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integers/ primes

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by jonnyais » Thu Oct 16, 2008 12:11 pm
I don't think so...

I just took the 4 smallest primes, 2*3*5*7=210, which is not the square of an integer. maybe I'm misunderstanding the question
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Re: integers/ primes

by Stuart@KaplanGMAT » Thu Oct 16, 2008 1:10 pm
brandonw3 wrote:If k is a positive integer, is k the square of an integer?

1) k is divisible by 4
2) k is divisible by exactly four different prime numbers

does statement 2 have a "yes" outcome?

thanks
The wording of (2) may be a bit tricky.

(2) does NOT say that k has only 4 prime factors - it says that k has only 4 different prime factors.

For example, k could be:

2*2*3*3*5*5*7*7, which would be a perfect square.
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by lunarpower » Fri Oct 17, 2008 3:05 am
yep, stuart is right. just to clarify, make sure that you understand the following:
if the problem says that a number is divisible by the prime factor p, then you know NOTHING about how many times the number is divisible by that prime factor.

the prime factor could appear only once, or it could appear multiple times (e.g., each prime in stuart's example appears twice).
Ron has been teaching various standardized tests for 20 years.

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by ddo » Fri Oct 17, 2008 6:49 am
Answer would be E then.?

K could be 2*2*3*5*7 = 420 multiple of 4 but not perfect square
or could be 2*2*3*3*5*5*7*7 multiple of 4 and perfect sq.

I think the rule is: a sq of a prime nbr has always 3 factors
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by lunarpower » Fri Oct 17, 2008 11:54 am
ddo wrote:Answer would be E then.?

K could be 2*2*3*5*7 = 420 multiple of 4 but not perfect square
or could be 2*2*3*3*5*5*7*7 multiple of 4 and perfect sq.

I think the rule is: a sq of a prime nbr has always 3 factors
correct.
your stated rule is also correct, although it's completely irrelevant to the problem at hand.

here's a more general fact: all perfect squares - and ONLY perfect squares - have an odd number of total factors.
there are some clever little ways to show that this is true, but, for gmat style time management, you should just know it without having to mentally re-derive it every time.
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by dally_gmat » Fri Oct 17, 2008 12:05 pm
Perfect square is same as square or it is sub set of squares??

May be lame question..but i m confused..:
lunarpower wrote:
ddo wrote:Answer would be E then.?

here's a more general fact: all perfect squares - and ONLY perfect squares - have an odd number of total factors.
there are some clever little ways to show that this is true, but, for gmat style time management, you should just know it without having to mentally re-derive it every time.
:D :)
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by lunarpower » Fri Oct 17, 2008 1:36 pm
dally_gmat wrote:Perfect square is same as square or it is sub set of squares??
perfect squares are integers that are squares of other integers: 1, 4, 9, 16, 25, ...

therefore, the answer to your question is probably "it's the same as 'square' ", but the gmat (as will as other formal mathematical resources) is very exacting about usage: the unadorned word "square" would be used only to refer to a geometrical figure.
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