CAT Quant Content - Conceptual Problems [Solved]

@mathbyvemuri-ipvdTv • Oct 26, 2024

Oct 26, 2024

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Hi all
I am a math lover.
This is introduction to my blog: < Advertisement Removed By Administrator >
This blog is a hub of CONCEPTUAL problems (of course it is in developing stage). This blog centres around aptitude and reasoning. Generally concentrates on math content of CAT/XAT, GMAT, UPSC, CSAT, GATE, GRE, Placement Exams, Talent Search Exams and all concept and logic oriented exams.
This is not a sort of stereotypical Q and A content.
This is not for remembering and reproducing tons of formulas. This is a quest for logic, quest for reasoning, quest for success and kick...

Through this thread, we will have discussion on those problems and concepts.

This is not for promoting my blog but to open out myself by giving out what I feel important about math, about strategies in solving quality math problems etc..

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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 23, 2011

In continuation to my earlier post, pl find the following puzzle:

Q1)Find the number of triangles in the above diagram?
(A) 32 (B)23 (C)26 (D) 27 (E) 16

I hope you enjoy this one, this is one of the popular ones on my blog.
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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 24, 2011

Solution for the triangle problem- Q1:

First we start from each of the 3-corners.

From corner-1 : (1,2,3), (1,4,6), (1,7,10), (1,11,15) --- 4

From corner-11 : (11,7,12), (11,4,13), (11,2,14) --- 3

From corner-15 : (15,10,14), (15,6,13), (15,3,12) --- 3

Now we count all the smallest triangles excluding (1,2,3), (11,7,12) and (15,10,14) which are already considered above:

(2,4,5), (2,3,5), (3,5,6) ---3

(4,7,8), (4,5,8), (5,8,9), (5,6,9), (6,9,10) ---5

(7,8,12),(8,12,13),(8,9,13),(9,13,14),(9,10,14) ---5

Now by considering “middle 3-points” of each side of the outer triangle, we get the following:

(2,7,9), (3,8,10), (12,5,14) ---3

Now by considering “single middle point” of each side of the outer triangle, we get the following:

(4,6,13) ---1

So the total number of triangles = 4+3+3+3+5+5+3+1 = 27

Answer (D)

How is it??????????????????
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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 24, 2011

Find out second problem here:
Q2) How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:
(A) 9
(B) 10
(C) 11
(D)12
This is a little controversial problem on my blog...
what do you feel?????
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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 25, 2011

Q3) The interior angles of a polygon are in A.P. If the smallest angle is 120[SUP]0[/SUP] and common difference is 5[SUP]0[/SUP], then the number of sides in the polygon is:
(A) 7
(B) 8
(C) 9
(D)None of the above
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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 26, 2011

Q4)If the positive real numbers a, b and c are in Arithmetic Progression, such that abc = 4, then minimum possible value of b is:
(A) 2[SUP]3/2[/SUP]
(B) 2[SUP]2/3[/SUP]
(C) 2[SUP]1/3[/SUP]
(D)None of the above
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Ankita Katdare

@abrakadabra • Oct 26, 2011

mathbyvemuri
Find out second problem here:
Q2) How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:
(A) 9
(B) 10
(C) 11
(D)12
This is a little controversial problem on my blog...
what do you feel?????
The answer is 11.
They are: A I H M O T U V W X Y
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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 27, 2011

This Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with theThis Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with the letter ‘Y’.
If ‘Y’ is written as ‘Y’, which is the most general case, it won’t come under our category of symmetry and answer will be 10. Detailed explanation for this is given in my blog (puzzle-9 on my blog). Let me know your take on that…
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Ankita Katdare

@abrakadabra • Oct 27, 2011

I feel 'Y' is mostly used as a capital letter. But, yeah It depends on the font we are using. If we consider general case of Times New Roman font, 'Y' is how they taught us to write y in capital.

I am not a CAT aspirant, but are such ambiguous questions asked in the actual test?
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mathbyvemuri

@mathbyvemuri-ipvdTv • Oct 31, 2011

Solution:
Given that smallest interior angle = 120[SUP]0[/SUP] and common difference 5[SUP]0[/SUP]
∴the series of interior angles is 120[SUP]0[/SUP], 125[SUP]0[/SUP], 130[SUP]0[/SUP],….
Exterior angle = 180[SUP]0[/SUP] – Interior angle
∴the series of corresponding exterior angles is 60[SUP]0[/SUP],55[SUP]0[/SUP],50[SUP]0[/SUP],…
This is a decreasing Arithmetic Progression with
initial term ‘a’ = 60; common difference ‘d’ = -5;
Let the polygon has ‘n’ sides.
Sum of n terms of AP = n(2a+(n-1)d)/2 ----- >(1)
Sum of exterior angles of any polygon = 360[SUP]0[/SUP] ----- >(2)
From (1) and (2),
360 = n(2a+(n-1)d)/2
360 = n(120+(n-1)(-5))/2
360 = n(125-5n)/2
720 = 5n(25-n)
144 = n(25-n)
Instead of solving the equation, we go for checking multiple choice options one by one:
Put n = 7, 144 = 7(18) wrong
Put n = 8, 144 = 8(17) wrong
Put n = 9, 144 = 9(16) correct
∴ Answer is (C)
Check for more related problems on my blog
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mathbyvemuri

@mathbyvemuri-ipvdTv • Nov 3, 2011

(Q5) In tennis, service alternates for each game between the two players and the first player to win 6 games wins. A player winning 6-2 indicates that 8 games were played, of which the winning player won 6 and loosing player won 2.
Rafa beat roger in a set of tennis, winning 6 games to Roger’s three. Five games were won by the player who did not serve. Who served first?

(1)Rafa (2) Roger (3) Inconsistent (4) Indeterminate

This is a good puzzle... Check out solution on my blog please...
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mathbyvemuri

@mathbyvemuri-ipvdTv • Nov 24, 2011

Q6) The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from digit 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?
(1)2201 (2)2202 (3)2600 (4)2960 (5)None of these options

This is a tricky one on numbers, for solution check for Numbers-17 problem on my blog on math
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mathbyvemuri

@mathbyvemuri-ipvdTv • Dec 19, 2011

(Q7)

Find the number of integers lying between 100 and 400 (excluding the two) and divisible by any one of the numbers 2 or 3 or 5 or 7?
Solution for this problem can be found at 'Numbers-22' on my 'Blog on Math' link provided right down at my signature. Let me know any other simpler way out is possible, given the limited availability of time in the competitive exams.

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graphite

@graphite-tkk1sC • Jul 16, 2012

(Q8)
Consider the following three polynomials
P1(x)=ax2-bx-c, P2(x)= bx2-cx-a, P3(x)=cx2-ax-b
Here a, b, c are non-zero real numbers. Let there exits a real number w, then P1(w)=P2(w)=P3(w) then

(1)ab+bc+ca=0 (2) a3+b3+c3=0 (3) a=b=c (4)a+b+c=0
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Lalit77

@lalit77-ITuWjY • Jul 30, 2012

mathbyvemuri
Find out second problem here:
Q2) How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:
(A) 9
(B) 10
(C) 11
(D)12
This is a little controversial problem on my blog...
what do you feel?????
ans. option C
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Lalit77

@lalit77-ITuWjY • Jul 30, 2012

mathbyvemuri
This Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with theThis Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with the letter ‘Y’.
If ‘Y’ is written as ‘Y’, which is the most general case, it won’t come under our category of symmetry and answer will be 10. Detailed explanation for this is given in my blog (puzzle-9 on my blog). Let me know your take on that…
then a,t also dont have to consider..So the actual answer is 8 now.Accordingly your options are wrong.
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graphite

@graphite-tkk1sC • Aug 25, 2012

Consider a quadratic equation;
x2 + 7x – 14(a2 + 1) = 0, … (where a is an integer)
For how many different value of a, the equation will have at least one integer root?

A) 0 B) 1 C) 2 D) More than 2

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Nithyasri

@nithyasri-PD1Z0H • Aug 26, 2012

ans for q.4
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