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24 Mar 2017, 19:14
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (02:08) correct
50%
(02:03)
wrong
based on 201
sessions
History
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Not Attempted Yet
If x and y are positive integers, is x a multiple of y?
(1) 2x is a multiple of y.
(2) 2(y^2) + y = 2x
(1) 2x is a multiple of y.
(2) 2(y^2) + y = 2x
25 Mar 2017, 03:04
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If x and y are positive integers, is x a multiple of y?
Is \(\frac{x}{y}=integer\)?
(1) 2x is a multiple of y --> \(\frac{2x}{y}=integer\) --> \(\frac{x}{y}=\frac{integer}{2}\). If that integer is even then the answer will be YES but if that integer is odd then the answer will be NO (for example, consider x=2 and y=2 AND x=1 and y=2). Not sufficient.
(2) 2(y^2) + y = 2x --> divide by 2y: \(y + \frac{1}{2} = \frac{x}{y}\). Thus \(\frac{x}{y}=y+ \frac{1}{2}=integer+noninteger=noninteger\). Sufficient.
Answer: B.
Is \(\frac{x}{y}=integer\)?
(1) 2x is a multiple of y --> \(\frac{2x}{y}=integer\) --> \(\frac{x}{y}=\frac{integer}{2}\). If that integer is even then the answer will be YES but if that integer is odd then the answer will be NO (for example, consider x=2 and y=2 AND x=1 and y=2). Not sufficient.
(2) 2(y^2) + y = 2x --> divide by 2y: \(y + \frac{1}{2} = \frac{x}{y}\). Thus \(\frac{x}{y}=y+ \frac{1}{2}=integer+noninteger=noninteger\). Sufficient.
Answer: B.
General Discussion
24 Mar 2017, 19:58
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Omar7235
Answer must be B
(1) if x= 4 && y=2 then YES
if x=3 && y=2 then NO
(2) y(2y+1)=2x
two options
(a) if y =odd
then 2y+1 is odd
then odd*odd never equals 2*odd
(2)y=even
then 2y+1 =odd
even*odd=even....satisfying
lets opt some values
if y=2 ,the least value ,then
2(y)*5(2y+1)= 2*5(x)...So we have x=5,y=2
for every y to be even , x must be odd
it is not a multiple..
suff
Ans B
