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PSAT Math : Arithmetic

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Example Questions

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Example Question #1 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Five friends go to a coffee shop, the menu for which is above. Each has a coupon that is good for one dollar off the price of a butter croissant with the purchase of a large drink, or fifty cents off the price of a butter croissant with the purchase of a small drink.

Mick buys one large iced coffee and one butter croissant.

Keith buys one small iced coffee and one butter croissant.

Bill buys one large cappucino and one butter croissant.

Charlie buys one small cappucino and one butter croissant.

Brian buys two butter croissants.

Who will pay the most, if everyone who can use his coupon does?

Possible Answers:

Keith

Charlie

Bill

Mick

Brian

Correct answer:

Bill

Explanation:

Mick orders a large drink, so he uses his coupon to save a dollar off his croissant. He will pay

$\$ 3.49 + \$2.29 - \$1.00 = \$4.78$

Bill orders a large drink, so he uses his coupon to save a dollar off his croissant. He will pay

$\$ 3.89 + \$2.29 - \$1.00 = \$5.18$

Keith orders a small drink, so he uses his coupon to save fifty cents off his croissant. He will pay

$\$ 2.49 + \$2.29 - \$0.50 = \$4.28$

Charlie orders a small drink, so he uses his coupon to save fifty cents off his croissant. He will pay

$\$ 2.99 + \$2.29 - \$0.50 = \$4.78$

Brian does not buy a coffee, so he will not use his coupon. He will pay full price for both croissants, which will be

$\$2.29 \times 2 = \$4.58$

Bill pays the most.

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Example Question #531 : Arithmetic

What is the median of the following numbers: 3.45 , 2.74 , 3.33 , 3.89 , and 3.56 ?

Possible Answers:

3.56

3.33

3.89

3.45

2.74

Correct answer:

3.45

Explanation:

The median of a given set of numbers is the number that occurs precisely in the middle of all the numbers when they are put in numerical order. Thus, in order to find the median of this set of numbers, you must first put then in order from least to greatest, then find the number in the middle (the third number, in this set of five).

Numerical order for these numbers is:

2.74, 3,33, 3.45, 3.56, 3.89

Thus, the median is 3.45.

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Example Question #1 : How To Square A Decimal

Simplify. Assume all integers are positive real numbers.

$\sqrt{0.04}$

Possible Answers:

0.20

0.40

0.04

0.02

Correct answer:

0.20

Explanation:

$\sqrt{0.04}$

There are two ways to solve this problem.

First, leave the question in decimal form.

$\sqrt{0.04}=0.20$

$0.20\cdot0.20= 0.04$

Second, put your question in fraction form.

$\sqrt{0.04}=\sqrt{\frac{4}{100}}=\frac{\sqrt{4}}{\sqrt{100}}= \frac{2}{10}= 0.20$

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Example Question #1 : How To Square A Decimal

If all real values of $x$ lie between 0 and 1, which of the following is always greater than 1?

Possible Answers:

$x^{4}$

$\frac{x}{10}$

$x^{2}$

$x+1$

$5x^{2}$

Correct answer:

$x+1$

Explanation:

If $x$ is greater than 0, then adding 1 to $x$ will make it greater than 1. Taking a number between 0 and 1 to a power results in a smaller number.

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Example Question #1 : Basic Squaring / Square Roots

Evaluate:

0.08²

Possible Answers:

0.00064

0.64

0.00064

0.0064

0.064

Correct answer:

0.0064

Explanation:

0.08 * 0.08

First square 8:

8 * 8 = 64

Then move the decimal four places to the left:

0.0064

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Example Question #11 : How To Find A Proportion

How many $\textup { centimeters}$ are in $5\textup { meters?}$

Possible Answers:

$500\textup { centimeters}$

$5\textup { centimeters}$

$50\textup { centimeters}$

$5\textup,000\textup { centimeters}$

$1.5\textup { centimeters}$

Correct answer:

$500\textup { centimeters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{5\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 5\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 5\ meters}{.01\ meter}= x\ centimeters$

The meters will cancel and we are left with $500\ centimeters$

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Example Question #2 : Conversions

How many $\textup{centimeters}$ are in $13\textup { meters?}$

Possible Answers:

$1\textup,300\textup { centimeters}$

$1.3\textup{ centimeters}$

$.0013\textup { centimeters}$

$130\textup { centimeters}$

$13\textup,000\textup { centimeters}$

Correct answer:

$1\textup,300\textup { centimeters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$

The meters will cancel and we are left with $1,300\ centimeters$

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Example Question #1 : Solving Word Problems With One Unit Conversions

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $98\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$9 \tfrac{1}{6} \ feet$

$9 \tfrac{5}{6} \ feet$

$7 \tfrac{5}{6} \ feet$

$8 \tfrac{5}{6} \ feet$

$8 \tfrac{1}{6} \ feet$

Correct answer:

$8 \tfrac{1}{6} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $98\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$98\ inches:x\ feet\rightarrow \frac{98\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{98\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=98\ inches \times (1\ foot)$

Simplify.

12x=98

Divide both sides by .

$\frac{12x}{12}=\frac{98}{12}$

Solve.

$x=8 \tfrac{2}{12} \ feet$

Reduce.

$x=8 \tfrac{1}{6} \ feet$

The carpenter needs $8 \tfrac{1}{6} \ feet$ of material.

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Example Question #1 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $124\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$10 \tfrac{3}{5} \ feet$

$10 \tfrac{1}{3} \ feet$

$10 \tfrac{2}{3} \ feet$

$11 \tfrac{1}{3} \ feet$

$9 \tfrac{2}{3} \ feet$

Correct answer:

$10 \tfrac{1}{3} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $124\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$124\ inches:x\ feet\rightarrow \frac{124\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{124\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=124\ inches \times (1\ foot)$

Simplify.

12x=124

Divide both sides by .

$\frac{12x}{12}=\frac{124}{12}$

Solve.

$x=10 \tfrac{4}{12} \ feet$

Reduce.

$x=10 \tfrac{1}{3} \ feet$

The carpenter needs $10 \tfrac{1}{3} \ feet$ of material.

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Example Question #2 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $39\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$3 \tfrac{1}{2} \ feet$

$3 \tfrac{2}{5} \ feet$

$3 \tfrac{1}{5} \ feet$

$3 \tfrac{1}{4} \ feet$

$3 \tfrac{3}{4} \ feet$

Correct answer:

$3 \tfrac{1}{4} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $39\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$39\ inches:x\ feet\rightarrow \frac{39\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{39\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=39\ inches \times (1\ foot)$

Simplify.

12x=39

Divide both sides by .

$\frac{12x}{12}=\frac{39}{12}$

Solve.

$x=3 \tfrac{3}{12} \ feet$

Reduce.

$x=3 \tfrac{1}{4} \ feet$

The carpenter needs $3 \tfrac{1}{4} \ feet$ of material.

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PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #531 : Arithmetic

Example Question #1 : How To Square A Decimal

Example Question #1 : How To Square A Decimal

Example Question #1 : Basic Squaring / Square Roots

Example Question #11 : How To Find A Proportion

Example Question #2 : Conversions

Example Question #1 : Solving Word Problems With One Unit Conversions

Example Question #1 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

Example Question #2 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

All PSAT Math Resources

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