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k a positive integer

Expert replies
Source: — Data Sufficiency |

by KapTeacherEli » Mon Oct 12, 2009 12:45 pm
K = 2 * 2 * 3 * 4 * 5 = 240; k matches statements 1 and 2, having 4 distinct prime factors and being divisible by 4, and is not a perfect square.

K = 2 * 2 * 3 * 3 * 4 * 4 * 5 * 5 is divisible by exactly 4 different primes and is divisible by 4, so is consistent with both statements. It is also equal to (2*3*4*5)^2, or 120 squared, so it is a perfect square.

Since numbers consistent with statements 1 and 2 can give us a Yes or a No answer, our answer is E, even together we don't know.
Eli Meyer
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by vaibhav.iit2002 » Mon Oct 12, 2009 6:13 pm
KapTeacherEli wrote:K = 2 * 2 * 3 * 4 * 5 = 240; k matches statements 1 and 2, having 4 distinct prime factors and being divisible by 4, and is not a perfect square.

K = 2 * 2 * 3 * 3 * 4 * 4 * 5 * 5 is divisible by exactly 4 different primes and is divisible by 4, so is consistent with both statements. It is also equal to (2*3*4*5)^2, or 120 squared, so it is a perfect square.

Since numbers consistent with statements 1 and 2 can give us a Yes or a No answer, our answer is E, even together we don't know.
Statement 2 says:"exactly 4 different primes"
doesn't it mean that k may consist prime no.s only once , i mean k=2x3x5x7 and not k=2x2x3x5x7 ?
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by KapTeacherEli » Thu Oct 22, 2009 8:27 am
vaibhav.iit2002 wrote:
Statement 2 says:"exactly 4 different primes"
doesn't it mean that k may consist prime no.s only once , i mean k=2x3x5x7 and not k=2x2x3x5x7 ?
K is divisble by exactly four primes--2, 3, 5, and 7. That doesn't meant it has exactly four prime facotrs; that's not the same thing. Further, if it WAS 2x3x5x7, it couldn't be divisible by 4. Remember, DS statements never conflict.
Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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