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# If x, y ≠ 0, is x/y an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
If x, y ≠ 0, is x/y an integer?  [#permalink]

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19 May 2017, 11:41
00:00

Difficulty:

15% (low)

Question Stats:

79% (00:52) correct 21% (00:54) wrong based on 49 sessions

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If x, y ≠ 0, is x/y an integer?

(1) x is prime.
(2) y is even.

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Senior Manager
Joined: 24 Apr 2016
Posts: 332
Re: If x, y ≠ 0, is x/y an integer?  [#permalink]

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19 May 2017, 11:52
If x, y ≠ 0, is x/y an integer?

(1) x is prime.

Let's say x is 3 and y is 1, then x/y = 3, which is an integer
But if x is 3 and y is 2, then x/y = 3/2, which is not an integer.

This statement is not sufficient.

(2) y is even.

Let's say x is 4 and y is 2, then x/y = 2, which is an integer
But if x is 3 and y is 2, then x/y = 3/2, which is not an integer.
This statement is not sufficient.

Combining both statements - X is prime and y is even

Let's say x is 2 and y is 2, then x/y = 1, which is an integer
But if x is 3 and y is 2, then x/y = 3/2, which is not an integer.

both statements together are also not sufficient.

Intern
Joined: 26 Jul 2016
Posts: 36
Location: India
Re: If x, y ≠ 0, is x/y an integer?  [#permalink]

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19 May 2017, 21:40
x/y---integer.
St. 1- X prime--- If y=x then 'yes'; if y not equal to x then 'no'
St. 2- y even--- no info about x--- insufficient.
St. 1+ St.2--- 2/2 is integer hence 'yes'; for all other values of y the answer is 'no'
Manager
Joined: 12 Jun 2016
Posts: 216
Location: India
WE: Sales (Telecommunications)
If x, y ≠ 0, is x/y an integer?  [#permalink]

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20 May 2017, 03:18
Stem rephrased : Is x=a.y where a is an integer? or Is x a Multiple of y? or Is Y a factor of X?

S1:x is prime.
No clear info on Y. insuff.

S1: y is even.
No clear info on x. insuff

S1+S2 : x is prime and y is even.
if both x and y = 2, x = 1.y => x/y is an integer.
if x = 2 and y=4, x/y = 1/4 = Fraction/Non integer.
So, insuff

Both statements together insuff. Hence, Final Answer : E
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If x, y ≠ 0, is x/y an integer? &nbs [#permalink] 20 May 2017, 03:18
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