The sum of these values is 200,000: 4x + 3x + x = 200,000. Manipulate to solve
for x:
8 x = 200,000
x = 25,000
The amount budgeted for product development is 3x = 3(25,000) = 75,000.- C, D, E and F Since the question provides ratios with no actual values,
represent the parts algebraically: number of number of brown eggswhite eggs = wb =^43 xx. The
total number of eggs in the basket is thus 4x + 3x = 7x. Since it is impossible to
have a fraction of an egg, x must be an integer, and thus 7x must be a multiple
of 7. The possible values must all be multiples of 7. Among the choices, 21, 70,
140, and 161 are the only multiples of 7. - A Let x be the total number of bonds and 3x be the total number of mutual
funds. The sum of these quantities will be 80, the total number of shares. Thus:
3 x + x = 80
4 x = 80
x = 20 and 3x = 60
Now that you know how many mutual funds and bonds there were originally,
use these values to set up a proportion with the second ratio in the question.
Let y = the number of bonds that will be added:
number of bonds
number of mutual funds =
5
6 =20 + y
60.
Cross-multiply:
5(60) = 6(20 + y)
300 = 120 + 6y
180 = 6y
y = 30- A, C, and D Since the ratios share the common element of directors, your
first step should be to manipulate the ratios so that the value for the number of
directors is the same in both. (Note: In the following ratios, m = the number of
managers, d = the number of directors, and a = the number of administrators).
number of managers
number of directors =
3 × 5
2 × 5 =15
10
number of directors/number of administrators = 14 × 25 × 2 =^1028
Thus the ratio of managers to directors to administrators is 15:10:28.
To determine the possible sum of the three, represent managers as 15x,
directors as 10x, and administrators as 28x. The sum of these values is 15x +
10 x + 28x = 53x. Since it is impossible to have a fraction of a person, x must
be an integer, and thus 53x must be a multiple of 53. The possible values
must all be multiples of 53.254 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 254 12/05/17 11:53 am