CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions

[rajeev_hts]

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Quantitative Question # 019
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The question is followed by two statements X and Y. Answer each question using the following instruction:

Choose 1 if the question can be answered by X only
Choose 2 if the question can be answered by Y only
Choose 3 if the question can be answered by either X or Y
Choose 4 if the question can be answered by both X and Y
Choose 5 if the question can be answered by neither X nor Y


The positive integers are such that p < q ≤ r < s < 100, ps = qr and √s - √p ≤ 1. What is the value of p?


(X) The last digit of s is either 1, 2 or 3

(Y) 50 < p and r < 90

[rajeev_hts]

This also looks pretty simple problem:-

For p=16, q=4, r=84, s=21

It satisfies both the conditions also for

p=20, q=10, r=44, s=22

so answer should be (5).

[rajeev_hts]

Hello Arav,

It is nice practice to put Old QQAD questions in parallel. Please keep it up.

[sabsebadapaagal]

Originally Posted by rajeev_hts

This also looks pretty simple problem:-

For p=16, q=4, r=84, s=21

It satisfies both the conditions also for

p=20, q=10, r=44, s=22

so answer should be (5).

as per question P< Q.... this question is violated in above...

[srikar2097]

Originally Posted by rajeev_hts

This also looks pretty simple problem:-

For p=16, q=4, r=84, s=21

It satisfies both the conditions also for

p=20, q=10, r=44, s=22

so answer should be (5).

Rajeev, It's given that p

[sabsebadapaagal]

Originally Posted by rajeev_hts

------------------------------------------------------
Quantitative Question # 019
------------------------------------------------------



The question is followed by two statements X and Y. Answer each question using the following instruction:

Choose 1 if the question can be answered by X only
Choose 2 if the question can be answered by Y only
Choose 3 if the question can be answered by either X or Y
Choose 4 if the question can be answered by both X and Y
Choose 5 if the question can be answered by neither X nor Y


The positive integers are such that p < q ≤ r < s < 100, ps = qr and √s - √p ≤ 1. What is the value of p?


(X) The last digit of s is either 1, 2 or 3

(Y) 50 < p and r < 90

It will be clear that p,q,r,s form an increasing GP.

Let a be the starting term of this GP and r be the common ratio.. now the terms come out to be a,ar,ar^2,ar^3

Now plugging these values in √s - √p <=1
√ar^3 - √a <=1

=> a^1/2(r^3/2 - 1) <=1

r^3/2 -1 <= 1

r^3/2 <=2

r<= 4^1/3

Now, applying this to both the conditions(X and Y) above we are not able to find the value of p

thus option 5

[ankaj]

Originally Posted by rajeev_hts

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Quantitative Question # 019
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The question is followed by two statements X and Y. Answer each question using the following instruction:

Choose 1 if the question can be answered by X only
Choose 2 if the question can be answered by Y only
Choose 3 if the question can be answered by either X or Y
Choose 4 if the question can be answered by both X and Y
Choose 5 if the question can be answered by neither X nor Y


The positive integers are such that p < q ≤ r < s < 100, ps = qr and √s - √p ≤ 1. What is the value of p?


(X) The last digit of s is either 1, 2 or 3

(Y) 50 < p and r < 90

P=64
Q=72
R=72
S=81

this is one set, which satisfies all the conditions. This set can be arrived by using only Y. Though after the result is known, X is derived from it.

Answer: 2, question is answered by Y only.

Correct me, not sure if missed some thing

[srikar2097]

Originally Posted by rajeev_hts

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Quantitative Question # 019
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The question is followed by two statements X and Y. Answer each question using the following instruction:

Choose 1 if the question can be answered by X only
Choose 2 if the question can be answered by Y only
Choose 3 if the question can be answered by either X or Y
Choose 4 if the question can be answered by both X and Y
Choose 5 if the question can be answered by neither X nor Y


The positive integers are such that p < q ≤ r < s < 100, ps = qr and √s - √p ≤ 1. What is the value of p?


(X) The last digit of s is either 1, 2 or 3

(Y) 50 < p and r < 90

My answer: 3

s can take {4,9,16,25,36,49,64,81} and p can take {1,4,9,16,25,36,49,64}. Please note that I'm talking about corresponding values to be taken here. i.e. for s=4 I take p=1. (this is based on the condition that s^1/2 - p ^1/2 = 1)

Now using inequalities ps = qr and p< q =< r < s < 100 the possible values that p, q, r and s can take are -

if p = 1, s = 4 and q=r=2
if p = 4, s = 9 and q=r=6
if p = 9, s = 16 and q=r=12
if p = 16, s = 25 and q=r=20
if p = 25, s = 36 and q=r=30
if p = 36, s = 49 and q=r=42
if p = 49, s =64 and q=r=56
if p = 64, s =81 and q=r=72

(X) states that s ends in either 1,2,3 (In fact s could never end in 2,3 as per the given conditions). The only case here satisfying is the last one. So Value of p=64.

(Y) states that 50 is less that p and r is less than 60. Again the only case here satisfying this is the last one. So value of p=64

Hence (3)

@Aarav - It's an excellent idea to post old QQAD questions. Thanks for that.

[sabsebadapaagal]

Can some one pls tell me what is wrong in my approach???? I am not able to figure it out

[srikar2097]

Originally Posted by sabsebadapaagal

Can some one pls tell me what is wrong in my approach???? I am not able to figure it out

I didn't get two things in your approach -
1) How did you declare that p,q,r,s is an increasing GP?

2) Initially, you had a^1/2(r^3/2 - 1). What happened to 'a^1/2'