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

Question

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 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

A. -2
B. -1
C. 0
D. 1
E. 2

fluke · Answer

Set A = {-8,-6,3,19} and Y
Set B = {-5,-3,0,9,16} and K

Now; Y>21. Let's consider Y=22.

This will make the median of Set A as 3.
Median = (n+1)/2 if n=number of terms in the set and n=odd
Here n=5. Median will be 6/2=3rd term of the set A arranged in ascending order.

Set A = {-8,-6,3,19,22}. Median = L = 3

Z=L^M 
 Z=3^M

We need to know what should M be for making Z a divisor of 26.

Since 26 contains only 2 and 13 as prime factors. The only option left for M is 0.
 Z=3^M=3^0=1 
Z=1 and is a factor of 26.

To make M=0; we need to have maximum number of 0's in the set B.
Since all of the elements are different in Set B. If we make K=0, we will have 2 0's and 0 will be the mode of the set.

Mode of Set B = {-5,-3,0,9,16,0} = 0

Ans: "C"

AnkitK · Answer

Excellent kudos to you fluke!

gmat1220 · Answer

Yeah Z is odd and 26 is even. It has to be zeroth power

Posted from my mobile device

subhashghosh · Answer

A = {3,-8,Y,19,-6}

B = {k,-3,0,16,-5,9}

Y > 21

So L = Median of A = 3

M = Mode of Set B

Z = (3)^M

If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor

=> M = 0

Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.

Answer - C

shalu · Answer

guys will u please tell me how long does it take u to solve questions like this....

fluke · Answer

There are few difficult ones in statistics, which may take well over 2 minutes. This particular one should not be more than 1min 20secs. The explanation may look convoluted and tedious. If you know about the basic concepts of mean, mode, median, range, std deviation and jot down only what's needed for the solution, omitting the aesthetics, you could even do it within a minute. Then again, I'd rather spend 20 seconds extra and solve a question correctly. Integrity holds the priority, however one must not be ignorant of the clock.

diebeatsthegmat · Answer

this question is weird although i can guess the answer C. 
because only C fits to find mode M

Bunuel · Answer

OPEN DISCUSSION OF THIS QUESTION IS HERE: set-a-126761.html

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

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