years.

*PS: Is this way right? I got Bank while giving the exam...*😐

**13. A cylindrical vessel of base area 154 sq.cm. and height 1.2 cm is filled with sand. The sand is emptied to form a conical heap of the same height on the ground. What is the base radius of the cone?**

Cyl Base: 154 sq.cm.

Cyl Height: 1.2 cm.

Cyl Area: 184.8 cm.

Cone Height: 1.2 cm.

Cone Area: 184.8 cm.

Cone Base: (Formula) = 12.16 cm.

Finding HCF.

**15. A student was asked to find the product of two 2-digit numbers but instead he reversed the position of the digits in both the numbers and calculated the answer and still managed to get the correct answer. Then, the number are:**

This one is a trial and error method. I checked with the calc for the first two answers and got them same. Immediately I answered all the above. Method:

31 x 39 = 93 x 13 = 1209

31 x 26 = 62 x 13 = 806

23 x 96 = 69 x 32 = 2208

**16. A boat going upstream takes 20 minutes while it takes 10 minutes for going downstream for the same distance. If speed of the boat in still water is 7.5 kmph, then find speed of the stream in kmph.**

Let x = rate of the boat (in still water)

and Let y = rate of the stream

Since it is upstream, boat goes against the rate of stream, hence the rate upstream = (x - y)

and in downstream, boat's rate and stream's rate are combined, so the rate downstream = (x + y)

Now, distance does not change and we know that Distance(D) = Rate x Time

Solution will be given soon. 😀

18. Two squirrels A & B are climbing up two separate 100 feet poles. Squirrel A climbs up 3 feet in 1 minute but slips back 1 foot for every 2 feet climbed. Squirrel B climbs up 4 feet in 1 minute but slips down 1.5 feet for every 2 feet climbed. Squirrel A stops for a minute after every 2 minutes, while Squirrel B stops for 1 minute after every 3 minutes. Assume that the slippage occurs continuously.

Which squirrel reaches the top first and in how many minutes?

Squirrel A in 101 minutes

Squirrel B in 132 minutes

Squirrel in 100 minutes (Answer)

Squirrel B in 133 minutes

Which squirrel reaches the top first and in how many minutes?

Squirrel A in 101 minutes

Squirrel B in 132 minutes

Squirrel in 100 minutes (Answer)

Squirrel B in 133 minutes

**Please explain....**
@Hadiq, all the answers were deeply SIMPLE. I will post all answers if anyone does not get them.

Let us calculate speed of each squirrel by unitary method.

3 feet-----------1min

1.5feet----------1min (slips 1 feet in 2 feet)

3 feet-----------3min speed of squirrel A->1ft/min

1feet/min hence it will require 100 min to climb 100 feet pole

4 feet---------1min

1feet ---------1min (considering 1.5 feet slip for 2 feet)

3feet----------3min

now consider rest.

3feet---------4min

hence

1feet---------4/3min.->speed of squirrel B

Hence B will require 133min for reaching 100ft pole. 😀

hence A wins. 😀

Let us calculate speed of each squirrel by unitary method.

**Squirrel A:**3 feet-----------1min

1.5feet----------1min (slips 1 feet in 2 feet)

3 feet-----------3min speed of squirrel A->1ft/min

1feet/min hence it will require 100 min to climb 100 feet pole

**Squirrel B:**4 feet---------1min

1feet ---------1min (considering 1.5 feet slip for 2 feet)

3feet----------3min

now consider rest.

3feet---------4min

hence

1feet---------4/3min.->speed of squirrel B

Hence B will require 133min for reaching 100ft pole. 😀

hence A wins. 😀

5. X's age after 6 years will be three-seventh of his father's age. 10 years ago, the ratio of their ages was 1:5. What is X's father's age at present?That was an editing mistake on my part. Answer is 50. The test was evaluated by taking the answer as 50.

40

45

50 (Answer)

49

Hmm.. Nobody wants to discuss the solutions?? Come on!!!

Anyway, continuing...

20) Ha.. Very easy!! You dont even have to calculate any probability at all..

There are 3 things to be matched.. You can get 1 correctly matched and the other 2 wrong.

Or, you can get all 3 correct. But you cannot get 2 correct and only on wrong, since, if you get 2 correct, the third automatically becomes correct, as there's only one option left.

So the probability is zero.

Anyway, continuing...

20) Ha.. Very easy!! You dont even have to calculate any probability at all..

There are 3 things to be matched.. You can get 1 correctly matched and the other 2 wrong.

Or, you can get all 3 correct. But you cannot get 2 correct and only on wrong, since, if you get 2 correct, the third automatically becomes correct, as there's only one option left.

So the probability is zero.

I'm skipping the verbal questions.. Coming to qn 31.

31) Well, without knowing the answer, it would've been difficult, I guess.. But since I know the answer, I got the series as follows..

5 = 1[sup]3[/sup]+4

13 = 2[sup]3[/sup]+5

71 = 4[sup]3[/sup]+7

133 = 5[sup]3[/sup]+8

So, the missing number should be 3[sup]3[/sup]+6 which is 33

31) Well, without knowing the answer, it would've been difficult, I guess.. But since I know the answer, I got the series as follows..

5 = 1[sup]3[/sup]+4

13 = 2[sup]3[/sup]+5

71 = 4[sup]3[/sup]+7

133 = 5[sup]3[/sup]+8

So, the missing number should be 3[sup]3[/sup]+6 which is 33

33) Nothing to say. Just write the alphabets and you will get it.. Answer is 'F'

34) Another easy problem. You don't need those family diagrams or venn diagram like things to solve this..

Given that C has 3 children. No info is given about the children's gender, whatsoever.

But the options all have genders, which we cannot know from the question. So, the answer is "None of the above".

34) Another easy problem. You don't need those family diagrams or venn diagram like things to solve this..

Given that C has 3 children. No info is given about the children's gender, whatsoever.

But the options all have genders, which we cannot know from the question. So, the answer is "None of the above".

35. I thought of putting a family tree for this question. But this is not that complicated to require that.

Vinod, Bhaskar and Manu are brothers and sisters. So, they belong to the same generation.

Biswal and Preetham are children of Bhaskar. So, they belong to the next generation.

Now, there are only 2 males in the first generation and an uncle must be someone who is not the father, but a male.

So, it's not Bhaskar. The only guy left is Vinod, which is the answer.

Vinod, Bhaskar and Manu are brothers and sisters. So, they belong to the same generation.

Biswal and Preetham are children of Bhaskar. So, they belong to the next generation.

Now, there are only 2 males in the first generation and an uncle must be someone who is not the father, but a male.

So, it's not Bhaskar. The only guy left is Vinod, which is the answer.

36) The total number of factors of 12!

Now, the total number of factors of any number can be found thus: Write the number as a multiple of it's prime factors.

If the number is of the form a[SUP]b[/SUP]*c[SUP]d[/SUP], where a and b are prime, the total number of factors of that number is (c+1)*(d+1)

Example, take 18. 18 = 2*3*3 = 2[SUP]1[/SUP]*3[SUP]2[/SUP]

So, the number of factors is (1+1)*(2+1) = 6

Now, this can be verified by writing all the factors of 18 which are 1,2,3,6,9,18 which comes to 6.

This is the prelude. Now, knowing this, how can you find the number of factors of 12!? Simple.. Write 12! as a multiple of prime factors.

So, 12! = 1*2*3*4*5*6*7*8*9*10*11*12 = 1*2*3*2*2*5*2*3*7*2*2*2*3*3*2*5*11*3*2*2 = 2[SUP]10[/SUP]*3[SUP]5[/SUP]*5[SUP]2[/SUP]*7[SUP]1[/SUP]*11[SUP]1[/SUP]

So, the number of factors is (10+1)*(5+1)*(2+1)*(1+1)*(1+1) = 11*6*3*2*2 = 792

Thus, 12! has a total of 792 factors.

Now, the total number of factors of any number can be found thus: Write the number as a multiple of it's prime factors.

If the number is of the form a[SUP]b[/SUP]*c[SUP]d[/SUP], where a and b are prime, the total number of factors of that number is (c+1)*(d+1)

Example, take 18. 18 = 2*3*3 = 2[SUP]1[/SUP]*3[SUP]2[/SUP]

So, the number of factors is (1+1)*(2+1) = 6

Now, this can be verified by writing all the factors of 18 which are 1,2,3,6,9,18 which comes to 6.

This is the prelude. Now, knowing this, how can you find the number of factors of 12!? Simple.. Write 12! as a multiple of prime factors.

So, 12! = 1*2*3*4*5*6*7*8*9*10*11*12 = 1*2*3*2*2*5*2*3*7*2*2*2*3*3*2*5*11*3*2*2 = 2[SUP]10[/SUP]*3[SUP]5[/SUP]*5[SUP]2[/SUP]*7[SUP]1[/SUP]*11[SUP]1[/SUP]

So, the number of factors is (10+1)*(5+1)*(2+1)*(1+1)*(1+1) = 11*6*3*2*2 = 792

Thus, 12! has a total of 792 factors.

37) Angle between the hands of a clock. There are many methods to solve this type of problems.. There are even ready made formulas for calculating the angle at any time..

Now, the main thing to know in these types of problems is that, the hour hand completes one full circle in 12 hours and the minute hand completes one circle in one hour.

Also note that, AM or PM doesn't matter in these problems, as the clock only has numbers upto 12.

Which means, the hour hand covers an angle of 360 degrees in 12 hours or 30 degrees in one hour.

Similarly, the minute hand covers 360 degrees in 1 hour and hence, 6 degrees in a minute.

Now, the question is the angle between the hands when the time is 3:40.

When the time is 12:00, the angle between the hands is zero. This is our reference.

In 3 hours and 40 minutes, the hour hand would've covered an angle of 110 degrees (30 degrees per hour = 90 degrees for 3 hours and 20 degrees for 40 minutes)

In 3 hours, the minute hand would've completed 3 complete circles. So, we can leave that part out. We only need to consider the 40 minutes.

In 40 minutes, the minute hand would've moved 40*6 = 240 degrees.

Now, the angle between the hands can be found from the difference of the angles covered by the 2 hands in the same time.. which is, 240 - 110 = 130 degrees.

Now, the main thing to know in these types of problems is that, the hour hand completes one full circle in 12 hours and the minute hand completes one circle in one hour.

Also note that, AM or PM doesn't matter in these problems, as the clock only has numbers upto 12.

Which means, the hour hand covers an angle of 360 degrees in 12 hours or 30 degrees in one hour.

Similarly, the minute hand covers 360 degrees in 1 hour and hence, 6 degrees in a minute.

Now, the question is the angle between the hands when the time is 3:40.

When the time is 12:00, the angle between the hands is zero. This is our reference.

In 3 hours and 40 minutes, the hour hand would've covered an angle of 110 degrees (30 degrees per hour = 90 degrees for 3 hours and 20 degrees for 40 minutes)

In 3 hours, the minute hand would've completed 3 complete circles. So, we can leave that part out. We only need to consider the 40 minutes.

In 40 minutes, the minute hand would've moved 40*6 = 240 degrees.

Now, the angle between the hands can be found from the difference of the angles covered by the 2 hands in the same time.. which is, 240 - 110 = 130 degrees.

38) Based on the same concept as above, this is just a simple modification from the above question.

If you imagine the clock going round and round, you can see, at some point in each hour, the clock forms 180 degrees. For the period from 6:30 to 7:30, it comes to be around 7:05

The angle when the time is 7:00 is 210 degrees. At 7:05, the angle is (212.5 - 30) which is 182.5. At 7:10, the angle is 155. So, somewhere between 7:05 and 7:10, the hands are at 180 degrees.

So, there's a time between 6:30 to 7:30, one between 7:30 to 8:30 etc.. for each hour, when the hands are at 180 degrees.. How many such hours are there? Don't tell 12 in a hurry..

Because, the last hour, ie., 5:30 to 6:30 and the first hour 6:30 to 7:30, share the same time when the hands are horizontal. So, there are totally 11 instances when the hands of the clock are horizontal.

Now, this can be done without any calculation as just your visualization is enough, if you manage to imagine it properly.

If you imagine the clock going round and round, you can see, at some point in each hour, the clock forms 180 degrees. For the period from 6:30 to 7:30, it comes to be around 7:05

The angle when the time is 7:00 is 210 degrees. At 7:05, the angle is (212.5 - 30) which is 182.5. At 7:10, the angle is 155. So, somewhere between 7:05 and 7:10, the hands are at 180 degrees.

So, there's a time between 6:30 to 7:30, one between 7:30 to 8:30 etc.. for each hour, when the hands are at 180 degrees.. How many such hours are there? Don't tell 12 in a hurry..

Because, the last hour, ie., 5:30 to 6:30 and the first hour 6:30 to 7:30, share the same time when the hands are horizontal. So, there are totally 11 instances when the hands of the clock are horizontal.

Now, this can be done without any calculation as just your visualization is enough, if you manage to imagine it properly.

39) This question falls under a category called "Derangement".

You might have come across the term arrangement. It denotes a way in which things can be arranged. Another popular term for arrangement is "permutation".

Now, Wikipedia says "In combinatorial mathematics, a

For the question, you may proceed with taking 1 letter at a time 😉

For only 1 letter, the no. of permutations such that no letter is in the correct envelope is 0, as only one letter is there and it should go to the correct envelope.

For 2 letters, there is only one way you can keep both the letters in the wrong envelop. So, no. of derangements is 1

For 3 letters, you can proceed by writing the permutations and then counting them..

Say, a,b and c are the letters and there are 3 envelopes, 1,2 and 3, which are addressed for a,b and c, in that order.

If you write the permutations of a,b and c, you have

abc, acb, bac, bca, cab, cba

Select only those which doesn't have a in the first place, b in the second place and c in the third place. Those are bca and cab.

In both these permutations, none of the three letters are in their correct place. So, the no. of derangements of 3 letters is 2

You can go ahead and calculate the same for 4 letters and 5 letters by writing all the permutations of 4 and 5, and then selecting only those which have all the places wrong.

4 letters will have 4! = 24 permutations and 5 letters will have 5! = 120 permutations.

The number of derangements of 4 and 5 are respectively 9 and 44. Hence the answer of this sum is 44.

Now, this is ok for understanding. But you can't sit and write 120 permutations and be analyzing them in the exam. So, there is a general formula for calculating derangements..

Say, you want the number of derangements for N, then,

!N = N! {1 - 1/1! + 1/2! - 1/3! + ... + (-1)[sup]N[/sup]1/N!}, where !N means no. of derangements of N and N! means factorial of N

The derivation of this formula is present in the net and if interested, just Google "derangement derivation"

You might have come across the term arrangement. It denotes a way in which things can be arranged. Another popular term for arrangement is "permutation".

Now, Wikipedia says "In combinatorial mathematics, a

**derangement**is a permutation of the elements of a set such that none of the elements appear in their original position."For the question, you may proceed with taking 1 letter at a time 😉

For only 1 letter, the no. of permutations such that no letter is in the correct envelope is 0, as only one letter is there and it should go to the correct envelope.

For 2 letters, there is only one way you can keep both the letters in the wrong envelop. So, no. of derangements is 1

For 3 letters, you can proceed by writing the permutations and then counting them..

Say, a,b and c are the letters and there are 3 envelopes, 1,2 and 3, which are addressed for a,b and c, in that order.

If you write the permutations of a,b and c, you have

abc, acb, bac, bca, cab, cba

Select only those which doesn't have a in the first place, b in the second place and c in the third place. Those are bca and cab.

In both these permutations, none of the three letters are in their correct place. So, the no. of derangements of 3 letters is 2

You can go ahead and calculate the same for 4 letters and 5 letters by writing all the permutations of 4 and 5, and then selecting only those which have all the places wrong.

4 letters will have 4! = 24 permutations and 5 letters will have 5! = 120 permutations.

The number of derangements of 4 and 5 are respectively 9 and 44. Hence the answer of this sum is 44.

Now, this is ok for understanding. But you can't sit and write 120 permutations and be analyzing them in the exam. So, there is a general formula for calculating derangements..

Say, you want the number of derangements for N, then,

!N = N! {1 - 1/1! + 1/2! - 1/3! + ... + (-1)[sup]N[/sup]1/N!}, where !N means no. of derangements of N and N! means factorial of N

The derivation of this formula is present in the net and if interested, just Google "derangement derivation"

With that, we come to the end of quants. I don't think verbal and DI needs such explanation, but still, if you have any doubts in any question, feel free to ask.

In quants too, if any of my solutions above is not clear, or if you have any alternate better solutions, please let me know 😀

In quants too, if any of my solutions above is not clear, or if you have any alternate better solutions, please let me know 😀

Wow SS. Good work... Went through all the answers. Still confused on the derangement part! 😔

Solution to the 20th please....

2

20th pleaseAnkita KatdareIf explanation regarding any solutions is needed, please post here.