GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

Example 2: If Art and Rita can do a job in 4 hours when working together at their respective constant

rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?

Solution:

1+_1=1

6 R 4

R+6 l

6R 4

4R+24=6R

24 =2R

l2= R

Working alone, Rita can do the job in 12 hours.

3. Mixture Problems
   In mixture problems, substances with different characteristics are combined, and it is necessary to
   determine the characteristics of the resulting mixture.

Example 1: If 6 pounds of nuts that cost $1.20 per pound are mixed with 2 pounds of nuts^1 hat cost

$1.60 per pound, what is the cost per pound of the mixture?

Solution: The total cost of the 8 pounds of nuts is

The cost per pound is

6($1.20) + 2($1.60) = $10.40.

$10.40 = $1.30.

8

Example 2: How many liters of a solution that is 15 percent salt must be added to 5 liters of a solution

that is 8 percent salt so that the resulting solution is 10 percent salt?

Solution: Let n represent the number ofliters of the 15% solution. The amount of salt in the 15%

solution [0.15n] plus the amount of salt in the 8% solution [(0.08)(5)] must be equal to the amount of

salt in the 10% mixture [0.lO(n + 5)]. Therefore,

0.l5n + 0.08(5) = 0.l0(n + 5)

l5n+40 = l0n+50

5n = 10

n = 2 liters

Two liters of the 15% salt solution must be added to the 8% solution to obtain the 10% solution.

4. Interest Problems
   Interest can be computed in two basic ways. With simple annual interest, the interest is computed on
   the principal only and is equal to (principal) x (interest rate) x (time). If interest is compounded, then
   interest is computed on the principal as well as on any interest already earned.