# Quant thread for CAT 2011

Hi Guys,

Lets start discussing about math and quantitative problems. Please post all your math related problems and get it solved by our Crazyengineers π You can also learn the easiest method of approach by discussing the answers!

I request all quant enthusiasts to post the questions here.Dont just give the answer alone. Post you method of approach too

Here goes my first question!

1.A dealer mixes tea costing Rs.8 per kg with tea costing Rs.7 per kg and sells the mixture at Rs.8 per kg with tea costing Rs.7 per kg. and sells the mixture at Rs.8 per kg.and earns a profit of Rs 15/2% on his sale price.In what proportion does he mix then?-

## Replies

• Reya
No takers??
• Ankita Katdare
I found this part a bit confusing:

sells the mixture at Rs.8 per kg with tea costing Rs.7 per kg. and sells the mixture at Rs.8 per kg
• Saandeep Sreerambatla
Is the answer 19 : 24 ??

If yes I will give you the detailed explanation.

If my answer is incorrect, I dont want to confuse others with a invalid solution.
• Reya
if the profit is 15/2 (7.5%) then i also get the same answer as ES 19:24
• Reya
No the answer is wrong! Anyone there to give the correct answer?

If not,I ll post the answer here.
• ISHAN TOPRE
Is the answer 2:15? 2 parts of Rs. 8 tea and 15 parts of Rs. 7 tea?
I will post the solution if you say it is correct.

Besides I found this part confusing too.
sells the mixture at Rs.8 per kg with tea costing Rs.7 per kg. and sells the mixture at Rs.8 per kg
• Reya
@Akd,Ishu: I just repeated the line again!

The question should be like

A dealer mixes tea costing Rs.8 per kg with tea costing Rs.7 per kg and sells the mixture at Rs.8 per kg and earns a profit of Rs 15/2% on his sale price.In what proportion does he mix then?-
• ISHAN TOPRE

P.S: This is my last try. π
• Reya
Wrong!!

@CT & CP: where are you?
• cooltwins
is it 2:3 ratio?
• Reya

2.Find the no of triangles in an octagon having no side common with the octagon?
• cooltwins
Method:
A dealer mixes tea costing Rs.8 per kg with tea costing Rs.7 per kg and sells the mixture at Rs.8 per kg and earns a profit of Rs 15/2% on his sale price.In what proportion does he mix then?

i think ES and Yadav made mistake in that bold part only...
15/2 = (SP-CP)/SP*100
so putting SP=8 => CP=7.4

then it is the usual allegation procedure to get the ratio π
• CIVILPRINCESS
is it 10? i'm not sure though...
• Sahithi Pallavi
Is it 6? I am not sure.
• Reya
Both of them are wrong!
• ISHAN TOPRE
• Saandeep Sreerambatla
It too think its 16.

8C3 - 32-8 = 56-40= 16.

@CP : Yes you are correct, the mistake was done in the bolded part π
• Reya
@ishu,sandy:Right!

3.

This expression is valid for a particular value of X? value of 5X?
• Reya
4. The ratio upto sum of n terms of the 2 A.Ps is 3n+2/4n-13.Find the ratio of 17th term of 2 A.Ps?
• ISHAN TOPRE
The value of 5X is -> 5*46656^(a square).
• Reya
ishutopre
The value of 5X is -> 5*46656^(a square).
Wrong ishu!
• ISHAN TOPRE
@Praveena: My last chance, either it is 2.78 or 2.18.
• Reya
@Ishu :wrong! Can you give me the value of x you arrived at?
• ISHAN TOPRE
2.78 is the value of X, which is also the value of natural base 'e'. So 5X is 13.591. π
• Reya
Ha Ha π

@ishu : Wrong!
• Saandeep Sreerambatla
101:119 ??

Logarithms are my least priority!!

I have to practise a lot to get to my old momentum! I dont want to see my score card with less marks than previous years in DI and Quant.
• Reya

Give me your method of approach!

Try to solve 3rd ques too.
• Saandeep Sreerambatla
Approach:

we need , a1+16d1/a2+16d2 -----(1)

Given that ratio of sum of n numbers in both the series,

so, [2a1+(n-1)d1]/[2a2+(n-1)d2] = 3n+2/4n-13

To get (1) we have to substitute n=33 , which gives 101:119
• Reya
3.

This expression is valid for a particular value of X? value of 5X?
No takers for 3rd quest??

5.a0, a1, a2, a3..an are (n + 1) vertices of a regular polygon. And functions f(x) and g(x) are defined in such a way that. f(n) = Total number of diagonals in a regular polygon of (n + 1) sides and g(n) = Total number of triangles that can be made using the vertices of the (n + 1) sided regular polygon, as its vertices (None of the sides of the triangle should be common with that of polygon.) If f(n) = 5, then what is the value of g(n)?
• CIVILPRINCESS
qn. 3: is it 30?
• Reya
@CP: Right!

• CIVILPRINCESS
the given expression can be written as a^(log (base 6) x ^ (log (base 4) a) ) = log (base 4) 256 = 4
(log (base 4) a)= (log (base 6) x ^ (log (base 4) a) = (log (base 4) a) * (log (base 6) x) => (log (base 6) x)=1 => x=6 ==> 5x =30 π
• CIVILPRINCESS
English-Scared
It too think its 16.

8C3 - 32-8 = 56-40= 16.
i don't understand the part in bold. can you please explain a little more in detail ? π
• Saandeep Sreerambatla
If you consider a octagon, it has 8 points.
We can draw straight lines from one end to other end 5 lines, which gives you 4 traingles.

so , total 8 points which gives you 32 triangles with one side of the octagon.

Next from center you can draw 8 lines where you get 8 more triangles.

total of 40.

So, in an regular octagon you can have 8C3 triangles.

so its 16.

Hope I am clear, I am not sure of the process but this is what I got when I was trying π
• Reya
6.A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There
is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey, The number of buses that the car encounter is ?

PS: I'm not sure of the answer. I want to check my answerπ
• Saandeep Sreerambatla
By counting I got the answer as 19 buses.
• cooltwins
yeah i also got 19...
• Reya
I too got the same answer.

7.X is a number of more than 4 digits.The digits of X increase from left to right.What can be sum of digits of number 9X?
• Saandeep Sreerambatla
5 = 0.

The number of diagonals for a n side regular polygon = n(n-3)/2
which gives n = 5.

So in order to draw a triangle without touching any of the side, we need more than 5 sides.

So there will be Zero triangles in this case.
• cooltwins
praveena211
7.X is a number of more than 4 digits.The digits of X increase from left to right.What can be sum of digits of number 9X?
is it 9? π
• Reya
yes you are right!

• Saandeep Sreerambatla
7. Answer is 9. For digits not more than 9.

Its a very big tedious process, I dont remember correctly. Will try posting it tomorrow.
• Saandeep Sreerambatla
IS the answer for Question 5 correct?
• Reya
8.Sandeep is planning to attend wedding.He starts at a specific time and specific speed so as to be there at the exact time.he was driving for exactly 1 hour when his car had a flat tyre.He changed the tyre in 10 minutes.He started driving the remaining distance @ 40 km/h.he was late for the wedding by 30 minutes.If the puncture had happened 25 km later,he would be late for wedding by 20 min.what is the total dist. travelled by him?
• Reya
ASsuming the number is N.
N = a(n)a(n - 1).....a(0), where 0 < a(n) < a(n - 1) < .... < a(0) < 10
->0 < a(k) - a(k + 1) < 10 ----(1)
N = a(n)10βΏ + .... + a(2)10Β² + a(1)10 + a(0)
9N = 9*10βΏa(n) + .... + 900a(2) + 90a(1) + 9a(0)

Now, 9*10βΏa(n) can be written as 10^(n + 1)a(n) - 10βΏa(n)
9*10^(n - 1)a(n - 1) can be written as 10βΏa(n - 1) - 10^(n - 1)a(n - 1)
.
.
900a(2) can be written as 1000a(2) - 100a(2)
90a(1) can be written as 100a(1) - 10a(1)
9a(0) can be written as 10a(0) - a(0)
Then subtract 10 and add 10 and keep all numbers of form 10^k together
Write coefficient of 10 as a(0) - a(1) - 1 and that of 1 as 10 - a(0)

So, it will become
-> 9N = 10^(n + 1)a(n) + 10βΏ{a(n - 1) - a(n)} + ..... + 1000{a(2) - a(3)} + 100{a(1) - a(2)} + 10{a(0) - a(1) - 1} + (10 - a(0)}

Using (1)equ, we will get
Sum of digits of 9N = a(n) + {a(n - 1) - a(n)} + .. + {a(2) - a(3)} + {a(1) - a(2)} + {a(0) - a(1) - 1} + (10 - a(0))
= 10 - 1 = 9

@ES,CT : Is this the way you arrived at the result?
• cooltwins
thats a good way to solve it... but no, i did not π i tried it using examples like 12345, 123456, 1234567 and found all of them gave the same answer "9" π trial and error method π
• CIVILPRINCESS
praveena211
8.Sandeep is planning to attend wedding.He starts at a specific time and specific speed so as to be there at the exact time.he was driving for exactly 1 hour when his car had a flat tyre.He changed the tyre in 10 minutes.He started driving the remaining distance @ 40 km/h.he was late for the wedding by 30 minutes.If the puncture had happened 25 km later,he would be late for wedding by 20 min.what is the total dist. travelled by him?
• Reya
@CP:wrong!
• CIVILPRINCESS
i think this is wrong.. but i'm getting 106.5
• Reya
9.A,B and C start from a point X, speeds of A,B and C are a, a+s and a+2s respectively. if A starts first and after x hours B starts, then after how many hours from starting time of B should C start so that all of them meet at the same time( in otherwords both B and C overtake A at the same time).
(a and s are positive and non-zero values).
• Saandeep Sreerambatla
After, ax/a+2s hours after B starts C should start such that they reach at the same time.
• Saandeep Sreerambatla
Solution:
t = time taken for A to reach the meeting point π
x = time at which B starts after A starts (Given)
y = time at which C starts after A starts (Given)

So, Distance = Speed * time
And, the distance travelled by all three is same.

So, at = (a+s)(t-x) = (a+2s)(t-y)
On solving first , we get => t = x(a+s)/s
On solving second , we get => y = 2st/(a+2s)
Putting the value of t above will give,
y = 2sx(a+s)/s(a+2s)

So, the solution is ax/a+2s.

I think its correct π
• cooltwins
but i got the answer as x... π
• Saandeep Sreerambatla
Explain your procedure too, lets see where did I or you went wrong π
• cooltwins
I'm not able to find a mistake in my approach: identify if any,

as B starts x minutes after A, A would have travelled some distance = ax

so now B must cover that distance + some distance that A will cover from the time B also starts = ax+D (say)

from the time B starts, both take the same time,
and time=dist/speed

so, D/a = (D+ax)/(a+s) =>x*(a)^2=Ds -------(1)

now let C start some time y after A starts,
so as usual, by the time C starts A would have covered ay distance,

so, D/a = (D+ya)/(a+2s) => y*(a)^2=2Ds-----(2)

using (1),(2) => y=2x

but that is the time at which C should start after A starts but the question is after B starts => 2x-x =x
• ISHAN TOPRE
My answer to Q8 in post number 46 by Praveena.

My answer is the distance between Sandeep's home and the wedding place is 73.333Km. I will post solution upon confirmation by Praveena that my answer is correct. π

P.S: It is better to reach late than meet an accident in a hurry. Drive safe Sandeep. π
• Reya
@CP: You are very close to the answer!

Post your procedure if you wanna know where you went wrong!

@Sandy : You gave the right answer π

@CT : Finding out your mistake!
• cooltwins
is the answer for the Q8 129.54?
• CIVILPRINCESS
for qn 8)

I got (25/v)-(25/40)=(10/60)
=> (25/v)=19/24 => v=600/19.

then the distance traveled in first one hour is 600/19.

if after 25 km the time delay reduced by 10 mins. after 50 km there will be no delay.

so the total distance is 600/19 + 50. so i got 106.9.

just tell me is my velocity correct...
• Reya
Distance travelled in first one hour is wrong!

Check it! It should be 600/11.
• Saandeep Sreerambatla
@Praveena: I would request you to post few more questions till this weekend.
I would be updating another thread with 5 questions per day starting August 1st .
• Reya
How many 10 digit positive integers with distinct digits are multiples of 11111 ???
• cooltwins
none? π π
• Reya
@Cooltwins : wrong!

Use divisibility rule π

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