If x and y are both integers greater than 1, is x a multiple

Question

If x and y are both integers greater than 1, is x a multiple of y?

(1) 3y^2 + 7y = x
(2) x^2 -x is a multiple of y

Bunuel · Accepted Answer

We don't know whether  \frac{k}{x-1}  is an integer, hence we can not write  x=yn  (where n is an integer) from  x(x-1)=yk .

If x and y are integers great than 1, is x a multiple of y?

Is  x=ny , where  n=integer\geq{1} ?

(1)  3y^2+7y=x  -->  y(3y+7)=x  --> as  3y+7=integer , then  y*integer=x  -->  x  is a multiple of  y . Sufficient.

(2)  x^2-x  is a multiple of  y  -->  x^2-x=my  -->  x(x-1)=my  -->  x  can be multiple of  y  ( x=2  and  y=2 ) OR  x-1  can be multiple of  y  ( x=3  and  y=2 ) or their product can be multiple of  y  ( x=3  and  y=6 ). Not sufficient.

Answer: A.

Hope it helps.

sondenso · Answer

Hi, it is long time to see you!

1 suff. no discustion
2. x(x-1) is multiple of y. So x may or may not is multiple of y.

a. x=5, y = 2
5*6 is multiple of 2, but x=5 is not multiple of 2

b. x=6
6*7 is multiple of 2, and x=6 is multiple of 2

bkk145 · Answer

A.

Given:
x > 1
y > 1
n, x, y = integer
Asking: Is x = ny?

(1) x = y*(3y + 7)
Because y is integer, (3y + 7) must be integer; therefore, x must equal integer * y
SUFFICIENT

(2) x^2 - x = ny
Plug in numbers to satisfy above condition...
Say x=3, n=1, then y=6. In this case, x is not a multiple of y.
Say x=6, n=15, then y=2. In this case, x is a multiple of y.
The solution actually depends on what n is, and the only condition we have is n is integer. Therefore, it is INSUFFICIENT

GMAT TIGER · Answer

(1) 3y^2 + 7y = x
y (3y + 7) = x
so x must be a multiple, (3y+7) times, of y. suff...

(2) x^2 -x is a multiple of y
x^2 - x = yk where k is an integer.
x (x-1) = yk
 from this we do not know whether x - 1 or x is equal to k. so nsf....

A.

AlinderPatel · Answer

What is the reasoning behind multiplying y by another variable in Statement 2 (in this case k)?

alpha_plus_gamma · Answer

2)x^2 -x is a  multiple  of y

let K be the multiple.

then x^2-x = K . y

Hope this helps

maxracing01 · Answer

so if we have

y^2-y = X

Then we could say with certitude that X is a multiple of Y?

sjayasa · Answer

Yes. If it was given that y^2-y = x, then x is certainly a multiple of y.

y^2-y = x
y(y-1) = x
y*k = x

dauntingmcgee · Answer

So from x(x-1)=yk, can we not derive:

x=y*k/(x-1)=yk?

In which case the answer is C, not A.

dauntingmcgee · Answer

Yes, that is great. Thank you. Guess I'm a little rustier than I thought.

SonGoku · Answer

could someone please explain me the option 2 by plugging numbers. I have not understood the above solutions.
Thank you.

Izzyjolly · Answer

(2)  x^2−x  is a multiple of y

Number plugging approach:
Let  y=2 
If  x=3  -->  x^2−x  =  3^2-3 = 6  -->  x^2−x  is a multiple of y BUT x is not a multiple of y --> NO
If  x=4  -->  x^2−x  =  4^2-4 = 12  -->  x^2−x  is a multiple of y and x is a multiple of y --> YES
--> Insufficient.

Hope it's clear.

Checkmate22 · Answer

For those confused with statement #2, follow this approach:

Statement #1) = 3y^2+7y=x -> y(3y+7)=x -> (y=2;x=26;Yes) (y=3;x=48;Yes) (y=4;x=76;Yes) -> Sufficient
Statement #2) = x^2-x is a multiple of y -> x(x-1) is a multiple of y 
 -> If x=3 then x(x-1)=6 so y is a factor of 6. (y=2;No) (y=3;Yes) -> Not Sufficient

Hope that helps.

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If x and y are both integers greater than 1, is x a multiple

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If x and y are both integers greater than 1, is x a multiple

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