Is the positive integer N a perfect square?

[jnelson0612]

The answer to this problem is D. Let us know if you need more clarification.

[shetty.nagraj1]

The answer to this problem is D. Let us know if you need more clarification.

Hi,

The explanation says " the sums of the factors are odd" -- which is makes sense and is correct.

however in the stem, the second statement states "(2) The sum of all distinct factors of N is even."

Then the answer should be A, shouldnt it?

Pls can you help me understand if I am missing something here.

Thank you.

[tim]

if a number is to be a square, its factors have to add to an odd number. this is true. now with that in mind let's take a look at statement 2 and ask if it helps to answer the question:

the question is: is N a perfect square?

statement 2 says the factors of N add to an even number. from this we conclude that N must not be a perfect square. now let's answer the question:

is N a perfect square? NO!

we know the answer to the question - it is NO!

remember, whenever you KNOW the answer to the question - as we do here - the statement is sufficient. so statement 2 is sufficient.

the ONLY time a statement is insufficient is when it does not answer the question at the top of the page.

[shetty.nagraj1]

thank you Tim.

I realized that I overlooked the sufficiency in getting No from both the statements. my bad.

I ll take care next time.

thanks again.

cheers.
Nagraj

[jnelson0612]

Great!

[jatin]

One is a perfect square.
But, the sum of distinct factors of one is one, which is odd. Therefore, the B is insufficient.
Am I wrong?

Regards,
Tanuj

[RonPurewal]

One is a perfect square.
But, the sum of distinct factors of one is one, which is odd. Therefore, the B is insufficient.
Am I wrong?

Regards,
Tanuj

this case is not relevant to either statement. take another look at the statements.

[RonPurewal]

One is a perfect square.
But, the sum of distinct factors of one is one, which is odd. Therefore, the B is insufficient.
Am I wrong?

Regards,
Tanuj

okay, i think i see what you're trying to do here: you're working the whole problem backward.

it seems you're taking perfect squares, and then asking yourself "does this satisfy the numbered statements?"
this is not how DS works.
you have to start from the statements, and use that information to answer the question.

so, for statement 1, you think ONLY about numbers that have an even # of factors. the number 1 does not, so it is irrelevant.
for statement 2, you think ONLY about numbers that have an even sum of factors. again the number 1 fails to satisfy the criterion, so, again, it is irrelevant.