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Minimum possible range of 2 combined sets

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by gmattesttaker2 » Mon Mar 31, 2014 9:20 pm
Hello,

Can you please tell me how to solve this:

If set A has range 35 and set B has range 42, which of the following is the
minimum possible range if sets A and B are combined?

(A) 45
(B) 42
(C) 38
(D) 35
(E) 32

OA: B

Thanks for your help.

Best Regards,
Sri
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by Brent@GMATPrepNow » Mon Mar 31, 2014 9:58 pm
gmattesttaker2 wrote:If set A has range 35 and set B has range 42, which of the following is the
minimum possible range if sets A and B are combined?

(A) 45
(B) 42
(C) 38
(D) 35
(E) 32
The range of a set of values = (biggest value) - (smallest value)

If set B has a range of 42, then the (biggest value) - (smallest value) = 42
If we take the values from set A and add them to set B, the range CANNOT get smaller.
For example, if set B = {1, 43}, what additional values could we add to this set to make the range less than 42? There are no such values, since we'd still have values 1 and 43, which would mean that the new range would be AT LEAST 42.
Since the range of sets A and B combined CANNOT be less than 42, we can ELIMINATE C, D and E

Can the range of sets A and B combined EQUAL 42?
Sure, if B = {1, 43} and set A = {2, 37}, the combined set is {1, 2, 37, 43} in which case the range = 42

Since we're looking for the MINIMUM possible range of sets A and B combined, the correct answer must be D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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