Can the positive integer y be expressed as the product of two integers : Data Sufficiency (DS)

DesiGmat

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12 Jan 2015, 09:23

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anupamadw

DesiGmat

Y is a positive integer (given)

St1 -

47 < y < 53

y can have any one of the following values

Y = 48-> (1*48)(6*8)(12*4)
Y = 49-> (1*49)(7*7)
Y = 50-> (1*50)(10*5)(2*25)
Y = 51-> (1*51)(3*17)
Y = 52-> (1*52)(2*26)

So in all possible values, Y can be expressed as the product of two integers, each of which is greater than 1

Note - There is no prime number between 47 to 53 (Easy way)

St1 is sufficient to answer the question.

St2 Y is even

Y = 2 -> (1*2)
Y = 6 -> (1*6) (2*3)

Clearly not sufficient

Option A is correct

Hi

Sorry, but can we consider Y = 49-> (7*7) as two integers?
I think we are using only one integer here i.e. 7
IMO C, because Y is even will exclude 49.

Please let me know, if this is correct.

Thanks

As per my understanding the question is -> Can the positive integer y be expressed as the product of two integers, each of which is greater than 1?

Had the question been Can the positive integer y be expressed as the product of two DIFFERENT integers, each of which is greater than 1?
I would have agreed with you.

Thanks

Bunuel

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19 Jan 2015, 03:48

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Bunuel

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

Kudos for a correct solution.

OFFICIAL SOLUTION:

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 (53), 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.

Bunuel

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19 Jan 2015, 03:49

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Similar question to practice: can-the-positive-integer-p-be-expressed-as-the-product-of-tw-166085.html

anupamadw

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19 Jan 2015, 08:56

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Bunuel

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

Kudos for a correct solution.

OFFICIAL SOLUTION:

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 (53), 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.

Sorry , range is 47 < y< 53 then 53 is not included right?
48,49,50,51,52 ---none is prime

Bunuel

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19 Jan 2015, 08:58

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anupamadw

Bunuel

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

Kudos for a correct solution.

OFFICIAL SOLUTION:

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 (53), 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.

Sorry , range is 47 < y< 53 then 53 is not included right?
48,49,50,51,52 ---none is prime

Its' 47 <= y <= 53.

anupamadw

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19 Jan 2015, 09:00

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anupamadw

Bunuel

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

Kudos for a correct solution.

OFFICIAL SOLUTION:

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 (53), 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.

Sorry , range is 47 < y< 53 then 53 is not included right?
48,49,50,51,52 ---none is prime

sorry I saw edited question now, thanks

kevinlnyc

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22 Jul 2017, 06:43

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how do negative numbers affect this question?

for example, if y = 50, -10 and -5 could be integers whose product equals 7. -10 and -5 are both less than 1.

Bunuel

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23 Jul 2017, 05:24

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kevinlnyc

how do negative numbers affect this question?

for example, if y = 50, -10 and -5 could be integers whose product equals 7. -10 and -5 are both less than 1.

When we combine the statements we get that y is 48, 50, or 52. All of them CAN be expressed as the product of two integers, each of which is greater than 1: 48 = 2*24, 50 = 2*25 and 52 = 2*26. So, we have a definite YES answer to the question.

Can the positive integer y be expressed as the product of two integers

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