# Arithmetic Preparation for SAT

**Question 1**

The sum of three consecutive integers is four times the first integer. What is the last of the three integers?

A 5

B 4

C 3

D 2

E 1

**Question 2**

What is the value of 1/2 + 1/4 + 1/8?

A 3/8

B 2/4

C 5/8

D 3/4

E 7/8

**Question 3**

What is the average (arithmetic mean) of the following

five numbers: -8, -6, 3, 7, and 19?

A 1.0

B 1.6

C 2.0

D 2.6

E 3.0

**Question 4 **

The product of 89 and 91 is closest to

A 810

B 900

C 8000

D 8100

E 18000

**Question 5**

Set S = {-2, -1, 1, 2}

Set T = {-2, -1, 0, 1, 2}

What is the value of the mean of set S minus the mean of set T?

A -2

B -4/5

C 0

D 4/5

E 1

**Question 6**

What is 10,000 divided by 6, when rounded off to the nearest whole number?

A 1667

B 167

C 1666

D 16.67

E 166.7

**Question 7**

What is the value of 31/2 + 7/4 + 6/8?

A 6.25

B 6.0

C 5.5

D 4.75

E 4.0

**Question 8**

If 5/25 is added to 421.467, what is the result?

A 421.469

B 421.487

C 421.667

D 421.967

E 423.467

**Question 9**

One box of pop tarts costs 1.73 dollars. If purchasing more than 10 boxes, each box costs 1.53 dollars. How many dollars are saved by purchasing 54 boxes of pop tarts all at once rather than one at a time?

A 5.40

B 8.80

C 10.80

D 12.40

E 16.20

**Question 10**

A class is divided so that one fifth of students take auto shop and the rest take woodwork. If one student moves from the woodwork group to the auto shop group, what is the percentage of students in the class taking auto shop?

A 19

B 20

C 21

D 25

E There is not enough information to solve the problem.

**Question 11**

What is the first integer larger than the positive square root of 39?

A 5

B 6

C 7

D 8

E 9

**Question 12**

If a = 3 and b = 4, what is the value of |a| – |b| + |a – b| ?

A 8

B 7

C 3

D 1

E 0

**Question 13**

3a + b = 11. What is the value of 9a + 3b?

A 22

B 24

C 30

D 32

E 33

**Question 14**

If a is positive, and if **a ^{1/2}** is greater than a, then what is one possible value for a?

A 0.0

B 0.5

C 1.0

D 1.5

E 4.0

**Question 15**

Let x@y be defined for all x,y as 3x + 2y

What is the value of 9@4?

A 30

B 32

C 35

D 38

E 40

**Question 16**

Let u^v be defined for all u,v as `u ^{2} - v^{2}`

What is the value of 5^3?

A 16

B 20

C 25

D 32

E 36

**Question 17**

How many positive integers less than 62 have 8 as a factor?

A 9

B 8

C 7

D 6

E 2

**Question 18**

What is 5% of y if y = 6500/5?

A 0.65

B 6.5

C 65

D 500

E 650

**Question 19**

What is the value of 2*5*2*5*2*5*2*5?

A 100

B 625

C 1000

D 10,000

E 15,000

**Question 20**

What is the value of ?

A 1,000,000

B 100,000

C 10,000

D 1,000

E 100

**ANSWERS**

1. A

The most direct way to solve this is to write out a mathematical expression that represents the statement.

Let n be the first integer. Then n + (n + 1) + (n + 2) = 4n. Solving for n we get 3n + 3 = 4n, or equivalently, n = 3 . So the sequence is 3, 4, 5 , and 5 is the correct answer.

2. E

It all works out when you have everything over a common denominator.

1/2 = 4/8 and 1/4 = 2/8 , so the final answer is (4 + 2 + 1)/8 = 7/8

3. E

There are 5 numbers in this sequence, so the average will be the total of all the sums in the sequence divided by 5. The sum of all the numbers (-8 + -6 + 3 + 7 +19) is 15, so the average must be 15/5, or 3.

4. D

It’s a valuable skill to be able to make quick judgments about numbers. In this case, it should be clear that 89 and 91 are very close to 90, so a rough approximation is 90*90 = 8100. More generally, the product of 89 and 91 can be rewritten:

(90 -1)*(90+1) = 902 – 1 = 8100 – 1 = 8099.

5. C

The mean is the sum of the elements of the set divided by the number of elements in the set. For both sets the sum of the elements is zero, therefore the mean of both sets is zero. It follows that there is no difference between the means.

6. A

10,000/6 = 1666.66667. The nearest whole number requires rounding up, so the answer is 1667.

7. B

Changing the fractions to decimals, becomes:

3.5 + 1.75 + 0.75 = 6.0. This is a logical way to solve this problem as the responses were all given in decimals.

8. C

You’re right. 5/25 = 0.20. So when this is added to 421.467, the result is 421.667.

9. C

When purchasing all at once, we save 0.20 dollars per box. Since we buy 54 boxes, we save (0.20)(54)=10.80 dollars.

10. E

In order to calculate a percentage, you need to know the total. Without the total, it is impossible to know what the new percentage is when one student moves into the auto group. We know that originally it was 20%, but we cannot figure out the new percentage unless we know how many students there are in the whole class.

11. C

You just need to interpret the question correctly. The positive square root of 39 will be slightly larger than 6, because the square root of 36 is 6. So the next largest integer is 7. (And you know that the square root of 39 must be less than the square root of 49 which is 7.)

12. E

Just fill in the values for a and b and carry out the operations.

|3| – |4| + |3 – 4| = 3 – 4 + 1 = 0.

13. E

(9a + 3b) can be rewritten as (3)(3a + b).

3×11 = 33.

14. B

If a number is between 0 and 1, then the square root of that number is greater than the number itself. The square root of 0.5 is 0.7071. For all other positive values, the square root of a is either equal to or less than a.

15. C

9@4 is 9*3 + 4*2 = 27 + 8 = 35.

16. A

Twenty five minus nine gives sixteen. Notice that the difference of two perfect squares gave a third perfect square. That because 3-4-5 are the side lengths of a right triangle and the Pythagorean Theorem gives 32+42=52.

17. C

The first thing to notice is that 8*8 = 64. So the number has to be less that 8. But 8*7 = 56, which is less than 62. That means that there are 7 positive integers less than 62 with 8 as a factor.

18. C

First you find that y = 1300. Then, you can multiply 1300 by 0.05, or you can multiply it by 1/20. Either way you get the correct answer: 65.

19. D

Not hard to do on a calculator, or if you take your time doing it out by hand. But the quickest way is to rewrite the question to get:

24*54 = 104 = 10,000

20. D

The number inside the radical is 106 = 1,000,000. If you know that 1000 is the square root of one million you’re done. You might notice that taking the square root of a number is equivalent to raising it to the power 1/2.

So (106)1/2 = 103 = 1000.