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x and y are positive integers. When x is divided by 2y

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x and y are positive integers. When x is divided by 2y  [#permalink]

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New post 30 Mar 2017, 08:23
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  65% (hard)

Question Stats:

63% (01:42) correct 37% (01:59) wrong based on 122 sessions

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x and y are positive integers. When x is divided by 2y, the remainder is y. What is the value of y?

(1) x is even
(2) y is a prime number

*kudos for all correct solutions

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Re: x and y are positive integers. When x is divided by 2y  [#permalink]

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New post 30 Mar 2017, 10:02
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GMATPrepNow wrote:
x and y are positive integers. When x is divided by 2y, the remainder is y. What is the value of y?

(1) x is even
(2) y is a prime number

*kudos for all correct solutions


x-2qy=y
x=(1+2q)y
1) x is even
x=odd*y
For x to be even y has to be even (2,4,6...)
Insuff
2) y is prime
x=(1+2q)*y
y can be 2,3,5,,,,
Insuff

1+2 combined, the only possible value of y is 2.
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Kudos for a correct solution :)

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Re: x and y are positive integers. When x is divided by 2y  [#permalink]

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New post 30 Mar 2017, 10:07
GMATPrepNow wrote:
x and y are positive integers. When x is divided by 2y, the remainder is y. What is the value of y?

(1) x is even
(2) y is a prime number

*kudos for all correct solutions


(1) x is even - Not sufficient
x=2, y=2, 2y=4, and Remainder of x/2y is 2. Hence y=2
x=4, y=4, 2y=8, and Remainder of x/2y is 4. Hence y=4

(2) y is a prime number - No sufficient
x=2, y=2, 2y=4, and Remainder of x/2y is 2. Hence y=2
x=3, y=3, 2y=6, and Remainder of x/2y is 3. Hence y=3

(1) + (2) - x=2, y=2, 2y=4, and Remainder of x/2y is 2. Hence y=2 - Sufficient.

Hence C.

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Re: x and y are positive integers. When x is divided by 2y  [#permalink]

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New post 14 Dec 2017, 09:10
When x is divided by 2y, the remainder is y
So, x=2y+y
1) x is even
As 2y is even so y will be even
x(even)= 2y(even)+y(even)
so y can have any value…..not sufficient

2) y is a prime number
For y=2, x=2 and 2y=4, we have x/2y as 2
For y=3, x=3 and 2y=6, we have x/2y as 3
For y=5, x=5 and 2y=10, we have x/2y as 5
and so on…
still not sufficient
Combining both (1) and (2) we have even prime number as ‘2’
Hence ‘C’ is the choice
Re: x and y are positive integers. When x is divided by 2y &nbs [#permalink] 14 Dec 2017, 09:10
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