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GMAT Diagnostic Test Question 18 Field: statistics Difficulty: 700

Is the mean of set S greater than its median?

(1) All members of S are consecutive multiples of 3 (2) The sum of all members of S equals 75

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
_________________

Statement 1 is sufficient. If this set contains an odd number of elements, say, 3, 6 and 9, then median of a set will equal its mean (both will equal the middle element). If set S contains an even number of elements, the median, as well as the mean of this set, will equal the mean of the two middle elements.

Statement 2 is insufficient. If we know only the sum of elements of set S, we can't be sure if the mean is greater than the median. Consider these two sets:

1. 25, 25, 25 --> mean is 25, median is 25, mean is not greater than median 2. 1, 2, 3, 4, 65 --> mean is 15, median is 3, mean is clearly greater than median
_________________

I have a little question regarding the explanation, the statement (1) says: All members of S are consecutive multiples of 3

and you say:

Quote:

Statement 1 is sufficient. If this set contains an odd number of elements [...]

and finally i ask: couldn't be possible that the set contained for example 3, 6, 9, 12? In other words, the statement doesn't say that the number of elements is odd, am I right?

You're right, it doesn't anywhere say that the number of elements is either odd or even. I was just going through the options. I've elaborated on either way in the explanation. You can see the highlighted part

dzyubam wrote:

Explanation:

Rating:

Official Answer: A

Statement 1 is sufficient. If this set contains an odd number of elements, say, 3, 6 and 9, then median of a set will equal its mean (both will equal the middle element). If set S contains an even number of elements, the median, as well as the mean of this set, will equal the mean of the two middle elements.

Statement 2 is insufficient. If we know only the sum of elements of set S, we can't be sure if the mean is greater than the median. Consider these two sets:

1. 25, 25, 25 --> mean is 25, median is 25, mean is not greater than median 2. 1, 2, 3, 4, 65 --> mean is 15, median is 3, mean is clearly greater than median

can you really say that the answer is A? I would have thought E. if Mean=Median, as it is with a set 3, 6, 9, then you can't really say Mean>median. Can you?

3, 6, 9. median = 6; mean = 6. so is mean greater than median? no

1, 3, 6, 9. Median = 9/2; mean = 19/4. so is mean greater than median? yes

insufficient.

Does the Gmat test that mean=median is similar to mean>median? Please let me know.
_________________

can you really say that the answer is A? I would have thought E. if Mean=Median, as it is with a set 3, 6, 9, then you can't really say Mean>median. Can you?

3, 6, 9. median = 6; mean = 6. so is mean greater than median? no

1, 3, 6, 9. Median = 9/2; mean = 19/4. so is mean greater than median? yes

insufficient.

Does the Gmat test that mean=median is similar to mean>median? Please let me know.

1 is not a multiple of 3. Consider {3, 6, 9, 12}. Here mean = 30/4 = 7.5 and median = 15/2=7.5 A is sufficient.

can you really say that the answer is A? I would have thought E. if Mean=Median, as it is with a set 3, 6, 9, then you can't really say Mean>median. Can you?

3, 6, 9. median = 6; mean = 6. so is mean greater than median? no

1, 3, 6, 9. Median = 9/2; mean = 19/4. so is mean greater than median? yes

insufficient.

Does the Gmat test that mean=median is similar to mean>median? Please let me know.

1 is not a multiple of 3. Consider {3, 6, 9, 12}. Here mean = 30/4 = 7.5 and median = 15/2=7.5 A is sufficient.

Oh i get it now. so it will always be mean=median. Great!! thanks for this. i appreciate it. Looks like its A.
_________________

Statement 1 is sufficient. If this set contains an odd number of elements, say, 3, 6 and 9, then median of a set will equal its mean (both will equal the middle element). If set S contains an even number of elements, the median, as well as the mean of this set, will equal the mean of the two middle elements.

Statement 2 is insufficient. If we know only the sum of elements of set S, we can't be sure if the mean is greater than the median. Consider these two sets:

1. 25, 25, 25 --> mean is 25, median is 25, mean is not greater than median 2. 1, 2, 3, 4, 65 --> mean is 15, median is 3, mean is clearly greater than median

What's the difference between your rational between statement 1 and 2?

3,6,9, yes mean = median but 25, 25, 25 is also yes i.e. mean = median but yet you say median is not greater than median.

I think the right answer is C, since 9 + 12 + 15 + 18 + 21 = 75 where mean = median, no negatives will work since the sum is +75.

By the two examples after S2 in the OE I meant to prove that S2 is not sufficient. In the first example, "3, 6, 9", the median = mean. In the second, "25, 25, 25", mean is greater than median. These examples are only related to S2. S1, on the contrary, is sufficient to answer the question. With S1 in mind we're sure that median will always equal the mean.

I hope it helps to clear the doubts .
_________________

GMAT Diagnostic Test Question 18 Field: statistics Difficulty: 750

Rating:

Is the mean of set S greater than its median?

(1) All members of S are consecutive multiples of 3 (2) The sum of all members of S equals 75

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient

I see! consecutive multiples of 3 => 3(x, x+1, x+2,...x+n) 3, 6, 9 => 3(1, 2, 3) The AP's (series of Arithmetic Progression) have mean = median.
_________________

KUDOS me if you feel my contribution has helped you.

Shouldn't the answer be C because statement A does not answer the question? I understand your explanation for statement A but isn't the purpose of data sufficiency to verify whether the information provided is sufficient to answer the question asked with a specific answer, in this case, yes or no?

Shouldn't the answer be C because statement A does not answer the question? I understand your explanation for statement A but isn't the purpose of data sufficiency to verify whether the information provided is sufficient to answer the question asked with a specific answer, in this case, yes or no?

Please help me on this

cheers

Is the mean of set S greater than its median?

(1) All members of S are consecutive multiples of 3 (2) The sum of all members of S equals 75

Stamt1: all members of S are consecutive multiples of 3 x-2, x-1, x, x+1, x+2, x+3: let x = 1 -3, 0, 3, 6, 9, 12 3(-1, 0, 1, 2, 3, 4) for this set, mean = median Hope this clear your confusion
_________________

KUDOS me if you feel my contribution has helped you.