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# If x and y are positive integers, what is the value of x ?

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Math Expert
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If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 01:42
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If x and y are positive integers, what is the value of x ?

(1) x, y, and xy are distinct perfect squares less than 100.
(2) x < 5
[Reveal] Spoiler: OA

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Senior Manager
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Re: If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 04:55
Statement 1: we can have (x, y) as (1, 4) or (4, 9)... so not sufficient
Statement 2: x can be 1, 2, 3 or 4.
Combining statement 1 &2
We can have (x,y) as (1,4) or (4,1)
hence the value of x can be 1 or 4; the unique value of x cannot be determined.
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Re: If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 05:55
Bunuel wrote:
If x and y are positive integers, what is the value of x ?

(1) x, y, and xy are distinct perfect squares less than 100.
(2) x < 5

Question : WHat is the value of x?

STatement 1: x, y, and xy are distinct perfect squares less than 100

Case 1: x = 4, y = 9, xy = 36
Case 2: x = 9, y = 4, xy = 36
Multiple values of x hence,
NOT SUFFICIENT

STatement 2: x<5
No information about y and xy and hence x may be 1 or 2 or 3 or 4 etc
NOT SUFFICIENT

Combining the two statements
x, y, and xy are distinct perfect squares and x <5

less than 5 theer are only two perfect squares 1 and 4
but x can NOT be 1 because x*y will be equal to y which is unacceptable because given that x, y and xy are distinct
hence
x = 4
SUFFICIENT

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If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 05:56
gmatbusters wrote:
Statement 1: we can have (x, y) as (1, 4) or (4, 9)... so not sufficient
Statement 2: x can be 1, 2, 3 or 4.
Combining statement 1 &2
We can have (x,y) as (1,4) or (4,1)
hence the value of x can be 1 or 4; the unique value of x cannot be determined.

None of x and y can be equal to 1 because if anyone of them is 1 then x, y and xy will not remain DISTINCT
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Re: If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 06:51
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?
Senior Manager
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If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 07:24
yes, you are right... but x can only be 4. hence Answer is C

chirkut1488 wrote:
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?

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Senior Manager
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Re: If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 07:49
thanks for pointing out my mistake...

GMATinsight wrote:
gmatbusters wrote:
Statement 1: we can have (x, y) as (1, 4) or (4, 9)... so not sufficient
Statement 2: x can be 1, 2, 3 or 4.
Combining statement 1 &2
We can have (x,y) as (1,4) or (4,1)
hence the value of x can be 1 or 4; the unique value of x cannot be determined.

None of x and y can be equal to 1 because if anyone of them is 1 then x, y and xy will not remain DISTINCT

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Re: If x and y are positive integers, what is the value of x ? [#permalink]

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17 Dec 2017, 12:03
Bunuel wrote:
If x and y are positive integers, what is the value of x ?

(1) x, y, and xy are distinct perfect squares less than 100.
(2) x < 5

Positive integers are numbers greater than 0 {1,2,3,4,5...}

(1) x, y, and xy are distinct perfect squares less than 100.

x = 4 (2*2), y = 9 (3*3) and xy = 9*4 = 36 (6*6); or,
x = 9 (3*3), y = 49 (7*7) and xy = 9*49 = 196 (14*14).

They are all distinct perfect squares and there is more than one value for x, so insufficient.

(2) x < 5.

So x can be {1,2,3 or 4}, insufficient.

(3) Combining both informations we can only have one value for x < 5 that is a perfect square: $$x=4$$, sufficient.

Re: If x and y are positive integers, what is the value of x ?   [#permalink] 17 Dec 2017, 12:03
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