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

Question

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

GMATBusters · Answer

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

GMATinsight · Answer

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

GMATinsight · Answer

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

chirkut1488 · Answer

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

GMATBusters · Answer

yes, you are right... but x can only be 4. hence Answer is C

GMATBusters · Answer

thanks for pointing out my mistake...

exc4libur · Answer

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.

CAMANISHPARMAR · Answer

Since X<5 then x has to be 4 hence the answer is C

niks18 · Answer

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

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