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If the range of set A is 5 and the range of set B is 11, whi

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by Max@Math Revolution » Sun Aug 05, 2018 11:26 pm

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[Math Revolution GMAT math practice question]

If the range of set A is 5 and the range of set B is 11, which of the following CANNOT be the range of sets A and B combined?

A. 10
B. 11
C. 12
D. 13
E. 14
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by Max@Math Revolution » Wed Aug 08, 2018 1:00 am
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For example, if A = {0,5} and B = { 0, 11 }, then the set A is included in the set B and the smallest possible range of the sets A and B combined is 11, which is the range of the set B.
Thus, any number less than 11 cannot be the range of sets A and B, combined.

Therefore, A is the answer.
Answer: A
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by deloitte247 » Wed Aug 08, 2018 10:19 am
Range of Set A = 5
Range of Set B = 11
Rang of Set A and B combined = the union of A and B = A U B,
Bearing in mind that Range is the difference between the highest and the least element.
The range of A U B is always greater than or equal to the Range of set with the greater range ( which is set B.)

Therefore, Range of Set A U B >/= Range of Set B.
Range of Set A U B >/= 11

Finally, Option A is the final answer because 10 is less than 11.
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