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 · 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?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards