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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: 7688
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, 08:11
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:18) correct 17% (01:48) wrong based on 30 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!!!..

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Joined: 18 Jun 2018
Posts: 267
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, 09:01
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: 2766
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, 11:02
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)

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Re: If x and y are integers and x is 10 percent more than 50 percent of y,   [#permalink] 15 Sep 2018, 11:02
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