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10 Dec 2016, 06:29
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A
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Difficulty:
25%
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Question Stats:
76% (01:25) correct
24%
(01:52)
wrong
based on 117
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Let x, y, and z be positive integers such that y is a multiple of x. Is y + z a multiple of x?
(1) z is a multiple of y.
(2) x is a prime.
(1) z is a multiple of y.
(2) x is a prime.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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10 Dec 2016, 08:52
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Here is my solution to this one.
Given that y is a multiple of x=> y=kx
We need to check if y+z is a multiple of x.
Since y is already a multiple of x => y+z will be a multiple of x only if z is a multiple of x.
Else it wont be.
RULE -> Multiple +Multiple = Multiple
Multiple +Non Multiple = Non Multiple
Statement 1-->
Z=yk'=> xk*k'
Hence z is a multiple of x
Hence y+z will be multiple of x
Hence sufficient
Statement 2-->
No clue of z
Hence not sufficient
Hence A
Given that y is a multiple of x=> y=kx
We need to check if y+z is a multiple of x.
Since y is already a multiple of x => y+z will be a multiple of x only if z is a multiple of x.
Else it wont be.
RULE -> Multiple +Multiple = Multiple
Multiple +Non Multiple = Non Multiple
Statement 1-->
Z=yk'=> xk*k'
Hence z is a multiple of x
Hence y+z will be multiple of x
Hence sufficient
Statement 2-->
No clue of z
Hence not sufficient
Hence A
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10 Apr 2019, 23:31
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As per statement 1:\(z=yb\)
that implies \(y+yb=xm\)
that implies \(y(1+b)=xm\),
hence \(y+z=xm\).
that implies \(y+yb=xm\)
that implies \(y(1+b)=xm\),
hence \(y+z=xm\).
