Question says
x,y > 1
Is x = ky where k is some integer number
1)
x = 3y^2 + 7y
= y(3y+7)
3y + 7 will always be a positive integer, hence we can say x = ky... sufficient
2)
x^2 - x = py
This doesn't give us enough information to prove x = ky. To prove this, lets assume for a minute x = ky, then the above becomes:
x(x-1) = py
ky(ky-1)=py
k(ky-1)=p
this is a very specific case, and it will only hold true for certain values of k, y and p, not for all... insufficient
Hence (A)
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GMAT Prep: 'x' and 'y' are integers
Source: Beat The GMAT — Data Sufficiency |
Given: x and y are integers greater than 1.euro wrote:If x and y are integers greater than 1, is x a multiple of y?OA is [spoiler](A)[/spoiler]
- (1) 3*y^2 + 7*y = x
(2) x^2 - x is a multiple of y.
Statement 1: 3*y^2 + 7*y = x => y*(3y + 7) = x
As y is an integer, (3y + 7) is also an integer. Therefore, x is an integer multiple of y.
Sufficient.
Statement 2: x^2 - x is a multiple of y.
We can assume, x^2 - x = k*y, where k is an integer.
As, x^2 - x = k*y
=> x*(x-1) = k*y
Thus either x or (x-1) is a multiple of y as both of them simultaneously cannot be multiple of y. (Two consecutive integers are always coprime)
Not sufficient.
The correct answer is A.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
