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In a certain class of 5 students, the average (arithmetic mean) weight

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In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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GMAT Club's Fresh Challenge Problem.



In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.
[Reveal] Spoiler: OA

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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 21 Jan 2018, 23:43
Bunuel wrote:

GMAT Club's Fresh Challenge Problem.



In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.



Answer should be E as none of the statements even if combined together is sufficient to answer the question.
[Given] : 5 students, average weight of any 2 students is less than 70 kg.
[Required] : Weight of all students

1. One of the students weight exceeds 70 kg. But we do not know if only one student exceeds 70 kg weight . Hence weight of other students cannot be derived . The only inference is, one student weights 70+ kg so one other student must weight less than 70 kg.
2. The median weight of all 5 students is 68 kg. So maybe all students weight 68 kg or maybe the sequence is 66, 67, 68, 69 ,70 or maybe the sequence is 66.5 67, 68, 69, 70.5 or maybe the sequence is 66 66 68 70 70 or maybe 65 65 68 71 71 .. many sequences are possible. So we do not get any definite answe.

Even if we combine the two statements, we do not achieve any concrete conclusion on how many students exceed 70 kg weight.

Hence, option E should be correct.
Please correct me if I am wrong :)
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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 22 Jan 2018, 05:22
Imo Answer will be :E

Correct mei id im woring

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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 22 Jan 2018, 05:31
Answer is C, I think.

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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 23 Jan 2018, 05:17
Bunuel wrote:

GMAT Club's Fresh Challenge Problem.



In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.




Only two cases:

1. None of the students is over 70. In that case the average of ANY two students would be assured to be below 70.
2. ONLY ONE of the students is over 70. For example, the average of 71 and 35 is clearly below 70, BUT the average of 71 and 71 is 71 what is not allowed.



S1.


Case 2. Only 1.


SUFF.



S2.

Two students on the right of 68 can be equal to 68 or greater. It can be either case.


INSUFF.




AC: A



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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 23 Jan 2018, 05:27
Statement 1 is sufficient.
Even if one of the student is more than 70, all the other students must weight lesser than 70. (as the average weight of any two students is 70)
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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 23 Jan 2018, 06:59
Question says mean of any 2 students less than 70. So sum of weights of any 2 students is less than 70. Statement 1 says 1 student is 70 and more. So if we compare other students with this student their weight should be less than 70. So sufficient. Statement 2 says median is 68. So if arrange is ascending order there will be 2 students before and 2 students after 68. Of 2 students who has weight beyond 68 both of them cannot be greater than 70. But we cannot say that either is one is more than 70 or both is between 68 and 70. So not sufficient. So answer is A

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Re: In a certain class of 5 students, the average (arithmetic mean) weight [#permalink]

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New post 23 Jan 2018, 07:30
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Bunuel wrote:

GMAT Club's Fresh Challenge Problem.



In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.


Half the problem is solved by the main statement..

Quote:
the average (arithmetic mean) weight of any two students in the group is less than 70 kg

If there are two numbers equal to or above 70, their average will surely be MORE than or equal to 70..
so MAX number above 70 can be ONLY one ..
second possibility is NONE ..


Our statement should be able to give us some info to eliminate any one of the two..

lets see the statements..
(1) One of the students weighs more than 70 kg.
so it gives us ONE as answer
suff
(2) The median weight of all 5 students is 68 kg.
nothing much..
all 68 ... ans 0
66,66,68,70,70.... ans 2
insuff

A
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Re: In a certain class of 5 students, the average (arithmetic mean) weight   [#permalink] 23 Jan 2018, 07:30
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