If k is a positivee integer, is k the square of an integer?
1. k is divisible by 4
2. k is divisible by exactly 4 different prime numbers
Sqaure of an integer
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1. 8 vs 16
2. k = p1 * p2 * p3 * ... * pK
p1, p2, .., pK are prime numbers in prime factorization
"exactly different prime numbers" -> p1 through pK are different (to my understanding)
hence k cannot be square of integer. Square of integers must have even numver of each prime number in its prime factorization
2. k = p1 * p2 * p3 * ... * pK
p1, p2, .., pK are prime numbers in prime factorization
"exactly different prime numbers" -> p1 through pK are different (to my understanding)
hence k cannot be square of integer. Square of integers must have even numver of each prime number in its prime factorization
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A cnt answer the question.. But in "B", i didnt understand ..
Does K should be divisible by all different prime numbers?
Does K should be divisible by all different prime numbers?
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There is an infinite number of primes, so it isn't possible for a number to be divisible by all primes. I think the second statement -viju9162 wrote: Does K should be divisible by all different prime numbers?
which is meaningless as written, is supposed to read "k is divisible by exactly four different prime numbers". This statement is not sufficient; our number might be equal to 2*3*5*7, which is not the square of an integer, or it might be equal to (2^2)(3^2)(5^2)(7^2), which is the square of an integer (it's the square of 2*3*5*7).sakurle wrote: 2. k is divisible by exactly different prime numbers
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obviously, 1 Is not sufficient. Since both 8 and 16 are divisible by 4 but 8 is not a square of an integer whereas 16 is.
From statement 2 we can deduce that K/2, K/3, K/5, K/7,..., If K = 14, 2 and 7 divide K, If K = 15, 3 and 5 divide k, if k = 21 3 and 7 divide k, If k is 30, 2, 3 and 5 divide K. We can go on and on. But it's worth noting here that K = 14, 15, 21, 30 are all not square of an integer.Hence, we can say No with statement 2. Therefore, Statement 2 is sufficient (B)
From statement 2 we can deduce that K/2, K/3, K/5, K/7,..., If K = 14, 2 and 7 divide K, If K = 15, 3 and 5 divide k, if k = 21 3 and 7 divide k, If k is 30, 2, 3 and 5 divide K. We can go on and on. But it's worth noting here that K = 14, 15, 21, 30 are all not square of an integer.Hence, we can say No with statement 2. Therefore, Statement 2 is sufficient (B)
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This is GMAT Prep question. I was also going with B. However the OA is E. Also as Ian mentioned there was a typo which I have fixed.
Thanks Ian, I understand your explanation. My reasoning was that 4 different prime numbers means 2x3x5x7 I did not think that they can appear twice.
Thanks Ian, I understand your explanation. My reasoning was that 4 different prime numbers means 2x3x5x7 I did not think that they can appear twice.