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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, 07:23
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A
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C
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E

Difficulty:

  75% (hard)

Question Stats:

60% (01:43) correct 40% (01:58) wrong based on 164 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, 09:02
1
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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Re: x and y are positive integers. When x is divided by 2y  [#permalink]

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New post 30 Mar 2017, 09:07
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, 08:10
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
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Re: x and y are positive integers. When x is divided by 2y  [#permalink]

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New post 28 Oct 2018, 06:25
Top Contributor
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


Target question: What is the value of y?

Given: x and y are positive integers. When x is divided by 2y, the remainder is y

--------ASIDE------------------------------------
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
---------------BACK TO THE QUESTION------------

From the given information, we can say that the possible values of x are: y, y + 2y, y + 4y, 6 + 6y, . . . etc.
In other words, the possible values of x are: y, 3y, 5y, 7y, . . . etc.


Statement 1: x is even
We already know that the possible values of x are: y, 3y, 5y, 7y, . . . etc
All of these possible x-values are in the form x = (ODD)(y)
So, if x is EVEN, it must be the case that y is EVEN

There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 12 and y = 4. In this case, the answer to the target question is y = 4
Case b: x = 6 and y = 2. In this case, the answer to the target question is y = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is a prime number
We already know that the possible values of x are: y, 3y, 5y, 7y, . . . etc
So, there are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 2 and y = 2. In this case, the answer to the target question is y = 2
Case b: x = 3 and y = 3. In this case, the answer to the target question is y = 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 told us that y is EVEN
Statement 2 told us that y is a prime number
Since 2 is the ONLY even prime number, the answer to the target question is y = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Re: x and y are positive integers. When x is divided by 2y &nbs [#permalink] 28 Oct 2018, 06:25
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x and y are positive integers. When x is divided by 2y

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