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

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Manager
Joined: 11 Feb 2011
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Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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23 Mar 2011, 22:39
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Question Stats:

82% (02:25) correct 18% (02:16) wrong based on 94 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 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
[Reveal] Spoiler: OA

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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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23 Mar 2011, 22:51
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AnkitK wrote:
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

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"
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Kudos [?]: 198 [0], given: 21

Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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23 Mar 2011, 23:10
Excellent kudos to you fluke!
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Kudos [?]: 359 [0], given: 123

Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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23 Mar 2011, 23:27
Yeah Z is odd and 26 is even. It has to be zeroth power

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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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24 Mar 2011, 06:31
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.

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Manager
Joined: 09 Jan 2010
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Kudos [?]: 34 [0], given: 12

Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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24 Mar 2011, 09:30
guys will u please tell me how long does it take u to solve questions like this....
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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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24 Mar 2011, 10:32
shalu wrote:
guys will u please tell me how long does it take u to solve questions like this....

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.
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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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26 Mar 2011, 19:30
1
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this question is weird although i can guess the answer C.
because only C fits to find mode M
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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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03 Mar 2015, 09:45
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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in [#permalink]

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03 Mar 2015, 09:52
AnkitK wrote:
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: set-a-126761.html
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Re: Set A consists of integers {3, -8, Y, 19, -6} and set B consists of in   [#permalink] 03 Mar 2015, 09:52
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