The average weight of people in a group is 150 pounds.

Question

The average weight of people in a group is 150 pounds. If no two people weigh the same, does a person in the group weigh 150 pounds?

(1) If the weights in pounds of all people in the group are arranged in increasing order, the difference between any two consecutive terms is 10.
(2) There are 8 people in the group.

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annantporwal · Answer

1) From the first statement, we can infer that it is an AP (arithmetic progression) in an AP, median= avg. If there is an odd number of people, then we may have someone who weighs 150; if there are an even number of people, then we can be sure that none weighs 150, since the median would be the average of the 2 middle terms. So 150 is between them. No one weighs 150. Not Sufficient

2) This does not help. We can have someone weigh 150, and we cannot. Not Sufficient

Combine

We know it's an AP with even terms. Now it is certain that no one weighs 150.

Sufficient

Ans- C

2) This does not help. We can have someone weigh 150, and we cannot.  Not Sufficient

Combine

We know it's an AP with even terms. Now it is certain that no one weighs 150.

Sufficient

Ans- C

Dereno · Answer

The average weight of the group of people is 150.

So, the total value = 150*n

Is there at least a person with a value of 150 ? And we can have two possible answer either Yes or No. in both case, the answer is sufficient.

Statement 1:

If the weights in pounds of all people in the group are arranged in increasing order, the difference between any two consecutive terms is 10.

Without knowing the number of terms, we cannot say anything conclusive.

When the number of terms is odd, in an arithmetic progression. The terms are a-10, a, a+10.

So, the sum = 3a = 150*3. Thus, a =150. (Sufficient).

But, when the number of terms is even, say for example 4.

a-10, a, a+10, a+20

4a+20 = 150*4

solving we get, a =145. (Insufficient, as an increase and decrease of 10, doesn’t lead to 150).

Hence,  Insufficient .

Statement 2:

There are 8 people in the group.

The total sum can be 150*8.

And the individual values can be split and arranged in any manner as possible.

so,  Insufficient.

Combining both, we get  an even number of element,

so, we can conclusively say that there is not even a single element with the value 150.

Hence,  Sufficient

Option C

ExpertsGlobal5 · Answer

Explanation Video:

https://www.youtube.com/watch?v=X2hGby66QoU

The average weight of people in a group is 150 pounds.

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GMAT Data Sufficiency (DS) Questions

The average weight of people in a group is 150 pounds.

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