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# If the average of four distinct positive integers is 60, how

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If the average of four distinct positive integers is 60, how [#permalink]  02 Jan 2010, 08:13
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If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.
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Re: Q#28 of GMATclub test # 8 [#permalink]  02 Jan 2010, 09:26
Expert's post
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

Note: we have four distinct positive integers and x1+x2+x3+x4=240.

(1) x1+x2+x3+200=240 --> x1+x2+x3=40, hence three integers are less than 50. Sufficient.

(2) Median of this set would be the average of middle numbers: x2+x3=100 --> x2<50 (as integers are distinct). x1<x2, hence we have two integers less than 50. Sufficient.

In your example {20,50,70,100} median is (50+70)/2=60 and not 50.

BUT there is another problem with this question: from (1) we got that there are 3 integers less than 50 and from (2) we got that there are 2 integers less than 50. In DS statements never contradict so either of the statement should be changed.
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Re: Q#28 of GMATclub test # 8 [#permalink]  02 Jan 2010, 09:32
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

SETS CHOSEN DOESN'T SATISFY s2) CONDITION

if we select a set as per 2 then its 2nd and 3rd element must be equidistant from 50 and therfore we have exactly two no's less than 50
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Re: Q#28 of GMATclub test # 8 [#permalink]  02 Jan 2010, 09:54
Sorry, I was not thinking in the right direction

Bunuel wrote:
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

Note: we have four distinct positive integers and x1+x2+x3+x4=240.

(1) x1+x2+x3+200=240 --> x1+x2+x3=40, hence three integers are less than 50. Sufficient.

(2) Median of this set would be the average of middle numbers: x2+x3=100 --> x2<50 (as integers are distinct). x1<x2, hence we have two integers less than 50. Sufficient.

In your example {20,50,70,100} median is (50+70)/2=60 and not 50.

BUT there is another problem with this question: from (1) we got that there are 3 integers less than 50 and from (2) we got that there are 2 integers less than 50. In DS statements never contradict so either of the statement should be changed.
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Re: If the average of four distinct positive integers is 60, how [#permalink]  29 Nov 2014, 08:52
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Re: If the average of four distinct positive integers is 60, how   [#permalink] 29 Nov 2014, 08:52
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