hbhardwaj wrote:Dear Friends,

Please review the following 2 DS problem below and sugest the answers.....

1. If k is a positive integer, is k the square of integer?

(1) K Is divisible by 4.
(2) k is divisible by exactly four different prime numbers.


According to me it should be "Statement 2 alone, but not 1"

2. What is the remainder when the positive integer n is divided by the positive integer k, where
k>1?
(1) n=(k+1)^3 (i.e. cube of (k+1))
(2) k=5

My answer "both statements together"....

Please suggest your answers..

Q1)
1) consider k=36 36 is a perfect square and is divisible by 4, also consider k=12; 12 is divisible by 4 but it is not a perfect square hence 1 is insufficient.

2) k=(2^2)*(3^4)*(5^2)*(7^2); now k is a perfect square and is divisible exactly by 4 prime factors, now consider k=2*3*5*7; now also k is divisible by 4 different prime numbers but it is not a perfect square... therefore 2 alone is not sufficient to answer the question..!!

combining 1 and 2,

consider k=(2^2)*(3^4)*(5^2)*(7^2); it is divisible by 4 and is a perfect square, now consider k=(2^2)*3*5*7; it is also divisible by 4 but is not a perfect square hence answer should be E

hbhardwaj wrote:Dear Friends,

Please review the following 2 DS problem below and sugest the answers.....

1. If k is a positive integer, is k the square of integer?

(1) K Is divisible by 4.
(2) k is divisible by exactly four different prime numbers.


According to me it should be "Statement 2 alone, but not 1"

2. What is the remainder when the positive integer n is divided by the positive integer k, where
k>1?
(1) n=(k+1)^3 (i.e. cube of (k+1))
(2) k=5

My answer "both statements together"....

Please suggest your answers..

Q.2
we have to find the remainder when n/k;
1) n=(k+1)^3; (k+1)^3 when divided by k will always give a remainder of 1...!! lets see why;
(k+1)^3=k^3+1+3k^2+3k;
(k(k^2+2k+3)+1); when the k(k^2+2k+3) will be divided by k remainder would be zero, and when 1 will be divided by k remainder would be 1 as k>1; hence remainder will be 1; therefore 1 is sufficient.

2) k=5; we don't know what is n; n=20; then n is divisible by k; if n=21 then n is not divisible by k; hence 2 alone is not sufficient to answer the question..!!

hence A