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Two sets, M and Q, include only consecutive multiples of 5 [#permalink]
21 Mar 2013, 09:06

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A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

62% (02:14) correct
38% (01:20) wrong based on 55 sessions

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

Re: Two sets, M and Q, include only consecutive multiples of 5 [#permalink]
21 Mar 2013, 10:17

Expert's post

guerrero25 wrote:

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

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

Re: Two sets, M and Q, include only consecutive multiples of 5 [#permalink]
08 Nov 2013, 01:11

1

This post received KUDOS

Expert's post

piyushmnit wrote:

Can someone please explain why C is correct

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. 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.

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