GMAT OFFICIAL GUIDE PS

Solution:

We can let the number of apples = x and the number of oranges = y. Using these variables we can create the following two equations:

1) x + y = 10

Using the formula average = sum/quantity, we have:

2) (40x + 60y)/10 = 56

Let’s first simplify equation 2:

40x + 60y = 560

4x + 6y = 56

2x + 3y = 28

Isolating for y in equation one gives us: y = 10 – x.

Since y = 10 – x, we can substitute 10 – x for y in the equation 2x + 3y = 28. This gives us:

2x + 3(10 – x) = 28

2x + 30 – 3x = 28

-x = -2

x = 2

Since x + y = 10, then y = 8.

We thus know that Mary originally selected 2 apples and 8 oranges.

We must determine the number of oranges that Mary must put back so that the average price of the pieces of fruit that she keeps is 52¢. We can let n = the number of oranges Mary must put back.

Let’s use a weighted average equation to determine the value of n.

[40(2) + 60(8-n)]/(10 – n) = 52

(80 + 480 – 60n)/(10 – n) = 52

560 – 60n = 520 – 52n

40 = 8n

5 = n

Thus, Mary must put back 5 oranges so that the average cost of the fruit she has kept would be 52 cents.

Answer: E

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Scott Woodbury-Stewart is the founder & CEO of Target Test Prep. A passionate teacher who is deeply invested in the success of his students, Scott began his career teaching physics, chemistry, math, and biology. Since then, he has spent more than a decade helping students gain entry into the world’s top business schools, logging 10,000+ hours of GMAT, EA, GRE and SAT instruction. Scott also served as lead content developer and curriculum architect for the revolutionary courses Target Test Prep GMAT, Target Test Prep EA, Target Test Prep GRE and Target Test Prep SAT Quant.