Data Sufficiency

Which is the correct answer


Can the positive integer y be expressed as
the product of two integers, each of which
is greater than 1?
(1) 47 < y < 53
(2) y is even

IMO A.

1: y can be 48,49,50,51,52

All of these can be product of two integers > 1. Sufficient

2: y is even
this does not hold valid for y = 0 and 2. Not Suff.

mbanit wrote:Which is the correct answer


Can the positive integer y be expressed as
the product of two integers, each of which
is greater than 1?
(1) 47 < y < 53
(2) y is even

But as per source book, answer is C. Any comments on why C can't be the answer.


C. This question essentially asks you whether the positive integer y is any number other than a prime number, because a prime number can be expressed only as a product of 1 and itself. Because the range provided by statement (1) contains a number that's prime (51), you can't determine whether y is a composite number from statement (1) alone. Statement (1) isn't sufficient by itself, and neither A nor D can be the answer. Consider statement (2). At first, statement (2) may seem sufficient to you. Almost no even numbers are prime. But 2 is the one even number that's prime, so knowing that y is even doesn't allow you to say that it can be expressed as the product of 2 integers that are both greater than 1. Because statement (2) isn't sufficient, the answer can't be B. Consider whether knowing both statements provides an answer to the question.
The two statements together narrow values for y to even numbers between 47 and 53. Those numbers are 48, 50, and 52, and none is a prime number. The information from both statements is sufficient to tell you that the possible values for y can be expressed as the product of two integers greater than 1, so the answer must be C.

mbanit wrote:But as per source book, answer is C. Any comments on why C can't be the answer.


C. This question essentially asks you whether the positive integer y is any number other than a prime number, because a prime number can be expressed only as a product of 1 and itself. Because the range provided by statement (1) contains a number that's prime (51), you can't determine whether y is a composite number from statement (1) alone. Statement (1) isn't sufficient by itself, and neither A nor D can be the answer. Consider statement (2). At first, statement (2) may seem sufficient to you. Almost no even numbers are prime. But 2 is the one even number that's prime, so knowing that y is even doesn't allow you to say that it can be expressed as the product of 2 integers that are both greater than 1. Because statement (2) isn't sufficient, the answer can't be B. Consider whether knowing both statements provides an answer to the question.
The two statements together narrow values for y to even numbers between 47 and 53. Those numbers are 48, 50, and 52, and none is a prime number. The information from both statements is sufficient to tell you that the possible values for y can be expressed as the product of two integers greater than 1, so the answer must be C.

I m sorry but who said 51 is a prime. Is not 17*3 = 51?

mbanit,

What is the source of this question?I think this is worst one.

As mentioned in the book/source,51 is not a prime number and can be expressed as product of 2 integers[17*3]

Always use the reliable source.