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HiSET Math practice questions

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Question 1Numbers and Operations on Numbers

What is the value of the digit 7 in the number 4,752?

  1. 700 Correct answer.
  2. 7
  3. 7,000
  4. 70

Explanation

In a base-ten number each place value is ten times the place to its right. The 7 sits in the hundreds place, so it represents 7 × 100 = 700.

Question 2Numbers and Operations on Numbers

Which number is equal to 3/8 written as a decimal?

  1. 0.83
  2. 0.375 Correct answer.
  3. 0.38
  4. 2.666

Explanation

Divide the numerator by the denominator: 3 ÷ 8 = 0.375. A fraction a/b always equals a divided by b.

Question 3Numbers and Operations on Numbers

What is the least common multiple (LCM) of 6 and 8?

  1. 24 Correct answer.
  2. 14
  3. 2
  4. 48

Explanation

List multiples of each number: 6, 12, 18, 24, ... and 8, 16, 24, ... The smallest value appearing in both lists is 24.

Question 4Numbers and Operations on Numbers

Which list orders the numbers from least to greatest?

  1. 0, -1, -5, 3
  2. -1, -5, 0, 3
  3. 3, 0, -1, -5
  4. -5, -1, 0, 3 Correct answer.

Explanation

On a number line, values increase as you move right. Negative numbers are less than zero, and among negatives the one with the larger absolute value is smaller, so -5 < -1 < 0 < 3.

Question 5Numbers and Operations on Numbers

Compute: -7 + 12

  1. 19
  2. 5 Correct answer.
  3. -5
  4. -19

Explanation

When adding numbers with opposite signs, subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value: 12 − 7 = 5, positive.

Question 6Numbers and Operations on Numbers

What is 0.6 × 0.4?

  1. 2.4
  2. 0.24 Correct answer.
  3. 24
  4. 0.024

Explanation

Multiply 6 × 4 = 24, then place the decimal point so the product has as many decimal places as the two factors combined (one plus one equals two).

Question 7Numbers and Operations on Numbers

Which of these numbers is prime?

  1. 17 Correct answer.
  2. 21
  3. 27
  4. 33

Explanation

A prime number has exactly two factors, 1 and itself. The number 17 has no whole-number factors other than 1 and 17.

Question 8Numbers and Operations on Numbers

A recipe uses 2/3 cup of sugar. If you make 1/2 of the recipe, how much sugar is needed?

  1. 5/6 cup
  2. 1/3 cup Correct answer.
  3. 1/6 cup
  4. 4/3 cups

Explanation

Taking half of a quantity means multiplying by 1/2: (2/3) × (1/2) = 2/6 = 1/3. Multiply numerators and denominators, then simplify.

Question 9Numbers and Operations on Numbers

Evaluate: 8 − 3 × 2

  1. 2 Correct answer.
  2. 16
  3. 10
  4. 5

Explanation

Order of operations requires multiplication before subtraction. Compute 3 × 2 = 6, then 8 − 6 = 2.

Question 10Numbers and Operations on Numbers

What is 5/6 ÷ 2/3?

  1. 10/18
  2. 5/4 Correct answer.
  3. 5/9
  4. 4/5

Explanation

To divide by a fraction, multiply by its reciprocal: (5/6) × (3/2) = 15/12 = 5/4. Simplify the result by dividing numerator and denominator by 3.

Question 11Numbers and Operations on Numbers

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

  1. $10
  2. $15
  3. $30 Correct answer.
  4. $35

Explanation

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

Question 12Numbers and Operations on Numbers

Which fraction is equivalent to 0.45?

  1. 9/20 Correct answer.
  2. 5/9
  3. 45/1000
  4. 4/5

Explanation

0.45 means 45 hundredths, so it equals 45/100. Dividing numerator and denominator by 5 gives 9/20.

Question 13Numbers and Operations on Numbers

What is the greatest common factor (GCF) of 36 and 48?

  1. 12 Correct answer.
  2. 144
  3. 6
  4. 4

Explanation

Factor each number: 36 = 2² × 3² and 48 = 2⁴ × 3. The GCF uses the lowest power of each shared prime: 2² × 3 = 12.

Question 14Numbers and Operations on Numbers

A temperature drops from 8°F to -6°F. By how many degrees did the temperature change?

  1. 48 degrees
  2. 2 degrees
  3. 14 degrees Correct answer.
  4. -14 degrees

Explanation

Change equals final minus initial: -6 − 8 = -14, meaning a drop of 14 degrees. The size of the change is 14 degrees.

Question 15Numbers and Operations on Numbers

Which number is the largest?

  1. 0.65
  2. 0.6
  3. 5/8
  4. 2/3 Correct answer.

Explanation

Convert each to a decimal: 2/3 ≈ 0.667, 0.65, 5/8 = 0.625, and 0.6. Comparing the decimals, 0.667 is the greatest.

Question 16Numbers and Operations on Numbers

Simplify: (2³ × 2⁴) ÷ 2²

  1. 2⁶
  2. 2⁵ Correct answer.
  3. 2¹
  4. 2⁹

Explanation

When multiplying powers with the same base, add exponents: 2³ × 2⁴ = 2⁷. When dividing, subtract exponents: 2⁷ ÷ 2² = 2⁵.

Question 17Numbers and Operations on Numbers

A store marks up a $60 item by 15%. What is the new price?

  1. $66
  2. $69 Correct answer.
  3. $9
  4. $75

Explanation

The markup is 15% of $60: 0.15 × 60 = $9. Add the markup to the original price: 60 + 9 = $69.

Question 18Numbers and Operations on Numbers

What is the value of |−9| + |4|?

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

Explanation

Absolute value gives the distance from zero, so |−9| = 9 and |4| = 4. Adding them gives 9 + 4 = 13.

Question 19Numbers and Operations on Numbers

A number is divisible by 6 exactly when it is divisible by which pair of numbers?

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

Explanation

Since 6 = 2 × 3 and 2 and 3 share no common factor, a number is divisible by 6 exactly when it is divisible by both 2 and 3.

Question 20Numbers and Operations on Numbers

Which expression is equal to 0.00032 in scientific notation?

  1. 32 × 10⁻⁵
  2. 3.2 × 10⁴
  3. 3.2 × 10⁻³
  4. 3.2 × 10⁻⁴ Correct answer.

Explanation

Scientific notation writes a number as a value between 1 and 10 times a power of 10. Moving the decimal point 4 places right from 0.00032 gives 3.2, so the exponent is -4.

Question 21Numbers and Operations on Numbers

A jar contains 12 red, 8 blue, and 5 green marbles. What is the probability of drawing a blue marble at random?

  1. 8/20
  2. 1/3
  3. 8/25 Correct answer.
  4. 8/17

Explanation

Probability equals favorable outcomes divided by total outcomes. There are 8 blue marbles out of 12 + 8 + 5 = 25 total, so the probability is 8/25.

Question 22Numbers and Operations on Numbers

Simplify the expression: 3(2x + 4) − 5x

  1. x + 4
  2. 11x + 12
  3. x + 12 Correct answer.
  4. 6x + 12

Explanation

Distribute the 3 to get 6x + 12, then combine like terms: 6x − 5x = x. The simplified result is x + 12.

Question 23Numbers and Operations on Numbers

A car travels 150 miles in 2.5 hours. What is its average speed in miles per hour?

  1. 75 mph
  2. 37.5 mph
  3. 375 mph
  4. 60 mph Correct answer.

Explanation

Average speed equals distance divided by time: 150 ÷ 2.5 = 60. Dividing by 2.5 is the same as multiplying by 0.4.

Question 24Numbers and Operations on Numbers

Which statement about the product of a nonzero rational number and its reciprocal is always true?

  1. The product equals the number itself.
  2. The product is 1. Correct answer.
  3. The product is negative.
  4. The product is zero.

Explanation

By definition, the reciprocal of a nonzero number a is 1/a, and a × (1/a) = 1. This holds for positive and negative rational numbers alike.

Question 25Numbers and Operations on Numbers

A quantity increases by 20% and then decreases by 20%. Compared with the original amount, the final amount is which of the following?

  1. 20% less
  2. 4% more
  3. 4% less Correct answer.
  4. the same

Explanation

Multiplying by 1.20 and then by 0.80 gives 1.20 × 0.80 = 0.96, which is 96% of the original. The final amount is therefore 4% less than the original.

Question 26Numbers and Operations on Numbers

A checking account has a balance of -$45. A deposit of $120 is made, and then a check for $30 is written. What is the new balance?

  1. $75
  2. $135
  3. $45 Correct answer.
  4. -$15

Explanation

Start at -45, add 120 to get 75, then subtract 30 to get 45. Combining signed quantities means adding deposits and subtracting withdrawals.

Question 27Numbers and Operations on Numbers

Which value is equal to 3/8 written as a decimal?

  1. 2.666
  2. 0.375 Correct answer.
  3. 0.38
  4. 0.267

Explanation

Divide the numerator by the denominator: 3 ÷ 8 = 0.375. The decimal terminates because 8 has only 2 as a prime factor.

Question 28Numbers and Operations on Numbers

What is 2/5 + 3/4?

  1. 23/20 Correct answer.
  2. 5/9
  3. 6/20
  4. 11/20

Explanation

Rewrite with the common denominator 20: 8/20 + 15/20 = 23/20. Denominators are never added directly.

Question 29Numbers and Operations on Numbers

A runner completes 3/4 of a 12-mile course. How many miles has the runner completed?

  1. 9 Correct answer.
  2. 8
  3. 4
  4. 16

Explanation

Multiply the whole distance by the fraction: 12 × 3/4 = 36/4 = 9. Taking a fraction of a quantity means multiplying.

Question 30Numbers and Operations on Numbers

Which list orders the numbers from least to greatest? -2.5, 1/3, -0.75, 0.4

  1. -2.5, 0.4, -0.75, 1/3
  2. -0.75, -2.5, 0.4, 1/3
  3. -2.5, -0.75, 1/3, 0.4 Correct answer.
  4. 1/3, 0.4, -0.75, -2.5

Explanation

Negative numbers come first, and -2.5 is farther left than -0.75. Then 1/3 ≈ 0.333 is less than 0.4.

Question 31Numbers and Operations on Numbers

What is the value of 4² + 2³?

  1. 24 Correct answer.
  2. 64
  3. 12
  4. 18

Explanation

4² = 16 and 2³ = 8, so the sum is 24. An exponent tells how many times the base is used as a factor.

Question 32Numbers and Operations on Numbers

A computer file is 2.4 × 10⁵ kilobytes. How is this number written in standard form?

  1. 240,000 Correct answer.
  2. 240
  3. 2,400,000
  4. 24,000

Explanation

Multiplying by 10⁵ moves the decimal point 5 places to the right: 2.4 becomes 240,000. The exponent gives the number of places to shift.

Question 33Numbers and Operations on Numbers

What is the least common multiple (LCM) of 12 and 18?

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

Explanation

Multiples of 12 are 12, 24, 36, and multiples of 18 are 18, 36, so the smallest shared multiple is 36. The LCM is always at least the larger number.

Question 34Numbers and Operations on Numbers

A jacket is priced at $80. The store applies a 10% discount, and then a 5% sales tax is added to the discounted price. What is the final cost?

  1. $75.60 Correct answer.
  2. $84.00
  3. $76.00
  4. $72.00

Explanation

After the 10% discount the price is $72; adding 5% tax gives 72 × 1.05 = $75.60. Percent changes apply in sequence to the running total.

Question 35Numbers and Operations on Numbers

Which number is the additive inverse of -7/4?

  1. 4/7
  2. 7/4 Correct answer.
  3. -7/4
  4. -4/7

Explanation

The additive inverse is the number that sums to zero with the given number, so it is the opposite sign: 7/4.

Question 36Numbers and Operations on Numbers

A recipe calls for 1 1/2 cups of flour. If a cook triples the recipe, how many cups of flour are needed?

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

Explanation

Multiply the mixed number by 3: 3/2 × 3 = 9/2 = 4 1/2. The whole-number part and the fraction both scale.

Question 37Numbers and Operations on Numbers

A number is divided by 4, and the result is -9. What is the number?

  1. -13
  2. 36
  3. -36 Correct answer.
  4. -2.25

Explanation

Let x/4 = -9, so x = -9 × 4 = -36. Multiplication undoes division, and a negative times a positive stays negative.

Question 38Numbers and Operations on Numbers

Which value is closest to the square root of 50?

  1. 25
  2. 7.1 Correct answer.
  3. 10.0
  4. 5.0

Explanation

Since 7² = 49 and 8² = 64, the square root of 50 is just above 7, about 7.07. Estimating between perfect squares locates the root.

Question 39Numbers and Operations on Numbers

Which expression is equivalent to 0.000705?

  1. 7.05 × 10⁻⁴ Correct answer.
  2. 70.5 × 10⁻⁵
  3. 7.05 × 10⁻³
  4. 7.05 × 10⁴

Explanation

Move the decimal 4 places right to get 7.05, so the exponent is -4. Scientific notation uses a coefficient between 1 and 10.

Question 40Numbers and Operations on Numbers

What is 5/8 expressed as a percent?

  1. 58%
  2. 0.625%
  3. 80%
  4. 62.5% Correct answer.

Explanation

Divide 5 by 8 to get 0.625, then multiply by 100 to get 62.5%. Converting a decimal to a percent shifts the decimal two places.

Question 41Numbers and Operations on Numbers

A credit card balance of $250 grows by 4% interest each month. Which expression gives the balance after one month of interest?

  1. 250 × 1.04 Correct answer.
  2. 250 × 4
  3. 250 + 0.04
  4. 250 × 0.04

Explanation

A 4% increase multiplies the balance by 1 + 0.04 = 1.04. The factor 1.04 keeps the original amount and adds the interest.

Question 42Numbers and Operations on Numbers

Which inequality correctly compares -3/5 and -0.5?

  1. -3/5 ≥ -0.5
  2. -3/5 > -0.5
  3. -3/5 < -0.5 Correct answer.
  4. -3/5 = -0.5

Explanation

Since 3/5 = 0.6, -3/5 = -0.6, which is farther left on the number line than -0.5. For negatives, the larger absolute value is the smaller number.

Question 43Numbers and Operations on Numbers

What is the value of 6 + (-9) − (-4)?

  1. -7
  2. 11
  3. 1 Correct answer.
  4. -1

Explanation

6 + (-9) = -3, and subtracting -4 is the same as adding 4, giving 1. Subtracting a negative reverses to addition.

Question 44Numbers and Operations on Numbers

A number is multiplied by 10³ and the result is 4,500. What is the original number?

  1. 450
  2. 45
  3. 0.45
  4. 4.5 Correct answer.

Explanation

Divide 4,500 by 1,000 to undo the multiplication by 10³, giving 4.5. Dividing by a power of ten shifts the decimal left.

Question 45Numbers and Operations on Numbers

Which fraction is the simplest form of 18/24?

  1. 6/8
  2. 3/4 Correct answer.
  3. 9/12
  4. 2/3

Explanation

The greatest common factor of 18 and 24 is 6, so dividing both by 6 gives 3/4. Simplest form requires the GCF to be removed.

Question 46Numbers and Operations on Numbers

A survey reports that 0.08% of a city's residents own a boat. Written as a fraction in simplest form, what portion is this?

  1. 1/125
  2. 8/100
  3. 2/25
  4. 1/1250 Correct answer.

Explanation

0.08% means 0.08 per 100, or 0.0008, which equals 8/10,000 = 1/1,250. Percent means per hundred, so divide by 100.

Question 47Numbers and Operations on Numbers

A student computes 48 ÷ 6 × 2 and gets 4. What error did the student make?

  1. The student should have added 6 and 2 first.
  2. The student divided before multiplying, which is always wrong.
  3. The student should have treated 6 × 2 as a single term.
  4. The student multiplied before dividing, but operations of equal rank go left to right. Correct answer.

Explanation

Multiplication and division have equal priority, so work left to right: 48 ÷ 6 = 8, then 8 × 2 = 16. Doing 6 × 2 first gives 48 ÷ 12 = 4, which is the error.

Question 48Numbers and Operations on Numbers

Which number is irrational?

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

Explanation

An irrational number cannot be written as a ratio of integers, and √2 has a non-terminating, non-repeating decimal. The others are all rational.

Question 49Numbers and Operations on Numbers

A store sells notebooks at 3 for $4.50. At this rate, what is the cost of 8 notebooks?

  1. $13.50
  2. $9.00
  3. $12.00 Correct answer.
  4. $36.00

Explanation

The unit price is 4.50 ÷ 3 = $1.50 per notebook, so 8 × 1.50 = $12.00. Unit rates let you scale to any quantity.

Question 50Numbers and Operations on Numbers

A number line shows a point exactly halfway between -6 and 10. What number is at that point?

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

Explanation

The midpoint is the average: (-6 + 10) ÷ 2 = 4 ÷ 2 = 2. Averaging the endpoints locates the halfway point.