Two sets, M and Q, include only consecutive multiples of 5

Question

Two sets, M and Q, include only consecutive multiples of 5 and only consecutive multiples of 10 as their members, respectively. Both sets M and Q contain more than one member each. Is the median of set Q more than the median of set M?

(1) Set M contains two times as many elements as set Q
(2) The smallest element in either set is 20

(1) Set M contains two times as many elements as set Q
(2) The smallest element in either set is 20

Zarrolou · Answer

Are you sure it's D?

M multiple of 5
Q multiple of 10

M={5,10,15,20} 
 Q={30,40}

median M < median Q

M={50,55,60,65} 
 Q={30,40}

median M > median Q

Maybe I'm missing something...

Bunuel · Answer

Edited the OA. It must be C, not D.

piyushmnit · Answer

Can someone please explain why C is correct

Bunuel · Answer

Two sets, M and Q, include only consecutive multiples of 5 and only consecutive multiples of 10 as their members, respectively. Both sets M and Q contain more than one member each. Is the median of set Q more than the median of set M?

(1) Set M contains two times as many elements as set Q
(2) The smallest element in either set is 20

(1) Set M contains two times as many elements as set Q. If M={5, 10, 15,   20  , 25, 30, 35} and Q={0,   10  , 20}, then the median of M (20) is greater than the median of Q (10) BUT if M={5, 10, 15,   20  , 25, 30, 35} and Q={20,   30  , 40}, then the median of M (20) is less than the median of Q (30). Not sufficient.

(2) The smallest element in either set is 20. If M={20, 25, 30,   35  , 40, 45, 50} and Q={20,   30  , 40}, then the median of M (35) is greater than the median of Q (30) BUT if M={20,   25  , 30} and Q={20,   30  , 40}, then the median of M (25) is less than the median of Q (30). Not sufficient.

(1)+(2) Set M contains two times as many elements as set Q AND the smallest element in either set is 20. This implies that the median of M always will be farther from 20 than the median of Q. Consider the examples:
M={20,   25, 30  , 35} and Q={  20, 30  };
M={20, 25,   30, 35  , 40, 45} and Q={20,   30  , 40};
M={20, 25, 30,   35, 40  , 45, 50, 55} and Q={20,   30, 40  , 45};
M={20, 25, 30, 35,   40, 45  , 50, 55, 60, 65} and Q={20, 30,   40  , 45, 50}.
Sufficient.

Answer: C.

piyushmnit · Answer

Thanks a lot for the reply !!!!

IanStewart · Answer

They don't affect the answer, which is presumably why no one noticed them, but there are some typos in the two examples of set Q above. Set Q is meant to increase by 10 each time.

I think it's perfectly fine to solve this question by inspection - you get a good idea of what's going on by looking at some examples. But if anyone wants a more algebraic proof that the answer is C:

Each Statement is clearly insufficient alone (Statement 1 gives no info about how big the values are in either set, and Statement 2 tells us nothing about how big each set is). Using both, we know our sets are equally spaced, so for each, the median equals the mean, and also equals the average of the largest and smallest values. But the smallest value is the same (20) in both sets. So the median of Q will be greater than the median of M if the largest value in Q is greater than the largest value in M. So that's all we need to know -- in which set is the largest element greatest?

Now say Q contains n elements. We know the smallest value in Q is 20. Proceeding from the smallest value to the largest value, we'll go up by "10" n-1 times (n-1, and not n, because we don't want to count the first element). So the largest element of Q is 20 + 10(n-1) = 10 + 10n

Similarly, M contains 2n elements, and increases by 5 each time. So the largest value in M will be 20 + 5(2n - 1) = 15 + 10n

Since 15 + 10n is clearly exactly 5 larger than 10 + 10n, the largest value in M is greater than the largest value in Q, so the median of M is greater than the median of Q, and the two Statements together are sufficient. C.

Two sets, M and Q, include only consecutive multiples of 5

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GMAT Data Sufficiency (DS) Questions

Two sets, M and Q, include only consecutive multiples of 5

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