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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