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Set A consists of integers {3, -8, Y, 19, -6} and Set B cons

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by Anaira Mitch » Sun Dec 11, 2016 4:43 pm
Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of integers {K, -3, 0, 16, -5, 9}. Number L represents the median of Set A, number M represents the mode of set B, and number Z = L^M. If Y is an integer greater than 21, for what value of K will Z be a divisor of 26?
(A) -2 (B) -1 (C) 0 (D) 1 (E) 2

Please help with above problem not able to understand the second part.
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by [email protected] » Sun Dec 11, 2016 6:39 pm
Hi Anaira Mitch,

This question is loaded with lots of little facts, so you have to be careful to take the proper notes and organize your work. Here's what we know about Set A and Set B..

Set A = {-8, -6, 3, 19 and Y} and we're later told that Y is an integer greater than 21.

Set B = {-5, -3, 0, 9, 16 and K} but we only know that K is an integer (it could be positive, negative or 0).

Then we're given additional information about 3 other variables..

L = the MEDIAN of Set A, so L = 3.
M = the MODE of Set B, so M = one of the values listed (-5 -3, 0, 9 or 16).
Z = L^M = 3^M

From the answer choices, we know that K is one of the 5 integers from -2 to +2, inclusive. Since we know that the value of M will be based on the value of K, we also know that M can be just one of the 5 following numbers: (-5 -3, 0, 9 or 16). There's only one value that 'overlaps': 0.

IF... K=0, then M=0 and Z = 3^0 = 1. The number 1 IS a divisor of 26, so we have the answer...

Final Answer: C

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