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Math Expert V
Joined: 02 Sep 2009
Posts: 58428

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Difficulty:   55% (hard)

Question Stats: 53% (00:52) correct 47% (01:19) wrong based on 116 sessions

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Set $$S$$ consists of consecutive multiples of 3 and set $$T$$ consists of consecutive multiples of 6. Is the median of set $$S$$ larger than the median of set $$T$$?

(1) The least element in both sets is 6.

(2) Set $$T$$ contains twice as many elements as set $$S$$.

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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

(1) The least element in both sets is 6. If $$S=\{6\}$$ and $$T=\{6\}$$ then the answer is NO but if $$S=\{6, 9\}$$ and $$T=\{6\}$$ then the answer is YES. Not sufficient.

(2) Set T contains twice as many elements as set $$S$$. If $$S=\{6\}$$ and $$T=\{6, 12\}$$ then the answer is NO but if $$S=\{6\}$$ and $$T=\{0, 6\}$$ then the answer is YES. Not sufficient.

(1)+(2) Since $$T$$ contains twice as many elements as set $$S$$ and the least element in both sets is 6 then the median of $$T$$ will always be more than the median of $$S$$, so the answer to the question is NO. For example we can have that $$S=\{6\}$$ and $$T=\{6, 12\}$$ or $$S=\{6, 9\}$$ and $$T=\{6, 12, 18, 24\}$$ or $$S=\{6, 9, 12\}$$ and $$T=\{6, 12, 18, 24, 30, 36\}$$ ... As you can see in each case the median of $$T$$ is more than the median of $$S$$. Sufficient.

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Can we consider only one element in a set and evaluate further if it is specifically mentioned in the question that the set has consecutive multiples/numbers.???? Because for the question to be justified there should be at least two elements in the set.
Manager  S
Joined: 17 Aug 2015
Posts: 100
GMAT 1: 650 Q49 V29 Show Tags

i think answer should be E, negative numbers are also the multiple, example -9 is multiple of 3

set T contains 13 elements all negatives

example ( -13*3, -12*3, -11*3 ........-1*3 ) so median is -7*3= -21

set S contains 06 elements- all positive integers, multiple of 3

example (3*1, 3*2, .......3*6) so median will be 10.5 so now median of S greater than median of T

if we take T set starting from 21 ( 21, 24,27,30..........57) set T will have much higher MEDIAN than S
Math Expert V
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vijaisingh2001 wrote:
i think answer should be E, negative numbers are also the multiple, example -9 is multiple of 3

set T contains 13 elements all negatives

example ( -13*3, -12*3, -11*3 ........-1*3 ) so median is -7*3= -21

set S contains 06 elements- all positive integers, multiple of 3

example (3*1, 3*2, .......3*6) so median will be 10.5 so now median of S greater than median of T

if we take T set starting from 21 ( 21, 24,27,30..........57) set T will have much higher MEDIAN than S

Notice that (1) says that the smallest element in either set is 6. So, when considering statements together we cannot take negative values.
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Manager  S
Joined: 17 Aug 2015
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GMAT 1: 650 Q49 V29 Show Tags

language is playing trick here,

if sentence 1 is as mentioned at below, E will be the right answer, one S makes the the difference

(1) The least elementS in either set is 6.

whenever we read least, it is always the numbers of elements in the set

smallest would have been more appropriate THAN LEAST,
looks like this is a question of sentence correction more than the question of DS
Retired Moderator P
Joined: 04 Aug 2016
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Bunuel wrote:
Set $$S$$ consists of consecutive multiples of 3 and set $$T$$ consists of consecutive multiples of 6. Is the median of set $$S$$ larger than the median of set $$T$$?

(1) The least element in either set is 6.

(2) Set $$T$$ contains twice as many elements as set $$S$$.

Shouldn't we use 'both' instead of 'either' in statement in (1). Either gives an impression that least element in either of the set is 6. Or am i over thinking this? Math Expert V
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warriorguy wrote:
Bunuel wrote:
Set $$S$$ consists of consecutive multiples of 3 and set $$T$$ consists of consecutive multiples of 6. Is the median of set $$S$$ larger than the median of set $$T$$?

(1) The least element in either set is 6.

(2) Set $$T$$ contains twice as many elements as set $$S$$.

Shouldn't we use 'both' instead of 'either' in statement in (1). Either gives an impression that least element in either of the set is 6. Or am i over thinking this? Edited as suggested. Thank you. Hope all is fine now.
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Math Expert V
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Bunuel wrote:
warriorguy wrote:
Bunuel wrote:
Set $$S$$ consists of consecutive multiples of 3 and set $$T$$ consists of consecutive multiples of 6. Is the median of set $$S$$ larger than the median of set $$T$$?

(1) The least element in either set is 6.

(2) Set $$T$$ contains twice as many elements as set $$S$$.

Shouldn't we use 'both' instead of 'either' in statement in (1). Either gives an impression that least element in either of the set is 6. Or am i over thinking this? Edited as suggested. Thank you. Hope all is fine now.

FYI. The way it was written was also correct. Here is an official guide question with the same usage of "either of the two": https://gmatclub.com/forum/if-r-and-t-a ... 43303.html
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Bunuel wrote:

FYI. The way it was written was also correct. Here is an official guide question with the same usage of "either of the two": https://gmatclub.com/forum/if-r-and-t-a ... 43303.html

Thank you Bunuel. I had a look at the question.

I feel the way it is worded makes it unambiguous (at least to my eyes) since it uses keyword "two" --> Phrase: The tens digit of r is less than either of the other two digits of r.

Not that I wanted to contest the wording of this question, just wanted to clarify my doubt in case I encounter similar wording in future.
Math Expert V
Joined: 02 Sep 2009
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warriorguy wrote:
Bunuel wrote:

FYI. The way it was written was also correct. Here is an official guide question with the same usage of "either of the two": https://gmatclub.com/forum/if-r-and-t-a ... 43303.html

Thank you Bunuel. I had a look at the question.

I feel the way it is worded makes it unambiguous (at least to my eyes) since it uses keyword "two" --> Phrase: The tens digit of r is less than either of the other two digits of r.

Not that I wanted to contest the wording of this question, just wanted to clarify my doubt in case I encounter similar wording in future.

Understood. Anyway, now the wording is clear as it is. Thank you fro the suggestion.
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