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DS MEDIAN

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by [email protected] » Wed Sep 07, 2011 1:37 pm
Q: SET A CONSIST OF FIVE CONSECUTIVE INTEGERS AND SET B CONSIST OF 7 CONSECUTIVE INTEGERS
IS THE MEDIAN OF SET A EQUAL TO THE MEDIAN OF SET B?

A: THE MEDIAN OF THE SET A IS = 0
B: THE SUM OF THE INTEGERS OF SET A IS EQUAL TO THE SUM OF INTEGERS IN SET B.
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Source: — Data Sufficiency |
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by cans » Wed Sep 07, 2011 8:55 pm
a) insufficient. no information about set b median.
b) sum set A = sum set B.
A = a-2,a-1,a,a+1,a+2 and B = b-3,b-2,b-1,b,b+1,b+2,b+3
5a = 7b. medians are a and b. insufficient. (a=b=0 can be possible)
a&b) a=0 and thus b=0
Sufficient
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by [email protected] » Thu Sep 08, 2011 1:58 pm
cans wrote:a) insufficient. no information about set b median.
b) sum set A = sum set B.
A = a-2,a-1,a,a+1,a+2 and B = b-3,b-2,b-1,b,b+1,b+2,b+3
5a = 7b. medians are a and b. insufficient. (a=b=0 can be possible)
a&b) a=0 and thus b=0
Sufficient
Ms. CAN, I LIKE YOUR EXPLANATION. I DON'T THINK THAT STATEMENT B IS SUFFICIENT.
CONSIDER THIS EXAMPLE:
SET A: 5,6,7,8,9 THEIR SUM IS 35
SET B: 2,3,4,5,6,7,8. THEIR SUM IS ALSO 35

BUT THE MEDIAN IS DIFFERENT IN THIS CASE
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by Whitney Garner » Thu Sep 08, 2011 9:50 pm
[email protected] wrote:
cans wrote:a) insufficient. no information about set b median.
b) sum set A = sum set B.
A = a-2,a-1,a,a+1,a+2 and B = b-3,b-2,b-1,b,b+1,b+2,b+3
5a = 7b. medians are a and b. insufficient. (a=b=0 can be possible)
a&b) a=0 and thus b=0
Sufficient
Ms. CAN, I LIKE YOUR EXPLANATION. I DON'T THINK THAT STATEMENT B IS SUFFICIENT.
CONSIDER THIS EXAMPLE:
SET A: 5,6,7,8,9 THEIR SUM IS 35
SET B: 2,3,4,5,6,7,8. THEIR SUM IS ALSO 35

BUT THE MEDIAN IS DIFFERENT IN THIS CASE
You're exactly right [email protected] that statement (2) is also NOT sufficient! Let's look at it this way. When we have a consecutive set of integers, the mean=median. And for ANY set of numbers, the mean can be calculated by taking the sum of the numbers and dividing by the number of numbers.

So the mean = median for Set A:
(sum of set A)/5

And the mean = median for Set B:
(sum of set B)/7

So what we want to know: Does (sum of set A)/5 = (sum of set B)/7??

Statement (1):
If the median of set A is 0, then the new question becomes:

0 = (sum Set B)/7 ??
or
0 = (sum Set B) ??

We don't know so Not Sufficient

Statement (2):
If (sum Set A) = (sum Set B), let's call those sums the variable X. Therefore, we want to know if

X/5 = X/7 ??
7X = 5X ??
2X = 0 ??
X = 0 ??

But we don't know if the sum of Set A or Set B is equal to 0 from statement 2 alone, so Not Sufficient!

Statement (1+2) Together:
From 1 we know that the median (and therefore mean) is =0, and for a median to =0, the sum must =0. From 2 we know that A and B have the same sum so X = 0. Sufficient!

The correct answer is C.

Hope this Helps!
Whit
Whitney Garner
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