SAT Sample Test I Part B

1. Mary bought three hamburgers and one cola for $4.20, which included the tax. Carroll bought two hamburgers and one cola for $3.00, tax included. If Karen wants one cola and one hamburger, how much will she need?

(A) $0.60

(B) $1.20

(D) $2.40

(E) $3.60

1. Answer: C

Let H represent the price of a hamburger and C represent the price of a cola. Then

3H + C = $4.20

2H + C = $3.00.

Subtracting the second equation from the first yields

H = $1.20.

Now use substitution into either equation to find C

3($1.20) + C = $4.20

$3.60 + C = $4.20

C = $0.60

Therefore, the price of one hamburger and one cola is $1.20 and $0.60 which is $1.80.

2. If 4x + 16 > 8x + 8 then

(A) x = 2

(B) x > 2

(D) x < 2

(E) -x > 4

2. Answer: D

4x + 16 > 8x + 8

4x + 8 > 8x

8 > 4x

2>x

Since 2>x then x<2.

3. Four people drive to school together each day in a car. Two people sit in front and two sit in back. If the same person drives each day, how many different seating arrangements are there?

(A) 2

(B) 4

(D) 12

(E) 24

3. Answer: C

Make a list. Besides the driver there are three other passengers, say A, B, and C. There are six possibilities.

Front seat, passenger	Back seat, left side	Back seat, right side
A	B	C
A	C	B
B	A	C
B	C	A
C	A	B
C	B	A

4. What is the slope of line t?

(A) –4

(B) –1/4

(D) 1/4

(E) 4

4. Answer: A

Use two points, such as (0,4) and (1,0) to find the slope.

Slope = (change in y)/(change in x) = (4-0)/(0-1) = (4)/(-1) = -4.

5. Which of the following must be odd?

I. The sum of two odd numbers

II. The product of two odd numbers

III. The product of two prime numbers

(A) I only

(B) II only

(D) I and III

(E) II and III

5. Answer: B

Plug in numbers.

I. No. The sum of two odd numbers is even. Example: 3+5=8

II. The product of two odd numbers is odd: 5x7=35. Note that for a product to be even at least one of the factors must be even.

III. No. If one of the prime numbers is 2 the product of two prime numbers can be even. Note that 2 is the only even prime number!

Extra: Use algebra on I and II to examine the general case. Let an even number be represented by 2n since all even numbers are divisible by 2. Then any odd number can be represented by 1 more than an even number, such as 2n+1.

I. The sum of two odd numbers: (2n+1)+(2m+1)= 2m+2n+2, which is even since every term is a multiple of 2.

II. The product of two odd numbers: (2n+1)(2m+1)=4mn+2m+2n+1. This must be an odd number since the 4mn+2m+2n is even.

6. If a copy machine can produce 5 copies in 12 seconds, how many copies can be made in 10 minutes?

(A) 25

(B) 50

(D) 250

(E) 300

6. Answer: D

Use ratios: ( 5)/(12 seconds) = (5x5)/(12 seconds x 5) = (25)/(1 minute) = (25x10)/(1 minute x 10) = (250)/(10 minutes).

7. If the ratio of a to c is 3 to 4 and if the ratio of b to c is 5 to 7, then the ratio of a to b is

(A) 3 to 5

(B) 7 to 28
(C) 15 to 28
(D) 12 to 35
(E) 21 to 20

7. Answer: E

Given a/c = 3/4 and b/c =5/7

Find a common denominator so that you can compare numerators.

a/c = 3/4 = 21/28

b/c = 5/7 = 20/28

Now since the denominator is the same you can compare a and b.

a/b = 21/20.

Extra: Note that a/c ÷ b/c = a/c x c/b = ac/bc = a/b.

Plug in a/c = 3/4 and b/c = 5/7.

3/4 ÷ 5/7 = 3/4 x 7/5 = 21/20.

8. In the figure below, what is the value of x + y ?

(A) 50°

(B) 130°

(D) 360°

(E) It cannot be determined from the information given.

8. Answer: B

Let 'a' represent the measure of the vertical angles formed by the intersection of the two lines as shown in the figure below. Using the fact that the sum of the measures of the interior angles of a triangle is 180° we have

180 = a + x + y = a + 90 + 40

Þ x + y = 90 + 40

Þ x + y = 130.

9. From a recipe for cookies Dana makes a batch of two dozen (24) cookies of a certain diameter. Using the same recipe and keeping the cookies the same thickness, Dana makes another batch of cookies, except that the cookies in the second batch have twice the diameter of the cookies in the first batch. How many cookies will be in the second batch?

(A) 6

(B) 12

(D) 48

(E) 96

9. Answer: A

Let r be the radius of the cookies in the first batch and R be the radius of the cookies in the second batch, which are larger.

Since the diameter of the cookies in the second batch is twice as big as the cookies in the first batch, the radius is also twice as large. Therefore, R = 2r.

The area of a cookie in the first batch is πr². The area of a cookie in the second batch is πR² = π (2r)² = π4r². =4πr². The area, or size of each cookie in the second batch is therefore 4 times as large as the area of a cookie in the first batch. Therefore, the same amount of batter will only make 1/4 as many cookies, or 6 cookies.

10. In the figure below, AB = 3, BC = 4, AD = 13 and AE = CD. Find the perimeter.

(A) 20 (B) 31 (C) 36 (D) 40 (E) not enough information

10. Answer: C

This problem uses two Pythagorean triangles: the 3-4-5 triangle and the 5-12-13 triangle.

Note that angle ABC is a right angle, AB = 3, BC = 4 and by the Pythagorean Theorem AC must be 5. Since AE=CD and since angles AED and CDE are right angles, ACDE is a rectangle and ED is also 5.

Again, note that angle AED is a right angle so that triangle AED is a right triangle with hypotenuse 13. Therefore, AE = 12. Again, since ACDE is a rectangle, CD = AE and so CD is also 12. Adding up the lengths of the sides (3+4+12+5+12) yields a perimeter of 36.