1. If pencils are 2 for $0.25 and notecards are $.50 for a pack of 100 (including tax) how much change will Mariam get out of $10.00 if she buys a dozen pencils and 500 notecards?

SAT Sample Test I Part A

1. 3(x+4) = 5x

x =

(A) -6

(B) -2

(D) 3

(E) 6

1. Answer: E

3(x+4) = 5x

3x + 12 = 5x

12 = 2x

6 = x

2 If a + b = 10 and b = 4 then 2a + 3b =

(A) 20

(B) 24

(D) 28

(E) 30

2. Answer: B

If b = 4 and a+b = 10,

then a + 4 =10

a = 6

Therefore, 2a + 2b = 2(6) + 3(4) = 24

3. If (¹/₅ ) x = ³/₄, then x =

(A) 3 ³/₄

(B) ³/₂₀

(D) 8 ¹/₃

(E) 5 ³/₄

3. Answer: A

To solve for x when x is multiplied by a fraction, multiply both sides of the equation by the reciprocal of the fraction.

If (1/5)x = 3/4

Then 5 ·(1/5)x = 5 · (3/4)

Therefore x = 15/4 or 3 3/4.

4. How many different ways are there to get from Point A to Point B, assuming one is always traveling from left to right or from top to bottom?

(A) 2

(B) 3

(D) 7

(E) 12

4. Answer: C

Make a list. The small letters between A and B represent turning points on different paths.

A f B

A a g B

A b h B

A c i B

A d j B

A e B

5. Harold knows he has exactly $0.18 on his dresser. He can't remember what coins he has, however. If he could have pennies, nickels, or dimes, how many different ways could he have coins on his dresser?

(A) 3

(B) 4

(D) 6

(E) 7

5. Answer: D

Make a list.

Dimes	Nickels	Pennies
1	1	3
1		8
	3	3
	2	8
	1	13
		18

6. Which expression represents the average (arithmetic mean) of 88, 92, 78, and x?

(A) x + (88 + 92 + 78)/3

(B) (x + 88 + 92 + 78)/3

(D) 4(x + 88 + 92 + 78)

(E) x/4 + (88 + 92 + 78)/3

6. Answer: C

Solution: To find the arithmetic mean add the numbers and divide by the number of items being averaged. In this case, the arithmetic mean of 88, 92, 78, and x is (x+88+92+78)/4.

7. In terms of average life spans, one dog year is equivalent to seven human years. If Windy the dog is 6 years and 2 months old, what is the closest approximation to her age in human years?

(A) 41

(B) 42

(D) 44

(E) 45

7. Answer: C

Six years and two months is equal to 6 2/12 or 6 1/6 years. Multiply by seven to find Windy's age in human years:

(6 1/6) x 7 = 43 1/6 which is closest to answer C.

Extra: Note that 1/6 is close to 1/7. Then

(6 1/7)x7 = 43

8. If y = -2x + 4, and if x = 3 find the value of y.

(A) -10

(B) -6

(D) 2

(E) 10

8. Answer: C

y = -2x + 4

= -2(3) +4

= -6 + 4

= -2

9. If Saul earns 80% of David's salary and Tim earns 60% of David's salary, then approximately what is Saul's salary in relationship to Tim's salary?

(A) 48%

(B) 60%
(C) 75%
(D) 80%
(E) 133%

9. Answer: E

Let S = Saul's salary, D = David's salary, and T =Tim's salary.

Then S = .8D and T = .6D.

Therefore, the ratio of S/T = .8D/.6D = .8/.6 = 8/6 = 4/3. So if S/T = 4/3 then S=(4/3)T ≈ 133%.

Shortcut: Assume that David's salary is $100. Then Saul's salary is $80 and David's salary is $60 so that Saul's salary is 80/60 of David's salary, or 133% times David's salary.

Great shortcut: Since Saul earns more than David, Saul's salary is more than 100% of David's salary and (E) is the only answer that is greater than 100%.

10. If the width of a rectangular area is increased by 40% and the length is increased by 50% then the area is increased by

(A) 20%

(B) 90%

(D) 210%

(E) 200%

10. Answer: C

The area of the rectangle is given by the formula: A=lw. If the width is increased by 40% the new width is 140%w = 1.4(w), and if the length is increased by 50% the new length is 150%l = 1.5(l). The new area is then A=1.4(w)x1.5(l)=1.4x1.5x(wl)=2.10wl=210%wl. Since the old area was 100%wl, the new area is 110% greater.

11. What percent of 5 is 8?

(A) 30

(B) 62¹/₂

(D) 130

(E) 160

11. Answer: E

Set this problem up as a proportion.

Part/Whole = Rate/100

In this problem 8 is the part and 5 is the whole or base.

8/5 = 160/100 = 160%.

Be careful. There is a tendency to set this up as a proper fraction since 5 is less than 8.

Extra: Think of 'is' as the numerator, and 'of' as the denominator.

8 is part of 5

is/of = 8/5 = 1.6 = 160%

12. In the rectangle below two circles are to be cut out. if each circle has an area of 5π units, what is the area of the remaining region?

(A) 10 p
(B) 40 - 10 p
(C) 30 p
(D) 8√5 - 5 p
(E) 40p

12. Answer: B

The area of each circle is 5p, so the area of both circles is 10 p. Since the area of both circles must be subtracted from the area of the rectangle, (B) appears to be a good choice of answers. However, let's find the area of the rectangle.

Since the area of the circle is 5π we have

A = 5π =πr². Dividing both sides by π we have

5 = r²

√5 = r.

Since the circles fit into the rectangle exactly, the width and height of the two circles is the same as the width and the height of the rectangle. The width of one circle is 2r = 2√5, so the width (or base) of the rectangle is 2x2√5=4√5 and the height is 2√5. Therefore the area of the rectangle is

A = bh = (4√5) · (2√5) = 4 · 2 · √5 · √5 = 8 · 5 = 40.

Finally, the area of the rectangle minus the area of the two circles is

40-10π.
The next two questions refer to the problem below:

There are 50 seniors in a school, 24 of whom take art and 40 of whom take biology.

13. At least how many students are enrolled in both art and biology classes?

(A) 0

(B) 10

(D) 24

(E) there is not enough information to answer this problem

14. How many students are taking neither class?

(A) 0

(B) 10

(D) 24

(E) there is not enough information to answer this problem

13. Answer: C

Note that if there were no students taking both art and biology there would be 64 (=24+40) students in the classes. However, there are only 50 seniors, so some students must be in both classes. There must be at least 14 students in both classes.

14. Answer: E

Note that in the first diagram all students are enrolled in one of the classes, 10 take art only, 14 take both, and 26 take biology only. If there were some students who take neither class, the number of the students taking both classes would be larger (see the second diagram). However, it is impossible to tell whether there are students who take neither class.
15. If Bob is three times as old as Daniel and if Daniel is four times as old as Janet, and if the sum of their ages is 85 how old is Janet?

(A) 3

(B) 5

(D) 15

(E) 17

15. Answer: B

Solution:

Let J = Janet's age

Then 4J = Daniel's age

Since Bob is three times as old as Daniel, Bob's age is 3(4J)=12J.

J + 4J + 12J = 85

17J = 85

J = 5

16. Find the area of the triangle.

(A) 0.25 w²

(B) 0.5 w²

(D) 2w²

(E) (Ö3/4)w²

16. Answer: A

The base of the triangle is w units and the height is .5w, so use the formula for the area of a triangle to answer the question.

A = (1/2)bh

= (1/2)w(0.5w)

= (0.5)w(0.5)w

= 0.25w².

17. A triangle has vertices at (-3, -3), (7, -3) and (-2, 5). What is the area of the triangle?

(A) 16

(B) 28

(D) 40

(E) 80

17. Answer: D

Draw a picture. The base of the triangle is from (-3,-3) to (7,-3). The y-values of the two points are the same, so the length can be measured by using the x-values of the points and finding the absolute value of the difference. Note that length is always positive: 7-(-3)=10. However, it is easier to visualize by looking at the graph: there are 3 units to the left of the y-axis and 7 units to the right of the y-axis, so 3+7=10. Similarly, the height is the distance from the base to the vertex, from y=-3 to y=5, or 8 units.

A=(1/2)bh=(1/2)(10)(8)=40.

18. If 4 books cost d dollars, then 6 books cost

(A) d + 2

(B) 6d

(D) 2d/3

(E) 2 + d/4

18. Answer: C

Use ratios, cross-multiply, and divide: 4 books for d dollars is equal to d books for x dollars.

4/d = 6/x

Þ 4x = 6d

Þ x = 6d/4

Now look for an answer choice equal to 6d/4.

6d/4 = (6/4) · d = (3/2) · d = 1.5d.

19. If two six-sided cubes each have faces numbered one through six, what is the probability of getting one even number and one odd number face up, if the two cubes are rolled simultaneously?

(A) 1/2

(B) 1/3

(D) 1/9

(E) 1/36

19. Answer: A

There are two possibilities: Cube 1 is even and Cube 2 is odd, or Cube 1 is odd and Cube 2 is even. The probability of a cube being even is 3/6 or 1/2. Of course this is also the probability of a cube being odd.

P(Cube 1 even) x P(Cube 2 odd) = (1/2)x(1/2) = 1/4

P(Cube 1 odd) x P(Cube 2 even) = (1/2)x(1/2) = 1/4

The probability of either of these events happening is (1/4)+(1/4)=1/2

Extra: Make a list of all possible outcomes. The ones with one even and one odd cube are underlined.

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

There are 18 outcomes with one even and one odd cube. Since there are 36 possible outcomes, the probability of getting one even and one odd is 18/36 = 1/2.

20. If n* = (n² – n) then 5* – 3* is

(A) 8

(B) 12

(D) 14

(E) 26

20. Answer: D

Plug in. If n*= (n² -n) then 5*=(25-5)=20 and 3*=(9-3)=6.

Therefore, 5*-3*=20-6=14.

21. If 2^x = a and 2^y = a², then y =

(A) 2x

(B) x²

(D) 4

(E) √a

21. Answer: A

If a = 2^x then a² = (2^x )² = 2^2x. Therefore, if 2^y = 2^2x, then y = 2x.

22. A number that is divisible by 8 and 9 must be divisible by all of the following except

(A) 2

(B) 6

(D) 15

(E) 24

22. Answer: D

The smallest number that is divisible by both 8 and 9 is 72 (the least common multiple). Therefore, any number that is divisible by both 8 and 9 will also be divisible by 72. Note that any number that is divisible by 72 will also be divisible by factors of 72. Now 2, 6, 12, and 24 are all factors of 72, but 15 is not a factor of 72.

23. The Gourmet Pizza Palace makes only one size of pizza but offers four different kinds of cheese, three different kinds of meat, and six other vegetable toppings. If a family wishes to order a pizza with one cheese topping, one meat topping, and one vegetable topping, how many different pizzas can they choose from?

(A) 8

(B) 13

(D) 72

(E) 216

23. Answer: D

Use the multiplication principle of counting. If there are 4 different kinds of cheese, and each cheese can be combined with one of 3 kinds of meat, there are 4x3=12 cheese/meat combinations. And if each of these cheese/meat combinations can be combined with 6 different vegetables, there are 12x6=72 cheese/meat/vegetable combinations.

24. In order to sell a used car the owner decided to ask for $4000 beginning Sunday morning. At the end of each day that the car didn't sell he planned to mark the price down by 20% of that day's price. If the car sold the following Thursday, which expression accurately reflects the final selling price?

(A) $4000 x 5 x 0.2

(B) ($4000 x 0.2)⁵

(D) $4000 x 5 x (0.8)

(E) $4000 x (0.8)⁵

24. Answer: E

If the car doesn't sell by Sunday it is marked down 20% so that Monday it will be

80% of $4000 = 0.8. x $4000

Again, on Monday evening, if the car still hasn't sold, if will be marked down so that Tuesday's price will be 80% of Monday's price, or

(0.8)(0.8 x $4000) = (0.8)² x $4000.

Therefore, by Friday, the price has been marked down five times (Sunday evening through Thursday evening) and will be

(0.8)⁵ x $4000.

25. A cube has a surface area of 54 square centimeters. What is the volume of the cube in cubic centimeters?

(A) 3

(B) 9

(D) 54

(E) 108

25. Answer: C

A cube has six faces so each face has an area equal to 1/6 of the total surface area, or 9 square centimeters. If the area of a face is 9 then one edge must be 3 cm. (=Ö9).

The volume of a cube is given by the formula V=s³ so that V=3³= 27.