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

Question

If x and y are integers great than 1, is x a multiple of y? (1) 3y^2+7y=x (2) x^2-x is a multiple of y Prep1.jpg

Bunuel · Accepted Answer

Question: is  x=ny ?

(1)  3y^2+7y=x  -->  y(3y+7)=x  --> as  3y+7  is an integer, so  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.

pradeepskunwar · Answer

I also fell for D. But thanks to Bunel's explanation, i spotted the detail.

GMATinsight · Answer

Please find the solution as mentioned in attachment

BrentGMATPrepNow · Answer

Target question :    Is x a multiple of y?  
Asking whether x is a multiple of y is the same as asking whether x = (y) (some integer) 
For example, 12 is a multiple of 3 because 12 = (3) (4) 
So, let's rephrase the question as...
  REPHRASED target question :    Does x = (y)(some integer)?

Statement 1 : 3y² + 7y = x   
Factor to get x = y( 3y + 7 )
If y is an integer, then (3y + 7) must be an integer
In other words:  x = y(some integer )
Since we can answer the  REPHRASED target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : x² - x is a multiple of y 
There are several values of x and y that satisfy this condition. Here are two: 
Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case,  x IS a multiple of y  
Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case,  x is NOT a multiple of y  
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

ypetrunina · Answer

If 20 is a multiple of 2 then how X is not a multiple of Y?

BrentGMATPrepNow · Answer

When x = 5 and y = 2, we see that x² - x = 20, and 20 is a multiple of 2
In other words, x² - x is a multiple of 2 
However, the target question asks b] Is x a multiple of y?  (not  Is x² - x a multiple of y? )

If x = 5 and y = 2, then  x is NOT a multiple of y

Cheers, 
Brent

petsitter · Answer

Would this be a valid way of looking at it?

Target Question: is x = y*I (where I is an integer)

Statement I: same as all of your solutions above - SUFF.

Statement II :

x^2 - x = y*I (where I is some integer)
x (x - 1) = y*I
x = (y*I)/(x-1)
 x = y* (I/(x-1))

Now, we know (x-1) is definitely an integer and so is I, but we have no idea whether the ratio of I and (x-1) is ALSO an integer. Thus, statement II is INSUFF.

Thoughts?

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

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GMAT Data Sufficiency (DS) Questions

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

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