If K is an integer, is K the square of an integer ? 1. K is

Question

If K is an integer, is K the square of an integer ? 

1. K is divisible by 4 
2. K has exactly 4 prime factors.

yezz · Answer

Can you please explain??

FN · Answer

sorry...

i shud show my working..

(1) well pick a number 8 is divisible by 4, 12 is as well and they are not perfect squares...16 is divisible and is a perfect sq...insuff

(2) four prime factors

well 24 has 4 prime factors 2, 3, 2, 2 and its not a perfect sq..
16 has 2, 2, 2, 2 prime factors..and its a perfect sq

insuff

combinging...24 is divisble by 4..16 is divisible by 4...

see the key word is 4 prime factors..had the stem stated 4 DIFFERENT prime factors we may have a different answer...

kevincan · Answer

Be careful here! 24 has two prime factors, 2 and 3

ps_dahiya · Answer

E

Question is asking: Is K a perfect square?

St1: 60 and 16 are both divisible by 4 but only 16 is a perfect square: INSUFF

St2: K may be 2*3*5*7 (Not a perfect square) OR 2*2*3*3*5*5*7*7 (a perfect square): INSUFF

Together:
K = 2*2*3*5*7: Divisible by 4 and have 4 prime factors but NOT a perfect square
K = 2*2*3*3*5*5*7*7: Divisible by 4 and have 4 prime factors and ALSO a perfect square
: INSUFF

GMATT73 · Answer

In this case, (B) would be possible.

yezz · Answer

GMATT73... CAN U EXPLAIN UR REASONING

THANKS

FN · Answer

yes..2 distinct prime factors, however, the question says 4 prime factors...which means...2,2,2, 3 are 4 prime factors..but agreed they are not distinct..

gk3.14 · Answer

1. 24, 16 - INSUFF
2. Exactly 4 prime factors ...if this means distinct and not repeated and no other factor except these prime factors, then it has to be the square of a prime number for example: 17. if the number was 17^4, then it has 4 distinct prime factors : 17, 17^2, 17^3, 17^4.
so SUFF..

It depends on how you interpret it.. to be exactly implies no other factors except prime factors. If we have a number like 2*3*5*7 there are 4 prime factors but there are also other factors like 6, 10, 21 etc..

In my opinion - B
OA please??

yezz · Answer

sumitsarkar82 sent this post on the 2rd of Aug and no one replied.....

So unfortuanately i do not have the OA

SORRY

jjhko · Answer

The OA is E. 

However, I got this question from GmatPrep, but with one slight modification that for (2), it asks for divisible by exactly four different prime numbers.

ps_dahiya, I liked your approach and explanation... thx!

jjhko

Futuristic · Answer

I would go with E.

From 1:
K/4 is an integer

K could be 4, but could be 8, 12 which are not all perfect squares. Hence insuff.

From 2:
K has exaclty 4 prime factors. Let them be 2.3.5.7
Then K=2.3.5.7 or (2.3.5.7)^2....insuff

From 1, 2
K=2(2.3.5.7) or (2.3.5.7)^2 satisfies both 1 and 2 but may or may not be a perfect square....insuff

If K is an integer, is K the square of an integer ? 1. K is

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