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The range of set X is 9 and the range of set Y is 18. Which

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by Max@Math Revolution » Wed Nov 14, 2018 12:22 am
[Math Revolution GMAT math practice question]

The range of set X is 9 and the range of set Y is 18. Which of the following cannot be the range of the union of sets X and Y?

A. 9
B. 18
C. 27
D. 36
E. 45
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The range of set X is 9 and the range of set Y is 18. Which

by fskilnik@GMATH » Wed Nov 14, 2018 3:27 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

The range of set X is 9 and the range of set Y is 18. Which of the following cannot be the range of the union of sets X and Y?

A. 9
B. 18
C. 27
D. 36
E. 45
\[?\,\,\,\,:\,\,\,\,{\text{impossible}}\,\,{\text{range}}\left( {X \cup Y} \right)\]
The range of Y guarantees that there are two elements in Y that differ by exactly 18 units.

Those elements are also in the union of X and Y, therefore the range of XUY is at least 18.

The correct answer is therefore (A).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by swerve » Wed Nov 14, 2018 8:17 am
The minimum range will be the maximum of the range of the two sets.

The maximum range is 18 of the sets so the minimum range of two sets is 18.

Now, notice the options all are greater than equal to 18 except option A, hence this is the correct answer.
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by Max@Math Revolution » Fri Nov 16, 2018 2:06 am
=>

The range of a union is greater than or equal to the maximum of the ranges of the two sets. Thus, the range of the union of X and Y is greater than or equal to 18.

Therefore, the answer is A.
Answer: A
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