SAT Mc Graw Hill 2011

Concept Review 5

1.x, y,or any unknown; ×; is;÷ 100

2.

3. 1.30 4. 0.81 5. 2.20 6. − 20

7.

8. .35x= 28 x= 80


9. 60 =.15xx= 400


10. 175%. Rephrase: What percent of 20 is 35?(or re-
    member is over ofequals the percent)

3,500 = 20 xx=175(%)

11. 25%. Use the “percent change” formula:

1 500 1 200

1 200

100

300

1 200

100 25

,,

,

%

,

%%

−

×= ×=

xx

100

20 35

35

20 100

×= or =

5

100

=× = 26 19 23

x

x .%

final amount starting amount

starting amount

−

××100%

12.

13. 40%.

14. 
    
    
    
    26. To increase a number by 30%, multiply by
        1.30: 20 ×1.30 =26.
    
    
    
    


15. 0.96. x(1.20)(.80) =0.96x


16. Because the two percentages are “of” different
    numbers.


17. 9.75%. Assume the original square has sides of
    length xand area x^2. The new square, then, has
    sides of .95xand area of .9025x^2.


18. 50% of 28, which equals 14


19. 25% of 48, which equals 12

.

%

.

%.%

9025

100

0975

100 9 75

22

2

2

2

xx

x

x

x

−

×=

−

×=−

44 800 32 000

32 000

100

12 800

32 000

100

,,

,

%

,

,

%

−

×= ×= 4 40%

−

−

×=

−

15 ×=−

168 80

80

100

12

80

%. % 100 % 15 %

Answer Key 5: Percents

290 MCGRAW-HILL’S SAT

SAT Practice 5

1. D Miscellaneous expenses =$3,500 −$2,200 −$600
   =$700. As a percent of the total, 700/3,500=20%. The
   total number of degrees in a pie graph is 360°, so the
   sector angle =20% of 360°=.20 × 360 = 72 °.


2. 32% Assume the starting price is x.The final
   price is x(1.20)(1.25)(.80)(1.10) = 1.32x,which
   represents a 32% increase. Notice that you can’t
   just “add up” the percent changes, as we saw in
   Question 16 of the Concept Review.


3. C The total number of points is 40 + 80 =120.
   The number of points she earned is .60(40) +.90(80)
   = 24 + 72 =96. 96/120 =.80 =80%.


4. D If you chose (A), remember: 2/3% is NOT the
   same thing as 2/3! Don’t forget that % means ÷100.
   x=2/3% of 90 =(2/3) ÷ 100 × 90 =0.6
   1 −0.6 =0.4


5. C If you chose (B), remember that the tax is 5%
   of the starting amount, not the final amount. The
   final price must be 5% higher than the starting
   price. If the starting price is x,then $8.40 =1.05x.
   Dividing by 1.05, x=$8.00.
   6. B Let a=population of Town A, b=population
   of Town B, and c=population of Town C. Since b
   is 50% greater than a, b=1.50a.Since cis 20%
   greater than a, c=1.20a.

You can also set a=100, so b=150 and c=120.

7. C If the rectangle has length aand width b,then
   its area is ab.The “new” rectangle, then, has
   length 1.2aand width 1.3band so has an area of
   1.56ab,which represents an increase of 56%.


8. C The total amount of salt is .30(12) +.60(24)
   =3.6 +14.4 =18 ounces. The total amount of so-
   lution is 36 ounces, and 18/36 =50%. Or you might
   notice that 24 is twice as much as 12, so the con-
   centration of the mixture is the average of “two
   60s and one 30.”
   (60% +60% +30%)/3 =50%


9. D The number of girls is n+45, so the total num-
   ber of students is 2n+45. So the percentage of
   girls is
   100 45
   245

n

n

()+

+

%

15 12

12

100

3

12

100 25

..

.

%

.

.

%%

aa

a

a

a

−

×=×=