If x y, and x, y and x/y are all positive integers, is x/y 10?

Question

If  x > y , and  x ,  y  and  x/y  are all positive integers, is  x/y > 10 ?

(1)  y^2 < 36

(2)  x = 53

chetan2u · Answer

Hi all,

INFO first 
 1) x>y
2) x,y, and x/y are positive integers..
3) x/y as integer means x is a multiple of y..
4) check if x/y>10

lets check the statement 
  (1) y^2 < 36 
this means y=1,2,3,4,5 , but no info about x..
Insuff

(2) x = 53 
x=53, which is a prime number..
but we know x/y is an integer, meaning y is a factor of x..
factor of a prime number is either teh number itself or 1...
since x>y, y cannot be 53...
hence y=1..
x/y=53/1, which is >10..
Suff

B

Nevernevergiveup · Answer

Nice question Marty.

case I:  y^2=36 
Thus y has range of values between  -6<y<6 
but since y is given positive integer in the stem.
 y=1,2,3,4,5 
with no single value for x we cannot determine whether fraction value is more than 10.

case II: x=53 
 y  can be anything but since  \frac{x}{y}  is a positive integer where  x,y  are positive.
and  53  is a prime number.
 y  can only be  1 .
Hence we can say that \frac{x}{y} > 10 .

This statement II is sufficient. 
 B is the answer.

KarishmaParmar · Answer

Beautiful Question!

The catch is to notice and remember that x/y too, is an integer. B in itself answers the question.

MartyTargetTestPrep · Answer

Maybe the key takeaway from this one is to NOTICE RED FLAGS.

There are a few red flags waving in this case.

Answering the question seems to involve simply noticing that since y is a positive integer, y ≤ 5, but the question is described as 700 Level.

Also, C seems very obvious. Hmm.

Meanwhile, as of the writing of this post, only 20% of people had gotten the right answer. That statistic itself tends to suggest that there is SOMETHING going on beyond dividing 53 by 5.

Noticing red flags can be integral to getting right answers.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.