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What is the value of x + y?

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What is the value of x + y?

by Max@Math Revolution » Thu Aug 06, 2020 2:35 am

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[GMAT math practice question]

What is the value of x + y?

1) x and y are positive integers.
2) 1/x+1/y=1/5.
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Source: — Data Sufficiency |
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Re: What is the value of x + y?

by deloitte247 » Sat Aug 08, 2020 3:13 am

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Statement 1 => x and y are positive integers
The value of x and y is not definite and it could be any value between 0 and infinity. Since this statement does not provide information that could give a definite answer to the target question, statement 1 is NOT SUFFICIENT

$$Statement\ 2=>\frac{1}{x}+\frac{1}{y}=\frac{1}{5}$$
$$\frac{y+x}{xy}=\frac{1}{5}$$
$$\frac{5\left(x+y\right)}{5}=\frac{xy}{5}$$
$$x+y=\frac{xy}{5}$$
The definite value of xy remains unknown. Statement 2 is NOIT SUFFICIENT

Combining both statements together =>
The only information gotten from the statement is that x and y are positive integers, definitely, x + y will be a positive integer
and from statement 2; x + y = xy/5


The only conclusion here is that xy/5 is a positive integer. This does not answer the target question with a definite value so both statements together ARE NOT SUFFICIENT

Answer = E
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