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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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chetan2u
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If x and y are integers and x is 10 percent more than 50 percent of y, [#permalink] New post   15 Sep 2018, 08:11
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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
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B
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Re: If x and y are integers and x is 10 percent more than 50 percent of y, [#permalink] New post   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.
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Re: If x and y are integers and x is 10 percent more than 50 percent of y, [#permalink] New post   15 Sep 2018, 11:02
Expert Reply
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)

Answer B
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Re: If x and y are integers and x is 10 percent more than 50 percent of y, [#permalink] New post   16 Apr 2021, 22:03
Quote:
If x and y are integers and x is 10 percent more than 50 percent of y, what cannot be the value of y?


Adding to the first two methods given in the earlier answers, here is another approach.

x and y are integers.

If 10% of a number, say n, is an integer, then 'n' has to be a multiple of 10.
Because x is 10% more half of y, half of y has to be a multiple of 10. Else, x cannot be a multiple of 10.

From answer choices, half of 50 is the only number that is not a multiple of 10. Hence, 50 is the only value that y cannot take.
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Re: If x and y are integers and x is 10 percent more than 50 percent of y, [#permalink] New post   19 Apr 2024, 07:13
Hello from the GMAT Club BumpBot!

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Re: If x and y are integers and x is 10 percent more than 50 percent of y, [#permalink]
19 Apr 2024, 07:13
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