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# If x and y are integers and x is 10 percent more than 50 percent of y,

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Math Expert
Joined: 02 Aug 2009
Posts: 7028
If x and y are integers and x is 10 percent more than 50 percent of y,  [#permalink]

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15 Sep 2018, 07:11
00:00

Difficulty:

25% (medium)

Question Stats:

85% (01:04) correct 15% (01:28) wrong based on 26 sessions

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If x and y are integers and x is 10 percent more than 50 percent of y, what cannot be the value of y?

(A) 20
(B) 50
(C) 100
(D) 120
(E) 200

New question!!!..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 18 Jun 2018
Posts: 229
Re: If x and y are integers and x is 10 percent more than 50 percent of y,  [#permalink]

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15 Sep 2018, 08:01
OA: B

According to the question stem

$$x = \frac{10}{100}*\frac{50}{100}*y+\frac{50}{100}*y$$

$$x= \frac{50}{100}[ \frac{10}{100}+1]\quad y$$

$$x= \frac{1}{2}*\frac{11}{10}y$$

$$x= \frac{11}{20}y$$

As $$x$$ is an integer, $$y$$ should be a multiple of $$20$$.

Only option B i.e $$50$$ is not a multiple of $$20$$ , hence it is the answer.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2092
Re: If x and y are integers and x is 10 percent more than 50 percent of y,  [#permalink]

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15 Sep 2018, 10:02
chetan2u wrote:
If x and y are integers and x is 10 percent more than 50 percent of y, what cannot be the value of y?
(A) 20
(B) 50
(C) 100
(D) 120
(E) 200

New question!!!..

In 30 seconds we can test the answers. For each option:
1) take 50% or $$\frac{1}{2}$$ to find $$y$$, then

2) Multiply that result by $$\frac{11}{10}$$ to find $$x$$
"Ten percent more than" = $$1.1=\frac{11}{10}$$

$$x$$ must be an integer

(A) $$20$$: $$y=(\frac{1}{2}*20)=10$$
$$x=(\frac{11}{10}*10)=11$$. Integer. REJECT

(B) 50: $$y=25$$, and
$$x=(\frac{11}{10}*25)=\frac{55}{2}=27.5$$
Not an integer. This option is the answer.

(C = 55, D = 66, E = 110)

Re: If x and y are integers and x is 10 percent more than 50 percent of y, &nbs [#permalink] 15 Sep 2018, 10:02
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