HESI A2 — All Questions

What is 3/4 + 1/6?

• a.7/12
• b.11/12✓
• c.1/2
• d.4/10

Find a common denominator of 12: 3/4 = 9/12 and 1/6 = 2/12. Adding gives 9/12 + 2/12 = 11/12, which cannot be reduced.

Subtract: 5/6 - 1/4.

• a.1/2
• b.4/2
• c.2/3
• d.7/12✓

The least common denominator is 12. Convert 5/6 to 10/12 and 1/4 to 3/12. Then 10/12 - 3/12 = 7/12.

Multiply: 2/3 x 3/5.

• a.5/8
• b.1/5
• c.1/3
• d.2/5✓

Multiply numerators and denominators: (2x3)/(3x5) = 6/15. Reducing by dividing top and bottom by 3 gives 2/5.

Divide: 3/8 divided by 1/2.

• a.3/10
• b.3/4✓
• c.3/16
• d.4/3

Dividing by a fraction means multiplying by its reciprocal: 3/8 x 2/1 = 6/8. Reducing 6/8 by 2 gives 3/4.

Convert the mixed number 2 1/4 to an improper fraction.

• a.8/4
• b.9/4✓
• c.6/4
• d.7/4

Multiply the whole number by the denominator and add the numerator: 2 x 4 + 1 = 9. Place that over the original denominator to get 9/4.

What is 0.6 written as a fraction in lowest terms?

• a.3/5✓
• b.6/100
• c.2/3
• d.1/6

The digit 6 is in the tenths place, so 0.6 equals 6/10. Dividing numerator and denominator by 2 reduces it to 3/5.

Add the decimals: 4.25 + 3.7.

• a.8.05
• b.7.95✓
• c.7.32
• d.7.92

Align the decimal points and add: 4.25 + 3.70. The sum of the columns is 7.95.

Multiply: 0.4 x 0.05.

• a.0.002
• b.0.02✓
• c.0.2
• d.0.45

Multiply as whole numbers: 4 x 5 = 20. The two factors have a total of three decimal places, so the product is 0.020, which is 0.02.

What is 12.6 divided by 3?

• a.3.6
• b.42
• c.4.02
• d.4.2✓

Divide 12.6 by 3 by treating it as 126 divided by 3, which is 42, then place the decimal: 4.2. You can check by multiplying 4.2 x 3 = 12.6.

Round 7.348 to the nearest hundredth.

• a.7.348
• b.7.34
• c.7.4
• d.7.35✓

The hundredths digit is 4 and the digit to its right is 8. Because 8 is 5 or greater, round the 4 up to 5, giving 7.35.

Solve the proportion: 3/4 = x/20.

• a.16
• b.10
• c.12
• d.15✓

Cross multiply to get 4x = 3 x 20 = 60. Dividing both sides by 4 gives x = 15.

A recipe uses a ratio of 2 cups flour to 3 cups water. How much water is needed for 8 cups of flour?

• a.12 cups✓
• b.16 cups
• c.10 cups
• d.6 cups

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

If a car travels 150 miles on 5 gallons of gas, what is the rate in miles per gallon?

• a.30 mpg✓
• b.25 mpg
• c.35 mpg
• d.20 mpg

Divide total miles by total gallons: 150 / 5 = 30. The car travels 30 miles per gallon.

The ratio of nurses to patients is 1:8. How many nurses are needed for 56 patients?

• a.6
• b.7✓
• c.8
• d.5

Set up 1/8 = x/56. Cross multiplying gives 8x = 56, so x = 7 nurses.

What is 25% of 80?

• a.25
• b.32
• c.15
• d.20✓

Convert 25% to the decimal 0.25 and multiply: 0.25 x 80 = 20. Alternatively, 25% is one quarter, and 80 / 4 = 20.

15 is what percent of 60?

• a.15%
• b.25%✓
• c.20%
• d.30%

Divide the part by the whole: 15 / 60 = 0.25. Multiplying by 100 converts it to 25%.

A shirt costs $40 and is discounted 15%. What is the sale price?

• a.$34✓
• b.$38
• c.$25
• d.$36

The discount is 0.15 x 40 = $6. Subtracting from the original price gives 40 - 6 = $34.

A population grows from 200 to 250. What is the percent increase?

• a.30%
• b.20%
• c.25%✓
• d.50%

The increase is 250 - 200 = 50. Divide the change by the original amount: 50 / 200 = 0.25, or 25%.

Convert 0.35 to a percent.

• a.0.35%
• b.35%✓
• c.3.5%
• d.350%

To convert a decimal to a percent, multiply by 100, which moves the decimal two places right. So 0.35 becomes 35%.

How many milliliters are in 2.5 liters?

• a.0.0025 mL
• b.2500 mL✓
• c.250 mL
• d.25 mL

One liter equals 1000 milliliters. Multiplying 2.5 x 1000 gives 2500 mL.

Convert 5000 grams to kilograms.

• a.5 kg✓
• b.500 kg
• c.0.5 kg
• d.50 kg

One kilogram equals 1000 grams. Dividing 5000 by 1000 gives 5 kilograms.

A patient weighs 154 pounds. About how many kilograms is that? (1 kg = 2.2 lb)

• a.70 kg✓
• b.154 kg
• c.77 kg
• d.338.8 kg

Divide pounds by 2.2 to get kilograms: 154 / 2.2 = 70. The patient weighs about 70 kilograms.

How many milligrams are in 0.75 grams?

• a.7500 mg
• b.7.5 mg
• c.75 mg
• d.750 mg✓

One gram equals 1000 milligrams. Multiplying 0.75 x 1000 gives 750 mg.

A doctor orders 500 mg of medication. The tablets are 250 mg each. How many tablets are needed?

• a.4 tablets
• b.1 tablet
• c.3 tablets
• d.2 tablets✓

Divide the ordered dose by the dose per tablet: 500 / 250 = 2. The patient needs 2 tablets.

A solution contains 20 mg per 5 mL. How many milliliters provide 60 mg?

• a.12 mL
• b.20 mL
• c.15 mL✓
• d.10 mL

Use the unit rate of 20 mg in every 5 mL. Because 60 mg is 3 times 20 mg, you need 3 x 5 = 15 mL.

Convert the temperature 37 degrees Celsius to Fahrenheit. (F = 9/5 C + 32)

• a.99.5 F
• b.100.4 F
• c.98.6 F✓
• d.96.8 F

Multiply 37 by 9/5 to get 66.6, then add 32. The result is 98.6 degrees Fahrenheit, normal body temperature.

What is the average (mean) of 12, 18, 15, and 15?

• a.13
• b.16
• c.14
• d.15✓

Add the values: 12 + 18 + 15 + 15 = 60. Divide by the count of four numbers: 60 / 4 = 15.

Solve for x: 4x - 3 = 21.

• a.6✓
• b.4
• c.7
• d.5

Add 3 to both sides to get 4x = 24. Dividing both sides by 4 gives x = 6.

Which of these fractions has the greatest value?

• a.2/3✓
• b.5/8
• c.3/5
• d.7/12

Rewrite all four over 120: 2/3 = 80/120, 5/8 = 75/120, 3/5 = 72/120 and 7/12 = 70/120. Comparing numerators shows 80/120 is the largest, so 2/3 wins; the other three fall just below it in the order listed.

Subtract the mixed numbers: 5 1/3 - 2 3/4.

• a.3 5/12
• b.2 7/12✓
• c.2 5/12
• d.3 7/12

The common denominator is 12, giving 5 4/12 - 2 9/12. Since 4/12 is smaller than 9/12, borrow one whole to get 4 16/12 - 2 9/12, which leaves 2 7/12. Answers near 3 come from forgetting to borrow, and 5/12 comes from subtracting the fractions in the wrong order.

Multiply: 1 1/2 x 2 2/3.

• a.4✓
• b.2 2/6
• c.3 1/3
• d.2 1/2

Change both to improper fractions first: 1 1/2 = 3/2 and 2 2/3 = 8/3. Multiplying gives 24/6, which reduces to exactly 4. Multiplying only the whole numbers and only the fractions separately is the usual error and produces the smaller answers shown.

Divide: 3 1/2 divided by 1 1/4.

• a.4 3/8
• b.2 4/5✓
• c.2 1/2
• d.3 1/8

As improper fractions this is 7/2 divided by 5/4. Invert the divisor and multiply: 7/2 x 4/5 = 28/10, which reduces to 14/5 or 2 4/5. Multiplying instead of inverting gives 4 3/8, which is the trap answer here.

Write the improper fraction 17/5 as a mixed number.

• a.3 2/5✓
• b.2 7/5
• c.3 1/5
• d.5 2/3

Divide 17 by 5: it goes in 3 times with 2 left over, so the answer is 3 whole and 2/5. A mixed number is never written with a fraction larger than one, which rules out 2 7/5, and the remainder is 2 rather than 1.

Add: 1/2 + 1/3 + 1/6.

• a.3/11
• b.5/6
• c.1✓
• d.2/3

The least common denominator is 6, so the sum is 3/6 + 2/6 + 1/6 = 6/6, which equals one whole. Adding the numerators and the denominators straight across gives 3/11 and is always wrong, while 5/6 comes from leaving out the 1/6.

What is 2/5 of 45?

• a.22.5
• b.18✓
• c.90
• d.9

Of means multiply, so 45 x 2/5 = 90/5 = 18. Dividing by 2 instead gives 22.5, multiplying by 2 without dividing by 5 gives 90, and dividing by 5 alone leaves 9, which is only one fifth.

Reduce the fraction 36/48 to lowest terms.

• a.3/4✓
• b.6/8
• c.9/16
• d.2/3

The greatest common factor of 36 and 48 is 12, and dividing both by 12 gives 3/4. The value 6/8 is equal but not fully reduced, while 9/16 and 2/3 are not equal to 36/48 at all.

A 900 mL bag of solution is two-thirds empty. How many milliliters have been given?

• a.300 mL
• b.450 mL
• c.600 mL✓
• d.675 mL

Two thirds of 900 is 900 divided by 3, which is 300, multiplied by 2, which is 600 mL. The figure 300 mL is the one third still remaining, 450 mL would be half the bag, and 675 mL is three quarters.

Subtract: 9.4 - 3.75.

• a.6.75
• b.5.75
• c.6.35
• d.5.65✓

Line up the decimal points and write 9.4 as 9.40, then subtract to get 5.65. Borrowing errors in the hundredths column produce 5.75, and subtracting the smaller digit from the larger in each column regardless of position gives the answers in the six range.

Divide: 0.72 by 0.8.

• a.9
• b.0.9✓
• c.0.09
• d.0.576

Move the decimal one place in both numbers to make it 7.2 divided by 8, which equals 0.9. Answers of 9 or 0.09 come from shifting the decimal point the wrong number of places, and 0.576 is the product rather than the quotient.

Round 3,682 to the nearest hundred.

• a.3,600
• b.3,680
• c.4,000
• d.3,700✓

The hundreds digit is 6 and the digit to its right is 8, so round up to 3,700. Rounding down would require that next digit to be 4 or less, 3,680 is rounded to the nearest ten, and 4,000 is rounded to the nearest thousand.

Which decimal has the greatest value?

• a.0.4
• b.0.39
• c.0.409✓
• d.0.4001

Give every number the same number of places: 0.4000, 0.3900, 0.4090 and 0.4001. Comparing them column by column shows 0.4090 is largest. A longer string of digits does not mean a larger number, which is why 0.4001 loses to 0.409.

Write 5/8 as a decimal.

• a.0.625✓
• b.0.58
• c.1.6
• d.0.8

A fraction is a division, so divide 5 by 8 to get 0.625. Reading the digits off the fraction gives 0.58, dividing 8 by 5 instead gives 1.6, and 0.8 would be 4/5.

Multiply: 4.6 x 1,000.

• a.46,000
• b.4,600✓
• c.460
• d.4.600

Multiplying by 1,000 moves the decimal point three places to the right, turning 4.6 into 4,600. Four places would give 46,000, two places would give 460, and leaving the point where it is does not change the value at all.

What is 0.5 + 1/4, written as a decimal?

• a.0.54
• b.0.75✓
• c.0.9
• d.1.5

One quarter written as a decimal is 0.25, so the sum is 0.5 + 0.25 = 0.75. Writing the 4 beside the 5 gives 0.54, treating 1/4 as 0.4 gives 0.9, and adding 0.5 to the 1 of the numerator gives 1.5.

Thirty percent of a number is 27. What is the number?

• a.90✓
• b.8.1
• c.81
• d.57

Divide the part by the rate: 27 divided by 0.30 equals 90. Multiplying instead of dividing gives 8.1, and simply adding 30 to 27 or subtracting gives the other choices. Checking the answer confirms it, since 30 percent of 90 is indeed 27.

A jacket marked $80 is reduced to $68. What is the percent decrease?

• a.15%✓
• b.12%
• c.17.6%
• d.20%

The drop is $12, and 12 divided by the original 80 is 0.15, or 15 percent. Using the dollar amount as the percent gives 12, dividing by the new price of 68 instead of the original gives about 17.6, and 20 percent would have brought the price down to $64.

Convert 3/8 to a percent.

• a.3.8%
• b.37.5%✓
• c.38%
• d.26.7%

Divide 3 by 8 to get 0.375, then move the decimal two places to get 37.5 percent. Reading the digits straight off the fraction gives 3.8, rounding too early gives 38, and dividing 8 by 3 gives about 26.7 percent for the wrong ratio.

A meal costs $48 and the diner leaves a 20 percent tip. What is the total paid?

• a.$9.60
• b.$68.00
• c.$57.60✓
• d.$50.40

Twenty percent of 48 is 9.60, and the question asks for the total, so add it to get $57.60. The figure $9.60 is the tip alone, $68 comes from adding a flat $20, and $50.40 uses a 5 percent tip.

A 500 mL bag of 5% dextrose solution contains how many grams of dextrose?

• a.5 g
• b.25 g✓
• c.50 g
• d.250 g

A 5 percent solution holds 5 grams in every 100 mL, and 500 mL is five of those units, so 5 x 5 = 25 grams. Reading the percent as the answer gives 5 g, multiplying by 10 gives 50 g, and 250 g would be half the bag by weight, which is impossible.

Increase 60 by 25 percent.

• a.15
• b.75✓
• c.85
• d.45

Twenty-five percent of 60 is 15, and increasing means adding it, so the result is 75. The value 15 is only the increase itself, 85 comes from adding 25 rather than 25 percent, and 45 is the result of subtracting instead of adding.