Check Your Skills Answer Key

1. 120

   PART	84	70
   WHOLE	x	100

   
2. 60

   PART	30	x
   WHOLE	50	100

   

3. 14.5028

   Move the decimal to the left one place: 145.028 → 14.5028

4. 14.6

   To find 20% of 73, first find 10% of 73. Move the decimal to the left one place: 73 → 7.3. 20% is twice 10%:

   7.3 × 2 = 14.6

5. 28%

   First find the change: 1600 − 1250 = 350.

   
6. 25.5

   CHANGE	x	15
   ORIGINAL	30	100

   

   However, the question asks how much water is remaining. Because 4.5 gallons have evaporated, then 30 – 4.5, or 25.5, gallons remain.

7. 42

   Recall that :

8. 20

   Recall that . Designate the original value x:

   

9. 100%

   Pick 100 for the original value of the portfolio. A 25% increase is:

   

   A 20% decrease is:

   

   The final value is 100. Because the starting value was also 100, the portfolio is 100% of its original value.

10. 90%

    Pick 100 for the original value of the portfolio. A 25% decrease is:

    

    A 20% increase is:

    

    The final value is 90 and the original value was 100. Thus, of the original value.

11. $5,040

    P × r × t = $12,000 × 14% × 3 = $5,040.

12. $17,778.53

    , where P − $12,000, r = 14%, n = 1 (annual compounding), and t = 3 years.

    (rounded to the nearest penny). This represents $17,778.53 − $12,000, or $5,778.53 in interest.

13. $18,132.82

    , where P = $12,000, r = 14%, n = 4 (quarterly compounding), and t = 3 years.

    (rounded to the nearest penny)

    This represents $18,132.82 − $12,000, or $6,132.82 in interest. As noted in the problem, you would not encounter an actual computation with an exponent this large on the GRE, because you would have to multiply 1.035 by itself over and over, until you raised 1.035 to the 12th power (there is no shortcut exponent key). But there’s a valuable real-life lesson here: quarterly compounding gives you slightly more interest in the end than annual compounding (compare to the previous answer).