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

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Math Expert
Joined: 02 Sep 2009
Posts: 54493
Can the positive integer y be expressed as the product of two integers  [#permalink]

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11 Jan 2015, 12:38
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:26) correct 46% (01:20) wrong based on 130 sessions

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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.

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Joined: 27 Oct 2013
Posts: 205
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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12 Jan 2015, 02:03
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
Manager
Joined: 31 Jul 2014
Posts: 127
GMAT 1: 630 Q48 V29
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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12 Jan 2015, 06:40
1
DesiGmat wrote:
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
Manager
Joined: 27 Oct 2013
Posts: 205
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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12 Jan 2015, 09:23
DesiGmat wrote:
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
Math Expert
Joined: 02 Sep 2009
Posts: 54493
Can the positive integer y be expressed as the product of two integers  [#permalink]

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19 Jan 2015, 03:48
2
Bunuel wrote:
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.
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Math Expert
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Posts: 54493
Can the positive integer y be expressed as the product of two integers  [#permalink]

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19 Jan 2015, 03:49
Similar question to practice: can-the-positive-integer-p-be-expressed-as-the-product-of-tw-166085.html
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Joined: 31 Jul 2014
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GMAT 1: 630 Q48 V29
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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19 Jan 2015, 08:56
Bunuel wrote:
Bunuel wrote:
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
Math Expert
Joined: 02 Sep 2009
Posts: 54493
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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19 Jan 2015, 08:58
Bunuel wrote:
Bunuel wrote:
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.
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Joined: 31 Jul 2014
Posts: 127
GMAT 1: 630 Q48 V29
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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19 Jan 2015, 09:00
Bunuel wrote:
Bunuel wrote:
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
Intern
Joined: 01 Aug 2014
Posts: 3
Can the positive integer y be expressed as the product of two integers  [#permalink]

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22 Jul 2017, 06:43
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.
Math Expert
Joined: 02 Sep 2009
Posts: 54493
Re: Can the positive integer y be expressed as the product of two integers  [#permalink]

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23 Jul 2017, 05:24
kevinlnyc wrote:
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.
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Re: Can the positive integer y be expressed as the product of two integers   [#permalink] 23 Jul 2017, 05:24
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