The average weight of people in a group is 150 pounds. If no two peop

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.

Allwin47 · Answer

(1) NS 
ex:140, 150, 160 and 
130, 140, 160, 170

(2)NS
ex: 130, 140, 150, 180 and 
130, 140, 160, 170

1 and 2, still not enough

GMATCoachBen · Answer

We can test some simple cases and try to get both a YES and NO answer to the question:

(1) 
145, 155 --> NO
140, 150, 160 --> YES

Insufficient

(2) 
Our instinct might tell us that it is optional to include "150". An average of 150 just requires that the total residual of the values below 150 be equal to the total residual above 150. (For example, 148 would be a -2 residual, which would be offset by 152, which is a +2 residual)

If we wanted to prove it with values:
146, 147, 148, 149, 151, 152, 153, 154 --> NO 
146, 147, 148, 149, 150, 151, 152, 157 --> YES

Insufficient

Together: 
We know from statement 1 that it's an evenly spaced set, which means that the median is equal to the average.
If there's 8 terms in an evenly spaced set, the median will be halfway BETWEEN the 4th and 5th terms.
Therefore, for 150 to be the median, the 4th term must be 145, and the 5th term must be 155.
So, the answer to the question is NO.

Sufficient together, so our answer is C.

TBT · Answer

Why is statement b not enough? 8(even) terms and no repetition means average will not be part of the set.What am I missing?

GMATCoachBen · Answer

TBT  You may be using information from statement 1 in your analysis here; your comment is true if we are talking about an evenly spaced set. However, from just the stem and statement 2, all we know is that there are 8 terms that are all different and an average of 150.

From statement 2 alone, the average could be part of the set.

Consider these values:

146, 147, 148, 149, 150, 151, 152, 157

(The easiest way to pick these values is to think about "residuals", which is the difference each value is from the average. The total magnitude of the negative residuals must be equal to the total of the positive residuals. 148 through 152 are evenly spaced, and offset each other; 146 and 147 are -4 and -3 from the average, respectively, for a total residual of -7, and 157 is +7 from the average)

Stella5200 · Answer

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?

Given: Average weight 
 Ask: Is there a person who weighs 150 lb?

What do you need? 
 > Number of people and some sense of how the distribution flows.

Statement 1

Gives distribution. great. Number of people? no.  Insufficient

Statement 2

Gives number of people. great. Distribution? no.  Insufficient

1 and 2?

Number of people and Distribution. Great.  Sufficient

<50s to work out.

Stella5200 · Answer

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?

Given: Average weight 
 Ask: Is there a person who weighs 150 lb?

What do you need? 
 > Number of people and some sense of how the distribution flows.

Statement 1

Gives distribution. great. Number of people? no.  Insufficient

Statement 2

Gives number of people. great. Distribution? no.  Insufficient

1 and 2?

Number of people and Distribution. Great.  Sufficient

<50s to work out.

The average weight of people in a group is 150 pounds. If no two peop

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GMAT Data Sufficiency (DS) Questions

The average weight of people in a group is 150 pounds. If no two peop

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