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Set S consists of five consecutive integers, and set T

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Set S consists of five consecutive integers, and set T

by BTGmoderatorDC » Fri Aug 30, 2019 5:06 pm

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Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

(1) The median of the numbers in Set S is 0
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T

OA C

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by Jay@ManhattanReview » Sun Sep 01, 2019 9:49 pm

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BTGmoderatorDC wrote:Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

(1) The median of the numbers in Set S is 0
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T

OA C

Source: GMAT Prep
Let's take each statement one by one.

(1) The median of the numbers in Set S is 0.

No information about SEt T. Insufficient.

(2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

Case 1: Ensuring that the sum of the numbers in set S is equal to the sum of the numbers in set T, let's say Set S: {-2, -1, 0, 1 , 2} and Set T: {-3, -2, -1, 0, 1 , 2, 3}. Median of Set S = Median of Set T = 0. The answer is Yes.

Case 2: Ensuring that the sum of the numbers in set S is equal to the sum of the numbers in set T, let's say Set S: {5, 6, 7, 8, 9} and Set T: {2, 3, 4, 5, 6, 7, 8}. Median of Set S = 7 and Median of Set T = 5. The answer is No.

No unique answer. Insufficient.

(1) and (2) together

In the light of Statement 1, Case 2 is not applicable, thus, only Case 1 stands; thus, Median of Set S = Median of Set T = 0. The answer is Yes. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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edited:

by deloitte247 » Thu Sep 05, 2019 6:23 am

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S = {s, (s+1), (s+2), (s+3), (s+4)}
T = {t, (t+1), (t+2), (t+3), (t+4), (t+5), (t+6)}
Question=> Is the median of the number in Set S equal to the median of the numbers in Set T?
Median of S = (s+2)
Median of T = (t+3)
So, is (s+2) = (t+3)
Statement 1: The median of Set S = 0
(s+2) = 0
s= -2.
However, we were not provided with information about the median of Set T. So, statement 1 is NOT SUFFICIENT.

Statement 2: The sum of the numbers in Set S is equal to the sum of the number in Set T.
Sum of S = s + (s+1) + (s+2) + (s+3) + (s+4) = 5s + 10
Sum of T = t + (t+1) + (t+2) + (t+3) + (t+4) + (t+5) + (t+6) = 7t + 21
5s +10 = 7t + 21
5(s + 2) = 7(t + 3)
Where (s + 2) = median of Set S
and (t + 3) = median of Set T.
But the value of s and t is unknown. So, we cannot find and compare the median of both sets.
Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together:
From statement 1, the median of Set S = 0. i.e s+2=0; where s = -2.
Using this information, we can find the median of Set T from statement 2.
From; 5(s + 2) = 7(t + 3)
5 (-2 + 2) = 7 (t + 3)
0 = 7 (t + 3)
(t + 3) = 0/7 = 0
t + 3 = 0.

Since t + 3 = 0 and s +2 =0 which thus validate that the median of Set S is equal to the median of Set T. Then both statements together are SUFFICIENT.
The correct option is option C.

Thanks.

-Deloitte
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