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

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Bunuel
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If x and y are positive integers, what is the value of x ? [#permalink] New post   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
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C
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Re: If x and y are positive integers, what is the value of x ? [#permalink] New post   17 Dec 2017, 04:55
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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.
Answer is E
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Re: If x and y are positive integers, what is the value of x ? [#permalink] New post   17 Dec 2017, 05:55
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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

Answer: Option C
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If x and y are positive integers, what is the value of x ? [#permalink] New post   17 Dec 2017, 05:56
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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.
Answer is E


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] New post   17 Dec 2017, 06:51
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?
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If x and y are positive integers, what is the value of x ? [#permalink] New post   17 Dec 2017, 07:24
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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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Re: If x and y are positive integers, what is the value of x ? [#permalink] New post   17 Dec 2017, 07:49
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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.
Answer is E


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] New post   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.

(C) is the answer.
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Re: If x and y are positive integers, what is the value of x ? [#permalink] New post   15 Jun 2018, 09:41
chirkut1488 wrote:
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?


Since X<5 then x has to be 4 hence the answer is C
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If x and y are positive integers, what is the value of x ? [#permalink] New post   06 Jul 2018, 23:21
TippingPoint93 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


Statement 1: as \(x\), \(y\) & \(xy\) are distinct perfect squares so \(x\) or \(y\) cannot be equal to \(1\) because in that case \(xy\) will be equal to either \(x\) or \(y\).

Some of the possible \(x\) & \(y\) combinations are \((4,9)\) & \((9,4)\). There are multiple values of \(x\). hence Insufficient

Statement 2: \(x\) could be \(1\) or \(4\). Insufficient

Combining 1 & 2: Only possible value for \(x=4\). Sufficient

Option C
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Re: If x and y are positive integers, what is the value of x ? [#permalink] New post   17 May 2022, 00:07
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Re: If x and y are positive integers, what is the value of x ? [#permalink]
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