In this case, the part is the number of freshmen after you add x. Of the
500 students, 15% were freshmen, so the original number of freshmen was
0.15(500) = 75. After the change, the number of freshmen is 75 + x. The
whole is the total number of students in the school after you add 50: 550. The
equation is 75 + 550 x = 10020. Reduce 10020 and arrive at 75 + 550 x =^15. Cross-multiply:
5(75 + x) = 550. Divide both sides by 5. 75 + x = 110. x = 35.- C If 25% of the original 800 employees are administrative, then there are
0.25(800) = 200 administrative employees. Since you don’t know how many
administrative employees you are adding, assign a variable: x. After the
increase, there will be 200 + x administrative employees. You know this
number will be 40% of the total number of employees. How many total
employees will there be? There were originally 800, but if you are adding
x administrative employees, then there will be 800 + x total employees.
You can therefore create the following equation:
200 + 800 + xx = 10040
200 + 800 + xx =^25
1,000 + 5x = 1,600 + 2x
3 x = 600
x = 200 - C Plug in a value for y. Let y = 5. Now use the simple interest formula:
interest accrued = principal × rate × time
= 10,000(0.05)5
= 2, 500
Substitute 5 for y into the choices and see which choice yields a value of 2,500. - C and D Since Bob paid $30 in tax, you know that $30 must be between 10%
and 15% of the total cost. The cost for which $30 represents a 10% tax will be
the higher bound of the price of the item, and the cost for which $30 represents
a 15% tax will be the lower bound of the price of the item. Determine these
bounds, and find which choices fall within the price range. Let the pretax cost
be x. For the 10% tax, you can create the equation: 30 = 0.1x → x = 300. For
the 15% tax, you can create the equation 30 = 0.15x → x = 200. Among the
choices, the values between 200 and 300 are C and D. - $5,624 Use the compound interest formula: P(1 + r)n = new. Thus you arrive
at 5,000(1.04)^3 = $5,624. - B Use the percent change formula: new – oldold × 100. Note that you are looking
for the percent change in the ratios of the two groups, not in their actual
values. The ratio of juniors to seniors in 2007 was^300200 =^32. The ratio of juniors
to seniors in 2008 was^400250 =^85. Plug^85 in for the new value and^32 for the old
value:
8
5 –
3
2
3
2× 100 = 6.66%
240 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 240 12/05/17 11:52 am