Problem Solving

Hi swerve,

This prompt gives us several Facts to work with:
1) There are 5 values
2) Both the MEAN and the MEDIAN = $7,000
3) There's only one MODE and it's $12,000
4) Each value is a multiple of $1,000

We're asked for the difference between the greatest and least of the five values.....

Since the MEAN = $5,000, we know that the TOTAL of the 5 values is... (5)($7,000) = $35,000

With a MEDIAN of $7,000, we know that two values are GREATER than $7,000 (and they're BOTH the MODE: $12,000 each) and two are LESS than $7,000.

_ _ $7,000 $12,000 $12,000 = two unknowns + $31,000 = $35,000
two unknowns = $4,000

The two unknowns must be DIFFERENT from one another (because there was just the one MODE) and both must be multiples of $1,000... thus, they must be $1,000 and $3,000. The difference between the greatest and least values is $12,000 - $1,000 = $11,000

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

swerve wrote:An analysis of the monthly incentives received by 5 salesmen: The mean and median of the incentives is $7,000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month?

A. $4000
B. $5000
C. $9000
D. $11,000
E. $13,000

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

From the information given in the problem, we see that the highest 3 incentives are $7,000, $12,000 and $12,000, and the total amount of the 5 incentives is 5 x 7,000 = $35,000. Therefore, the total of the lowest 2 incentives is 35,000 - (7,000 + 12,000 + 12,000) = 35,000 - 31,000 = $4,000. Since those 2 incentives are paid in full thousands and they can't be each $2,000 (since there is only one mode), they are in the amounts of $1,000 and $3,000. So the difference between the highest and the lowest incentives is 12,000 - 1,000 = $11,000.

Answer: D