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Praxis Core Math study materials
Praxis Core Math study resources

Praxis Core Math practice questions

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Question 1Number and Quantity

A recipe calls for 3/4 cup of sugar. If a baker makes 2/3 of the recipe, how much sugar is needed?

  1. 9/8 cups
  2. 5/12 cup
  3. 2/3 cup
  4. 1/2 cup Correct answer.

Explanation

Multiply the two fractions: (3/4) × (2/3). The numerator product is 6 and the denominator product is 12, giving 6/12, which simplifies to 1/2 cup.

Question 2Number and Quantity

Which value is greatest?

  1. 3/5
  2. 0.65
  3. 2/3
  4. 0.7 Correct answer.

Explanation

Convert each value to a decimal: 2/3 ≈ 0.667, 3/5 = 0.6, and 0.65 is already decimal. Comparing 0.7, 0.667, 0.65, and 0.6 shows 0.7 is the largest.

Question 3Number and Quantity

What is the value of |−7| + |3|?

  1. −10
  2. 10 Correct answer.
  3. 4
  4. −4

Explanation

Absolute value measures distance from zero, so |−7| = 7 and |3| = 3. Their sum is 7 + 3 = 10, which is positive.

Question 4Number and Quantity

A store sells pens for $1.25 each. What is the total cost of 8 pens?

  1. $9.00
  2. $8.75
  3. $11.25
  4. $10.00 Correct answer.

Explanation

Multiply the unit price by the quantity: 1.25 × 8 = 10.00. So eight pens cost $10.00.

Question 5Number and Quantity

Which number is equivalent to 0.00045 written in scientific notation?

  1. 4.5 × 10^−4 Correct answer.
  2. 4.5 × 10^4
  3. 4.5 × 10^−3
  4. 45 × 10^−5

Explanation

Scientific notation places one nonzero digit before the decimal, giving 4.5. Moving the decimal four places to reach 0.00045 means the exponent is −4.

Question 6Number and Quantity

What is the greatest common factor of 36 and 48?

  1. 6
  2. 24
  3. 12 Correct answer.
  4. 4

Explanation

The prime factorizations are 36 = 2² × 3² and 48 = 2⁴ × 3. Taking the lowest power of each shared prime gives 2² × 3 = 12.

Question 7Number and Quantity

A shirt originally priced at $40 is on sale for 25% off. What is the sale price?

  1. $35
  2. $10
  3. $30 Correct answer.
  4. $25

Explanation

The discount is 25% of $40, which is 0.25 × 40 = $10. Subtracting the discount from the original price gives 40 − 10 = $30.

Question 8Number and Quantity

Which of the following is an irrational number?

  1. −3
  2. √2 Correct answer.
  3. 0.75
  4. 22/7

Explanation

An irrational number cannot be written as a ratio of two integers and has a non-repeating, non-terminating decimal. The square root of 2 is a classic example, whereas the other choices are rational.

Question 9Number and Quantity

A car travels 150 miles on 6 gallons of gas. What is its fuel efficiency in miles per gallon?

  1. 25 Correct answer.
  2. 900
  3. 30
  4. 20

Explanation

Fuel efficiency is miles divided by gallons: 150 ÷ 6 = 25. The unit rate is 25 miles per gallon.

Question 10Number and Quantity

What is 5/8 expressed as a percent?

  1. 58%
  2. 16%
  3. 62.5% Correct answer.
  4. 80%

Explanation

Divide 5 by 8 to get 0.625, then multiply by 100 to convert to a percent: 62.5%.

Question 11Number and Quantity

Simplify the expression 2³ × 2⁴.

  1. 4⁷
  2. 2¹²
  3. 2¹
  4. 2⁷ Correct answer.

Explanation

When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷. This equals 128.

Question 12Number and Quantity

A number n is multiplied by −4 and the result is 28. What is n?

  1. −7 Correct answer.
  2. 7
  3. −112
  4. 32

Explanation

Solve −4n = 28 by dividing both sides by −4, giving n = −7. A negative divided by a negative yields a negative result here because 28 is positive and the divisor is negative.

Question 13Number and Quantity

A jacket costs $80. The price is increased by 15% and then reduced by 15% from the new price. What is the final price?

  1. $78.20 Correct answer.
  2. $68.00
  3. $92.00
  4. $80.00

Explanation

After the increase the price is 80 × 1.15 = $92. Reducing that by 15% gives 92 × 0.85 = $78.20. The two percent changes do not cancel because they apply to different bases.

Question 14Number and Quantity

Which list orders the numbers from least to greatest?

  1. −2.5, 0.3, −1/2, 3/4
  2. 0.3, 3/4, −1/2, −2.5
  3. −1/2, −2.5, 0.3, 3/4
  4. −2.5, −1/2, 0.3, 3/4 Correct answer.

Explanation

Convert to decimals: −2.5, −0.5, 0.3, and 0.75. On a number line, −2.5 is farthest left, followed by −0.5, then 0.3, then 0.75, so the first list is correct.

Question 15Number and Quantity

A recipe uses 2 cups of flour for every 3 cups of milk. If 12 cups of milk are used, how many cups of flour are needed to keep the ratio?

  1. 6
  2. 24
  3. 8 Correct answer.
  4. 18

Explanation

Set up the proportion 2/3 = x/12. Cross-multiplying gives 3x = 24, so x = 8 cups of flour.

Question 16Number and Quantity

What is the value of 3/4 ÷ 1/2?

  1. 3/8
  2. 3/2 Correct answer.
  3. 2/3
  4. 1/2

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 × 2/1 = 6/4 = 3/2.

Question 17Number and Quantity

A taxi charges a flat fee of $3 plus $2 per mile. If a rider pays $17, how many miles was the trip?

  1. 5
  2. 7 Correct answer.
  3. 8.5
  4. 10

Explanation

Set up 3 + 2m = 17. Subtracting 3 gives 2m = 14, so m = 7 miles.

Question 18Number and Quantity

Which expression in scientific notation is equivalent to 0.000000082?

  1. 8.2 × 10^−7
  2. 82 × 10^−9
  3. 8.2 × 10^−8 Correct answer.
  4. 8.2 × 10^8

Explanation

Place the decimal after the first nonzero digit to get 8.2, then count eight places moved to the right, giving an exponent of −8. So the value is 8.2 × 10^−8.

Question 19Number and Quantity

A quantity is 40% of a number, and that quantity is 60. What is the number?

  1. 240
  2. 100
  3. 150 Correct answer.
  4. 24

Explanation

Let x be the number, so 0.40x = 60. Dividing both sides by 0.40 gives x = 150.

Question 20Number and Quantity

What is the least common multiple of 12 and 18?

  1. 216
  2. 72
  3. 36 Correct answer.
  4. 6

Explanation

The prime factorizations are 12 = 2² × 3 and 18 = 2 × 3². Taking the highest power of each prime gives 2² × 3² = 36.

Question 21Number and Quantity

A worker's hourly wage increases from $12 to $15. What is the percent increase?

  1. 3%
  2. 80%
  3. 25% Correct answer.
  4. 20%

Explanation

The increase is 15 − 12 = 3 dollars. Divide the change by the original amount: 3 ÷ 12 = 0.25, which is a 25% increase.

Question 22Number and Quantity

Simplify the expression (3 × 10⁴) × (2 × 10³), writing the result in scientific notation.

  1. 5 × 10⁷
  2. 6 × 10¹²
  3. 6 × 10¹
  4. 6 × 10⁷ Correct answer.

Explanation

Multiply the coefficients: 3 × 2 = 6. Add the exponents: 10⁴ × 10³ = 10⁷. The result is 6 × 10⁷, already in proper scientific notation.

Question 23Number and Quantity

A store offers a 20% discount, and then an additional 10% off the discounted price. What single percent discount is equivalent to the two successive discounts?

  1. 28% Correct answer.
  2. 18%
  3. 25%
  4. 30%

Explanation

After the first discount the customer pays 80% of the original price. The second discount leaves 90% of that, so the final price is 0.80 × 0.90 = 0.72 of the original, a 28% total discount.

Question 24Number and Quantity

If x is a negative number and y is a positive number, which statement must be true?

  1. x × y is negative Correct answer.
  2. x + y is positive
  3. x ÷ y is positive
  4. x − y is positive

Explanation

A negative number times a positive number always yields a negative product. The other statements depend on the relative magnitudes of x and y and are not guaranteed.

Question 25Number and Quantity

A solution is made by mixing 3 parts concentrate with 5 parts water. If 24 liters of solution are made, how many liters of concentrate are used?

  1. 9 Correct answer.
  2. 8
  3. 15
  4. 3

Explanation

The ratio of concentrate to total is 3 to 8 (since 3 + 5 = 8). Multiply the total by that fraction: 24 × 3/8 = 9 liters of concentrate.

Question 26Number and Quantity

A number line shows a point located 3 units to the left of −2. What number is at that point?

  1. 5
  2. −6
  3. 1
  4. −5 Correct answer.

Explanation

Moving left on a number line means subtracting, so the point is at −2 − 3 = −5. The direction sign matters: subtracting a positive amount from a negative number moves further from zero in the negative direction.

Question 27Number and Quantity

Which fraction is equivalent to the repeating decimal 0.4444…?

  1. 4/10
  2. 4/9 Correct answer.
  3. 44/100
  4. 2/5

Explanation

A repeating decimal with a single repeating digit d equals d/9, so 0.4444… = 4/9. Checking by division confirms 4 ÷ 9 = 0.4444… indefinitely.

Question 28Number and Quantity

On the real number line, what is the distance between −7 and 4?

  1. 28
  2. 11 Correct answer.
  3. −3
  4. 3

Explanation

Distance between two points equals the absolute value of their difference: |4 − (−7)| = |11| = 11. Distance is always nonnegative, so the sign of the difference never carries into the answer.

Question 29Number and Quantity

Which value is the additive inverse of −3/4?

  1. −4/3
  2. 4/3
  3. 3/4 Correct answer.
  4. −3/4

Explanation

The additive inverse of a number is the value that sums with it to zero, found by changing its sign. Since −3/4 + 3/4 = 0, the additive inverse is 3/4.

Question 30Number and Quantity

A recipe calls for 3/4 cup of oil. A cook wants to make 2/3 of the recipe. How much oil is needed?

  1. 5/12 cup
  2. 1/2 cup Correct answer.
  3. 1/4 cup
  4. 9/8 cups

Explanation

Taking a fraction of a quantity means multiplying: (2/3) × (3/4) = 6/12 = 1/2. The 3 in the numerator and denominator cancel, leaving 2/4, which simplifies to 1/2.

Question 31Number and Quantity

A checking account balance of −$45 is changed by a deposit of $60. What is the new balance?

  1. −$15
  2. $15 Correct answer.
  3. $105
  4. −$105

Explanation

A deposit adds to the balance, so −45 + 60 = 15. The account moves from a deficit of $45 past zero to a positive balance of $15.

Question 32Number and Quantity

Which statement correctly compares the rational numbers −5/8 and −0.6?

  1. −5/8 < −0.6
  2. −5/8 = −0.6
  3. −5/8 > −0.6 Correct answer.
  4. −5/8 and −0.6 are not comparable

Explanation

Write −0.6 as −6/10 = −3/5 = −24/40 and −5/8 = −25/40. Since −25/40 is farther left, −5/8 is the smaller number, so −5/8 > −0.6 is false; the correct relation is −5/8 < −0.6. Wait: −25/40 < −24/40, so −5/8 < −0.6.

Question 33Number and Quantity

What is the value of |−9| + |4|?

  1. 36
  2. 5
  3. 13 Correct answer.
  4. −5

Explanation

Absolute value gives the distance from zero, so |−9| = 9 and |4| = 4. Their sum is 9 + 4 = 13.

Question 34Number and Quantity

A store marks up a wholesale price by 30%. Later the item is discounted 10% from the marked-up price. If the wholesale price is $50, what is the final price?

  1. $58.50 Correct answer.
  2. $55.00
  3. $65.00
  4. $60.00

Explanation

The markup gives 50 × 1.30 = 65, and the discount applies to that new price: 65 × 0.90 = 58.50. Percent changes applied in sequence multiply rather than add.

Question 35Number and Quantity

A machine produces 480 parts in 8 hours. At the same rate, how many parts will it produce in 5 hours?

  1. 384
  2. 600
  3. 240
  4. 300 Correct answer.

Explanation

The unit rate is 480 ÷ 8 = 60 parts per hour. Multiplying by 5 hours gives 60 × 5 = 300 parts.

Question 36Number and Quantity

A printer can finish a job in 6 hours, and a second printer can finish the same job in 3 hours. Working together at these rates, how long will the job take?

  1. 2 hours Correct answer.
  2. 1.5 hours
  3. 9 hours
  4. 4.5 hours

Explanation

Rates add: the first printer does 1/6 job per hour and the second does 1/3 = 2/6 per hour. Together they do 3/6 = 1/2 job per hour, so the job takes 2 hours.

Question 37Number and Quantity

A quantity decreases from 80 to 68. What is the percent decrease?

  1. 15% Correct answer.
  2. 17.6%
  3. 12%
  4. 85%

Explanation

Percent decrease is the change divided by the original amount: (80 − 68) ÷ 80 = 12/80 = 0.15, or 15%.

Question 38Number and Quantity

A map uses a scale of 1.5 centimeters to represent 12 kilometers. A road measures 7.5 centimeters on the map. What is the actual length of the road?

  1. 36 kilometers
  2. 48 kilometers
  3. 60 kilometers Correct answer.
  4. 90 kilometers

Explanation

Set up the proportion 1.5/12 = 7.5/x. Cross-multiplying gives 1.5x = 90, so x = 60 kilometers.

Question 39Number and Quantity

Which expression is equivalent to (2 × 10⁻³)(4 × 10⁵)?

  1. 8 × 10⁸
  2. 8 × 10⁻¹⁵
  3. 8 × 10² Correct answer.
  4. 6 × 10²

Explanation

Multiply the coefficients and add the exponents: 2 × 4 = 8 and −3 + 5 = 2, giving 8 × 10². This equals 800 in standard form.

Question 40Number and Quantity

A number is divisible by 6. Which statement must therefore be true?

  1. The number is odd
  2. The number is divisible by 12
  3. The number is divisible by both 2 and 3 Correct answer.
  4. The number is divisible by 4

Explanation

Because 6 = 2 × 3 and 2 and 3 are relatively prime, divisibility by 6 requires divisibility by both. For example, 18 is divisible by 6, and it is also divisible by 2 and by 3.

Question 41Number and Quantity

Which value is the multiplicative inverse of 5/6?

  1. 6/5 Correct answer.
  2. −6/5
  3. 5/6
  4. −5/6

Explanation

The multiplicative inverse is the number whose product with the given value is 1, found by swapping numerator and denominator. Since (5/6)(6/5) = 30/30 = 1, the inverse is 6/5.

Question 42Number and Quantity

A survey reports that 3 out of every 8 students walk to school. If 640 students are surveyed, how many walk?

  1. 240 Correct answer.
  2. 192
  3. 480
  4. 320

Explanation

Set up the proportion 3/8 = x/640. Cross-multiplying gives 8x = 1920, so x = 240 students.

Question 43Number and Quantity

A temperature drops 4 degrees Celsius each hour for 3.5 hours. What is the total change in temperature?

  1. −0.875 degrees
  2. 14 degrees
  3. −14 degrees Correct answer.
  4. −7.5 degrees

Explanation

A drop of 4 degrees per hour over 3.5 hours is 4 × 3.5 = 14 degrees downward, written as −14. The sign records direction of change.

Question 44Number and Quantity

A student claims that 0.3333… equals 1/3 exactly. Which reasoning best justifies the claim?

  1. The decimal terminates after many places, so it must equal 1/3
  2. Let x = 0.3333…; then 10x − x = 3, so 9x = 3 and x = 1/3 Correct answer.
  3. The decimal is less than 1, so it equals 1/3
  4. The decimal is close to 0.33, and 0.33 rounds to 1/3

Explanation

Subtracting x from 10x shifts the repeating part so it cancels, leaving 9x = 3 and x = 1/3. This algebraic argument shows the repeating decimal equals the fraction exactly, not approximately.

Question 45Number and Quantity

Which number is a rational number that is not an integer?

  1. √16
  2. π
  3. 0
  4. −7/2 Correct answer.

Explanation

A rational number can be written as a ratio of integers, and −7/2 fits, but it is not a whole number because it equals −3.5. Rational numbers include non-integers such as fractions.

Question 46Number and Quantity

A quantity is increased by 25%, and the result is 90. What was the original quantity?

  1. 67.5
  2. 72 Correct answer.
  3. 112.5
  4. 65

Explanation

An increase of 25% means the result is 1.25 times the original. Dividing 90 by 1.25 gives 72, and checking: 72 × 1.25 = 90.

Question 47Number and Quantity

A jar contains red and blue marbles in the ratio 5:3. If there are 64 marbles in all, how many are blue?

  1. 8
  2. 40
  3. 24 Correct answer.
  4. 21

Explanation

The ratio has 5 + 3 = 8 parts, so each part is 64 ÷ 8 = 8 marbles. Blue marbles are 3 parts, or 3 × 8 = 24.

Question 48Number and Quantity

A car's value of $24,000 depreciates by 20% in the first year and by 15% of the remaining value in the second year. What is its value after two years?

  1. $16,800
  2. $18,000
  3. $16,320 Correct answer.
  4. $15,600

Explanation

After year one: 24,000 × 0.80 = 19,200. After year two: 19,200 × 0.85 = 16,320. Successive percent decreases multiply the factors 0.80 and 0.85.

Question 49Number and Quantity

If a and b are both negative integers, which statement about their product ab is always true?

  1. ab lies between a and b
  2. ab is negative
  3. ab is positive and at least as large as the greater of |a| and |b| Correct answer.
  4. ab is positive but less than both a and b

Explanation

The product of two negative numbers is positive, so ab > 0. Also, since |a| and |b| are each at least 1, the product's magnitude |a||b| is at least max(|a|, |b|), so ab is at least that large.

Question 50Number and Quantity

Which expression equals (3/4) ÷ (9/8)?

  1. 3/2
  2. 27/32
  3. 2/3 Correct answer.
  4. 1/6

Explanation

Dividing by a fraction means multiplying by its reciprocal: (3/4)(8/9) = 24/36 = 2/3. Simplifying before multiplying, 8/4 = 2 and 3/9 = 1/3, giving 2/3.