Free SAT Math Questions - Math Concepts Practice Questions

8/6/2019 Free SAT Math Questions - Math Concepts Practice Questions

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Math Concepts:

Number and OperationsPractice Questions

1 Your answer (D) Correct!

What is the result when is rounded to the nearest thousand and then

expressed in scientific notation?

(A)

(B)

(C)

(D) Your Answer

(E)

Explanation

Difficulty: Easy

In the number , the thousands digit is and the hundreds digit is . Since the

hundreds digit of is more than , rounding to the nearest thousand gives

. When is expressed in scientific notation, the result is

, which is choice (D).

2 Your answer (A) Correct!

The positive integer is not divisible by . The remainder when is divided by and

the remainder when is divided by are each equal to . What is ?


2/5


3/5

. The set of all multiples of 3



(A) only

(B) only

(C) only Your Answer

(D) and only

(E) and only

Explanation

Difficulty: Medium

To solve this problem, consider the set in each of , , and separately and determine

whether that set is contained within set .

For , consider whether the set of all multiples of is contained within set . This will

be the case if every multiple of is also a multiple of . Since is a multiple of but

is not a multiple of , it follows that every multiple of is notnecessarily a multiple of

. Thus the set of all multiples of is not contained within .

For , consider whether the set of all multiples of is contained within set . This will

be the case if every multiple of is also a multiple of . Since is a multiple of but

is not a multiple of , it follows that every multiple of is notnecessarily a

multiple of . Thus the set of all multiples of is not contained within .

For , consider whether the set of all multiples of is contained within set . This

will be the case if every multiple of is also a multiple of . Every multiple of can

be written as for some integer , and a number is a multiple of if it can be

written as for some integer . If is any multiple of , then ;

since is an integer, it follows that can be written as , where is an integer,

and so is also a multiple of . Thus the set of all multiples of is contained

within .

Therefore, of the three sets given in , , and , only the set in is contained within

. Thus the correct answer is (C).

4 Your answer (E) Correct!


4/5

At the beginning of 2006, both Alan and Dave were taller than Boris, and Boris was tallerthan Charles. During the year, Alan grew inches, Boris and Dave each grew inches,

and Charles grew inches. Of the following, which could NOT have been true at the

beginning of 2007?

(A) Alan was shorter than Boris.

(B) Alan was shorter than Charles.

(C) Boris was shorter than Dave.

(D) Dave was shorter than Alan.

(E) Dave was shorter than Charles. Your Answer

Explanation

Difficulty: Medium

Consider the choices in turn. At the beginning of 2006, Alan was taller than Boris; duringthe year, Alan grew inches and Boris grew inches. Since Alan grew less than Boris, it

is possible that Alan was shorter than Boris at the beginning of 2007. So choice (A) is notthe correct answer.

At the beginning of 2006, Alan was taller than Boris, who was taller than Charles; thus,Alan was taller than Charles. During the year, Alan grew inches and Charles grew

inches. Since Alan grew less than Charles, it is possible that Alan was shorter thanCharles at the beginning of 2007. So choice (B) is not the correct answer.

At the beginning of 2006, Dave was taller than Boris; during the year, Boris and Daveeach grew inches. Thus Boris was still shorter than Dave at the beginning of 2007. So

choice (C) is not the correct answer.

At the beginning of 2006, Alan and Dave were each taller than Boris, but we cannotdetermine whether Alan was shorter than Dave or Dave was shorter than Alan, nor whatthe difference in their heights was. So even though Dave grew inches during the year

while Alan grew only inches, it is possible that Dave was shorter than Alan at the

beginning of 2007. So choice (D) is not the correct answer.

At the beginning of 2006, Dave was taller than Boris, who was taller than Charles; thus,Dave was taller than Charles. During the year, Dave grew inches and Charles grew only

inches, so Dave remained taller than Charles. Thus it could not be true that Dave was

shorter than Charles at the beginning of 2007. Therefore, choice (E) is the correct answer

5 Your answer (B) Correct!


5/5

If is an integer and if is a positive integer, which of the following must also be a

positive integer?

(A)

(B) Your Answer

(C)

(D)

(E)

Explanation

Difficulty: Medium

If is an integer and if is a positive integer, then is the sum

of two integers, and must therefore be an integer. Since is a positive integer, it

follows that . The integer will be positive if . Since , it

follows that , and so . Therefore, if is a positive integer,

must also be a positive integer.

If is a positive integer, then the expressions in the other choices must be integers, but

they need not be positive integers:

For , if , then , which is not

positive.

For , if , then , which is not positive

For , if , then , which is

not positive.

For , if , then ,

which is not positive.

Therefore, the correct answer is (B).

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Free SAT Math Questions - Math Concepts Practice Questions