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DivyanshuRohatgi
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of Updated on: 07 Jun 2018, 01:59
Originally posted by DivyanshuRohatgi on 07 Jun 2018, 00:59.
Last edited by DivyanshuRohatgi on 07 Jun 2018, 01:59, edited 1 time in total.
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C
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25% (medium)

Question Stats:

83% (02:53) correct 17% (02:48) wrong based on 146 sessions

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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
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C
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strangelrose
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of 07 Jun 2018, 01:54
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the mode represent the value repeated in a set if so K has to be equal to one of the other values repeated in the set so K should equal 0 which means that Z=0

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DivyanshuRohatgi
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of 07 Jun 2018, 02:00
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strangelrose
the mode represent the value repeated in a set if so K has to be equal to one of the other values repeated in the set so K should equal 0 which means that Z=0

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Can you please elaborate the solution.
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jackspire
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of 07 Jun 2018, 02:02
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DivyanshuRohatgi
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
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Common sense can solve this problem within 2 seconds.
Here, we have been asked to find out the value of K from which we will find m, which is the mode of set B.
But Mode means the highest number of frequency of an element.
From given options, only 0 is there in set B. So 0 can be the only answer.

Please correct me if my thought process is having flaw.
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of 07 Jun 2018, 02:17
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Solution



Given:
    • Set A = {3, -8, Y, 19, -6}
    • Set B = {K, -3, 0, 16, -5, 9}
    • L = median of set A
    • M = mode of set B
    • \(Z = L^M\)
    • \(Y > 21\)

To find:
    • For what value of K, Z will be a divisor of 26

Approach and Working:
As the value of Y is greater than 21, for set A
    • The elements in ascending order = { -8, -6, 3, 19, Y}
      o Median L = 3

For set B, all the elements except K appears only once
    • Hence, if K is equal to any of those values, the mode will be equal to K only
      o In that case, mode M = K = any of {-3, 0, 16, -5, 9}
    • Therefore, \(Z = L^M\) = any of {\(3^{-3}, 3^0, 3^{16}, 3^{-5}, 3^9\)}
    Or, Z = either of {\(\frac{1}{27}, 1, 3^{16}, \frac{1}{243}, 3^9\)}

As Z will be a divisor of 26, out of the possible values of Z, only possible value will be 1 (when \(Z = 3^0\))
    • In that case, K = 0

Hence, the correct answer is option C.

Answer: C
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of 07 Jun 2018, 02:57
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DivyanshuRohatgi

strangelrose
the mode represent the value repeated in a set if so K has to be equal to one of the other values repeated in the set so K should equal 0 which means that Z=0

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Can you please elaborate the solution.
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The set is (k,-3,0,16,5,9) so far we will only have a mode M if K equal to one of the other values. In the answer choices the choices that is equal to one of the values is C which means that k=0 and z=0 and 0/26=0 it is an easy questions but tricky because there is a lot of unneeded information to make you waste time
 
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Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of 10 Nov 2025, 14:44
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I used the fact that it's a divisor of 26 to get to the answer. There are no other modes based on the answer choices; only 0 would be a mode. M=0. Which means Z=1 and it's divisible by 26. Let's say the answer choice had -3 or maybe 9, I would simply plug in and recognize the number couldn't be divided by 26.
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