Official Quant thread for CAT 2013

techsurge · November 19, 2012, 9:58am

There are 2 prime numbers P and Q greater than 100 such that they P=Q+2

Now, which of the following will definitely be true

a) P^2-Q^2 is a multiple of 24

b) P^3 + Q^3 is a multiple of 24

c) Both A and B

d) None of the above

Souce CL MOCK IIFT

will post OA in a while

audiq7 · November 19, 2012, 10:01am

@techsurge a?

soumitrabengeri · November 19, 2012, 10:03am

@techsurge said:
There are 2 prime numbers P and Q greater than 100 such that they P=Q+2Now, which of the following will definitely be true a) P^2-Q^2 is a multiple of 24b) P^3 + Q^3 is a multiple of 24c) Both A and Bd) None of the aboveSouce CL MOCK IIFTwill post OA in a while

option a?

101,103

107,109

From these examples, we can conclude that only option 1 gets satisfied.

grkkrg · November 19, 2012, 10:05am

@techsurge said:
There are 2 prime numbers P and Q greater than 100 such that they P=Q+2Now, which of the following will definitely be true a) P^2-Q^2 is a multiple of 24b) P^3 + Q^3 is a multiple of 24c) Both A and Bd) None of the aboveSouce CL MOCK IIFTwill post OA in a while

(a)

P = Q + 2
P = 6k + 1
Q = 6k - 1

P^2 - Q^2 = (12k)(2) = 24k
(a) is correct

P^3 + Q^3 = (P + Q)((P + Q)^2 - 3PQ)
= (P + Q)(P^2 + Q^2 - PQ)
= (12k)(36k^2 + 1 + 36k^2 + 1 - 36k^2 + 1)
= (12k)(36k^2 + 3)
(b) is incorrect

brooklyn · November 19, 2012, 10:07am

@techsurge said:
There are 2 prime numbers P and Q greater than 100 such that they P=Q+2Now, which of the following will definitely be true a) P^2-Q^2 is a multiple of 24b) P^3 + Q^3 is a multiple of 24c) Both A and Bd) None of the aboveSouce CL MOCK IIFTwill post OA in a while

a

foolnfinal · November 19, 2012, 10:07am

@techsurge said:
There are 2 prime numbers P and Q greater than 100 such that they P=Q+2Now, which of the following will definitely be true a) P^2-Q^2 is a multiple of 24b) P^3 + Q^3 is a multiple of 24c) Both A and Bd) None of the aboveSouce CL MOCK IIFTwill post OA in a while

ONLY a

sarayusheshadri · November 19, 2012, 10:11am

@techsurge said:

There are 2 prime numbers P and Q greater than 100 such that they P=Q+2

Now, which of the following will definitely be true

a) P^2-Q^2 is a multiple of 24

b) P^3 + Q^3 is a multiple of 24

c) Both A and B

d) None of the above

Souce CL MOCK IIFT

will post OA in a while

A only..

The numbers are of the form 6k+5 and 6k+7

deedeedudu · November 19, 2012, 10:19am

@techsurge said:
There are 2 prime numbers P and Q greater than 100 such that they P=Q+2Now, which of the following will definitely be true a) P^2-Q^2 is a multiple of 24b) P^3 + Q^3 is a multiple of 24c) Both A and Bd) None of the aboveSouce CL MOCK IIFTwill post OA in a while

a)

deedeedudu · November 19, 2012, 10:21am

@audiq7 said:
last two digits of (1^3+2^3......49^3)?

25

techsurge · November 19, 2012, 10:27am

@techsurge said:

There are 2 prime numbers P and Q greater than 100 such that they P=Q+2

Now, which of the following will definitely be true

a) P^2-Q^2 is a multiple of 24

b) P^3 + Q^3 is a multiple of 24

c) Both A and B

d) None of the above

Souce CL MOCK IIFT

will post OA in a while

OA a)

use the numbers as 6k+1 and 6k -1

for solution

everyone got right :mg:

audiq7 · November 19, 2012, 10:31am

akash and prakash are swimming a two leg race. akash starts frm deep end and prakash from shallow end. they first meet at 18meters from shallow end. on reaching respective ends after first leg, they take rest for 2s. During the second leg, they pass each other at 10meters from shallow end. length of pool?

brooklyn · November 19, 2012, 10:38am

@audiq7 said:
akash and prakash are swimming a two leg race. akash starts frm deep end and prakash from shallow end. they first meet at 18meters from shallow end. on reaching respective ends after first leg, they take rest for 2s. During the second leg, they pass each other at 10meters from shallow end. length of pool?

20 ?>

sarayusheshadri · November 19, 2012, 10:41am

@audiq7 said:
akash and prakash are swimming a two leg race. akash starts frm deep end and prakash from shallow end. they first meet at 18meters from shallow end. on reaching respective ends after first leg, they take rest for 2s. During the second leg, they pass each other at 10meters from shallow end. length of pool?

40 mts..

nihilist1002 · November 19, 2012, 10:41am

@audiq7 32?

audiq7 · November 19, 2012, 10:43am

@audiq7 said:
akash and prakash are swimming a two leg race. akash starts frm deep end and prakash from shallow end. they first meet at 18meters from shallow end. on reaching respective ends after first leg, they take rest for 2s. During the second leg, they pass each other at 10meters from shallow end. length of pool?

OA:32 EDIT

krum · November 19, 2012, 10:46am

@audiq7 said:
OA:44

(D-18)/a=18/p
(D+10)/a=(2D-10)/p

=>(D-18)(2D-10)=18(D+10)

=>D=32

adwaitjw · November 19, 2012, 10:49am

@audiq7 said:
akash and prakash are swimming a two leg race. akash starts frm deep end and prakash from shallow end. they first meet at 18meters from shallow end. on reaching respective ends after first leg, they take rest for 2s. During the second leg, they pass each other at 10meters from shallow end. length of pool?

32m?

deedeedudu · November 19, 2012, 10:53am

@audiq7 said:
akash and prakash are swimming a two leg race. akash starts frm deep end and prakash from shallow end. they first meet at 18meters from shallow end. on reaching respective ends after first leg, they take rest for 2s. During the second leg, they pass each other at 10meters from shallow end. length of pool?

18/(x-18)=(x+10)/(2x-10)
x=44

audiq7 · November 19, 2012, 10:56am

A,B,C,D are 4 no.s. one of them is odd, one is even, one is a recurring decimal, one is an irrational sqr root of an odd no. AC divided by 6 gives an odd integer equal to BA while CD^2 gives an even integer to 5B. Find out the nature of the no.s

krum · November 19, 2012, 10:56am

@deedeedudu said:
18/(x-18)=(x+10)/(2x-10)x=44

yaar but aakash is from deep end, so he will be the slower guy