Two sets, A and B, have the same number of elements : GMAT Data Sufficiency (DS)
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# Two sets, A and B, have the same number of elements

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Manager
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Two sets, A and B, have the same number of elements [#permalink]

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01 May 2013, 21:55
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Two sets, A and B, have the same number of elements and the same median. Which set has the higher average?

(1) In Set A, 75% of the numbers are greater than or equal to the median. In Set B, 50% of the numbers are greater than or equal to the median.

The above question is from MGMAT flashcard of word translation section.
The question is for revision purpose and statement 2 is not given,
The above statement is insufficient to answer a question.
i dint understood an explanation given in flashcard.
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Re: Two sets, A and B, have the same number of elements [#permalink]

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02 May 2013, 00:05
The highest average translates into (beacuse they have the same number of elements): which set has the greatest sum of the elements?

Without using real numbers it's easy to see that this statement is not sufficient. Why? Because it gives us only the "upper" part of each set, but because we are asked: which has the greatest sum? the lower part can contain 0s or 1s (low numbers) that makes the statement insufficient.

Example median=50, elements=4
A{0,50,50,99} sum 199
B{48,49,51,52} sum 200

Those two sets respect the conditions above. Now just replace the 48 in B with a 0, its sum will be 152, less than A in this case.

Let me know if it's clear
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Manager
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Re: Two sets, A and B, have the same number of elements [#permalink]

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02 May 2013, 13:37
A = {1,4,4,4} and B = {2,2,6,6}
Both sets have same number of elements (n = 4) and same median (median = 4)

St1: Set A: 75% of terms >= median
Case 1: A = {1,4,4,4} and B = {2,2,6,6}
avg A (13/4) < Avg B (14/4)
Case 2: A = {1,4,4,10} and B = {2,2,6,6}
avg A (19/4) > Avg B (14/4)
Hence Insufficient

St2: Set B 50% of terms >= median
See explanation above (for St1)
Hence Insufficient

Together still Insufficient. See explanation for ST1
hence Ans E
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Re: Two sets, A and B, have the same number of elements [#permalink]

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03 May 2013, 16:06
1
KUDOS
Two sets, A and B, have the same number of elements and the same median. Which set has the higher average?

(1) In Set A, 75% of the numbers are greater than or equal to the median. In Set B, 50% of the numbers are greater than or equal to the median.

The above question is from MGMAT flashcard of word translation section.
The question is for revision purpose and statement 2 is not given,
The above statement is insufficient to answer a question.
i dint understood an explanation given in flashcard.

---
Just think about the question. What is the median ? If you arrange the number in ascending or descending order than the middle number gives the median.
Statement A says 75% of the numbers are greater than or equal too to the median. This means 3/4 of the numbers are equal to the median. Their is no way that 75% can be > the median because than that number is not the median. So this set is something like :

{4,5,5,5} -> median is 5 or {-1,2,2,10} median is 2.
Now Set B is something

Set B
2,4,6,10 -> median is 5 same as above or {0,1,3,4} - median is 2.

Now Avg in set B is greater than Avg in Set A. However Avg in Set A > Avg in set B for the 2nd case.

Hence, one cannot determine whose average is more than the other.
Re: Two sets, A and B, have the same number of elements   [#permalink] 03 May 2013, 16:06
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