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LANTITE Numeracy study materials
LANTITE Numeracy study resources

LANTITE Numeracy practice questions

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Question 1Number and algebra

A jacket has a marked price of $80. It is discounted by 15%. What is the sale price?

  1. $68 Correct answer.
  2. $72
  3. $65
  4. $12

Explanation

A discount of 15% means the customer pays 85% of the marked price. Multiplying $80 by 0.85 gives $68.

Question 2Number and algebra

What is the value of 1/4 + 1/8?

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

Explanation

Fractions can only be added once the denominators match. Rewriting 1/4 as 2/8 gives 2/8 + 1/8 = 3/8.

Question 3Number and algebra

What is the value of 20 - 4 × 3 + 6?

  1. 2
  2. 14 Correct answer.
  3. 26
  4. 54

Explanation

Multiplication is done before addition and subtraction, so 4 × 3 = 12 first. Then 20 - 12 + 6 is worked left to right to give 14.

Question 4Number and algebra

The number 4.678 is rounded to two decimal places. What is the result?

  1. 4.67
  2. 4.678
  3. 4.68 Correct answer.
  4. 4.7

Explanation

The third decimal digit decides the rounding of the second. Since the third digit is 8 (5 or more), the 7 in the second place rounds up to 8, giving 4.68.

Question 5Number and algebra

What is the value of -7 + 12 - 5?

  1. -24
  2. 0 Correct answer.
  3. -10
  4. 10

Explanation

Work from left to right on the number line: -7 + 12 = 5, then 5 - 5 = 0.

Question 6Number and algebra

What is 15% of 240?

  1. 36 Correct answer.
  2. 24
  3. 60
  4. 16

Explanation

Convert the percentage to a decimal and multiply: 0.15 × 240 = 36. A useful check is that 10% is 24 and 5% is 12, and 24 + 12 = 36.

Question 7Number and algebra

A sum of $60 is shared between two people in the ratio 2 : 3. How much does the person with the larger share receive?

  1. $30
  2. $24
  3. $36 Correct answer.
  4. $40

Explanation

The ratio has 2 + 3 = 5 equal parts, so each part is $60 ÷ 5 = $12. The larger share is 3 parts, which is 3 × $12 = $36.

Question 8Number and algebra

Which fraction is equal to the decimal 0.375 in simplest form?

  1. 5/8
  2. 3/4
  3. 3/8 Correct answer.
  4. 7/8

Explanation

0.375 means 375 thousandths, and dividing 375 and 1000 by 125 gives 3/8. Checking, 3 ÷ 8 = 0.375.

Question 9Number and algebra

Solve for x: 2x + 9 = 25.

  1. 4.5
  2. 8 Correct answer.
  3. 17
  4. 32

Explanation

Subtract 9 from both sides to get 2x = 16, then divide both sides by 2 to get x = 8.

Question 10Number and algebra

Expand and simplify 2(3x - 4) + 5x.

  1. 11x² - 8
  2. 6x - 4
  3. 11x - 8 Correct answer.
  4. 11x + 8

Explanation

Multiply each term inside the bracket by 2 to get 6x - 8, then collect like terms: 6x + 5x = 11x, so the result is 11x - 8.

Question 11Number and algebra

A sum of $4500 is invested at a simple interest rate of 6% per year. How much interest is earned in 3 years?

  1. $1350
  2. $270
  3. $810 Correct answer.
  4. $2700

Explanation

For simple interest, use I = P × r × t = 4500 × 0.06 × 3 = 810. The interest is $810.

Question 12Number and algebra

A recipe uses 3 cups of flour to make 12 muffins. Keeping the same ratio, how many cups of flour are needed to make 20 muffins?

  1. 5 Correct answer.
  2. 6
  3. 4.5
  4. 4

Explanation

The amount of flour per muffin is 3 ÷ 12 = 0.25 cups. For 20 muffins this is 20 × 0.25 = 5 cups.

Question 13Number and algebra

What is the highest common factor of 36 and 60?

  1. 18
  2. 180
  3. 6
  4. 12 Correct answer.

Explanation

Writing the factors in index form, 36 = 2² × 3² and 60 = 2² × 3 × 5. The highest common factor takes the lowest power of each shared prime: 2² × 3 = 12.

Question 14Number and algebra

Simplify (2⁵ × 2³) ÷ 2⁴, giving the answer as a whole number.

  1. 16 Correct answer.
  2. 32
  3. 8
  4. 64

Explanation

When multiplying powers with the same base, add the indices: 2⁵ × 2³ = 2⁸. When dividing, subtract the indices: 2⁸ ÷ 2⁴ = 2⁴ = 16.

Question 15Number and algebra

The price of a item rises from $48 to $60. What is the percentage increase?

  1. 20%
  2. 25% Correct answer.
  3. 12%
  4. 30%

Explanation

Percentage change is the change divided by the original amount, then multiplied by 100. The increase is $12, and 12 ÷ 48 × 100 = 25%.

Question 16Number and algebra

Solve the inequality 4x + 3 < 19.

  1. x < 5.5
  2. x < 4 Correct answer.
  3. x > 5.5
  4. x > 4

Explanation

Subtract 3 from both sides to get 4x < 16, then divide both sides by 4. Dividing by a positive number keeps the inequality sign the same, so x < 4.

Question 17Number and algebra

Written in scientific notation, 0.00047 is:

  1. 4.7 × 10⁻³
  2. 47 × 10⁻⁵
  3. 4.7 × 10⁻⁴ Correct answer.
  4. 4.7 × 10⁴

Explanation

Scientific notation writes a number as a value between 1 and 10 multiplied by a power of 10. Moving the decimal point 4 places to the right gives 4.7, so the power is 10⁻⁴.

Question 18Number and algebra

A television is advertised at $660 including 10% GST. What is the price of the television before GST is added?

  1. $600 Correct answer.
  2. $60
  3. $594
  4. $650

Explanation

The advertised price is 110% of the pre-GST price, so divide by 1.1: 660 ÷ 1.1 = 600. The pre-GST price is $600.

Question 19Number and algebra

If a = -2 and b = 3, what is the value of a² - 2ab?

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

Explanation

Square the value of a: (-2)² = 4. Then 2ab = 2 × (-2) × 3 = -12, so the expression becomes 4 - (-12) = 16.

Question 20Number and algebra

A car travels 180 km in 2.5 hours. What is its average speed?

  1. 75 km/h
  2. 60 km/h
  3. 90 km/h
  4. 72 km/h Correct answer.

Explanation

Average speed is distance divided by time. Here 180 ÷ 2.5 = 72, so the average speed is 72 km/h.

Question 21Number and algebra

Mia spends 2/5 of her pay on rent and then spends 1/4 of the remaining money on groceries. She saves the last $180. What is her pay?

  1. $360
  2. $450
  3. $600
  4. $400 Correct answer.

Explanation

After rent, 3/5 of the pay remains. Groceries take 1/4 of that, leaving 3/4 × 3/5 = 9/20 of the pay, which equals $180. So the pay is 180 × 20/9 = $400.

Question 22Number and algebra

Two numbers satisfy 2x + y = 11 and x - y = 1. What is the value of y?

  1. 3 Correct answer.
  2. 7
  3. 4
  4. 8

Explanation

Adding the two equations eliminates y: 3x = 12, so x = 4. Substituting into x - y = 1 gives 4 - y = 1, so y = 3.

Question 23Number and algebra

A price is increased by 20% and then the new price is reduced by 20%. What is the overall effect on the original price?

  1. an increase of 4%
  2. a decrease of 40%
  3. a decrease of 4% Correct answer.
  4. no change

Explanation

The two changes multiply as factors: 1.2 × 0.8 = 0.96, which is 96% of the original. The price therefore falls by 4%.

Question 24Number and algebra

Simplify (x + 3)(x - 3) - (x - 2)².

  1. 4x - 13 Correct answer.
  2. 2x² + 4x - 13
  3. -4x - 13
  4. 4x - 5

Explanation

The difference of two squares gives (x + 3)(x - 3) = x² - 9, and expanding the square gives (x - 2)² = x² - 4x + 4. Subtracting gives x² - 9 - x² + 4x - 4 = 4x - 13.

Question 25Number and algebra

One pipe can fill a tank in 6 hours and a second pipe can fill it in 12 hours. Working together, how long will the two pipes take to fill the tank?

  1. 9 hours
  2. 4 hours Correct answer.
  3. 3 hours
  4. 18 hours

Explanation

Add the rates rather than the times: the pipes fill 1/6 and 1/12 of the tank per hour, giving 1/6 + 1/12 = 1/4 of the tank per hour. Filling one whole tank therefore takes 4 hours.

Question 26Number and algebra

Evaluate 18 − 4 × 3 + 5.

  1. 26
  2. 11 Correct answer.
  3. 1
  4. 17

Explanation

Multiplication is performed before addition and subtraction, so 4 × 3 = 12 first. Then work left to right: 18 − 12 + 5 = 11.

Question 27Number and algebra

Calculate −7 + 12 − (−4).

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

Explanation

Subtracting a negative is the same as adding, so the expression becomes −7 + 12 + 4. Combining gives 5 + 4 = 9.

Question 28Number and algebra

Simplify 9m − 4m + 3m.

  1. 8m³
  2. 2m
  3. 16m
  4. 8m Correct answer.

Explanation

All three terms are like terms in m, so the coefficients are combined: 9 − 4 + 3 = 8. The result is 8m.

Question 29Number and algebra

Which of these numbers is prime?

  1. 33
  2. 51
  3. 39
  4. 41 Correct answer.

Explanation

A prime number has exactly two factors, 1 and itself. 41 is not divisible by 2, 3, 5 or 7, so it is prime.

Question 30Number and algebra

What is the lowest common multiple of 6 and 9?

  1. 3
  2. 18 Correct answer.
  3. 54
  4. 36

Explanation

List multiples of each: 6, 12, 18, 24 … and 9, 18, 27 … The smallest value appearing in both lists is 18.

Question 31Number and algebra

Calculate 0.4 × 0.6.

  1. 0.024
  2. 2.4
  3. 0.24 Correct answer.
  4. 1.0

Explanation

Multiply the digits: 4 × 6 = 24. There is one decimal place in each factor, so the answer needs two decimal places: 0.24.

Question 32Number and algebra

What is 1/4 + 1/6?

  1. 2/10
  2. 5/12 Correct answer.
  3. 2/12
  4. 1/24

Explanation

Rewrite the fractions with the common denominator 12: 3/12 + 2/12 = 5/12. The result is already in simplest form.

Question 33Number and algebra

What is 3/4 of 60?

  1. 80
  2. 15
  3. 24
  4. 45 Correct answer.

Explanation

Divide 60 into 4 equal parts to get 15, then multiply by 3: 15 × 3 = 45. Equivalently, 60 × 3 ÷ 4 = 45.

Question 34Number and algebra

On a map with scale 1 : 25 000, a straight road measures 4 cm. What real distance does this represent?

  1. 40 km
  2. 1 km Correct answer.
  3. 250 m
  4. 2.5 km

Explanation

Each centimetre on the map represents 25 000 cm in reality, so 4 cm represents 100 000 cm. Since 100 000 cm = 1000 m = 1 km, the road is 1 km long.

Question 35Number and algebra

$2000 is invested at 5% per year compounded annually. How much interest is earned after 2 years?

  1. $200
  2. $2205
  3. $210
  4. $205 Correct answer.

Explanation

Each year the balance is multiplied by 1.05, so after 2 years the amount is 2000 × 1.05² = $2205. The interest is the amount minus the principal: $2205 − $2000 = $205.

Question 36Number and algebra

Solve for x: x/3 + 4 = 9.

  1. 5
  2. 15 Correct answer.
  3. 27
  4. 39

Explanation

Subtract 4 from both sides to obtain x/3 = 5. Multiplying both sides by 3 gives x = 15.

Question 37Number and algebra

If p = 4 and q = −3, what is the value of 3p − 2q²?

  1. −6 Correct answer.
  2. 18
  3. −24
  4. 30

Explanation

First find q² = (−3)² = 9, then substitute: 3(4) − 2(9) = 12 − 18 = −6. Squaring must be done before multiplying by 2.

Question 38Number and algebra

Which expression is equal to 5⁻²?

  1. 1/25 Correct answer.
  2. −25
  3. 1/10
  4. −1/25

Explanation

A negative index means the reciprocal of the positive power: 5⁻² = 1/5². Since 5² = 25, the value is 1/25.

Question 39Number and algebra

What is (3 × 10⁴) × (2 × 10³) in scientific notation?

  1. 6 × 10⁷ Correct answer.
  2. 6 × 10⁵
  3. 5 × 10⁷
  4. 6 × 10¹²

Explanation

Multiply the coefficients: 3 × 2 = 6. Add the indices when multiplying powers of 10: 10⁴ × 10³ = 10⁷. The result is 6 × 10⁷.

Question 40Number and algebra

A shop sells four sizes of the same cereal. Which pack gives the lowest price per 100 g?

  1. 400 g for $4.80 Correct answer.
  2. 750 g for $9.60
  3. 250 g for $3.20
  4. 500 g for $6.50

Explanation

Divide each price by the number of hundreds of grams: $1.28, $1.30, $1.28 and $1.20 per 100 g respectively. The 400 g pack at $1.20 per 100 g is the cheapest per gram.

Question 41Number and algebra

Simplify 3x × 4x².

  1. 12x⁶
  2. 12x²
  3. 12x³ Correct answer.
  4. 7x³

Explanation

Multiply the coefficients: 3 × 4 = 12. Multiply the powers of x by adding the indices: x¹ × x² = x³. The simplified product is 12x³.

Question 42Number and algebra

A number pattern begins 4, 7, 10, 13, … Which expression gives the nth term?

  1. 3n − 1
  2. 3n + 1 Correct answer.
  3. n + 3
  4. 4n

Explanation

The terms increase by 3 each time, so the rule contains 3n. Testing n = 1 requires 3(1) + 1 = 4, which matches the first term, and the rule gives 7, 10, 13 for later terms.

Question 43Number and algebra

Solve the inequality −2x > 8.

  1. x > −4
  2. x < −4 Correct answer.
  3. x < 4
  4. x > 4

Explanation

Divide both sides by −2, and because the divisor is negative the inequality sign reverses. This gives x < −4.

Question 44Number and algebra

Four workers can build a wall in 9 days, all working at the same rate. How long would six workers take to build the same wall?

  1. 6 days Correct answer.
  2. 4 days
  3. 13.5 days
  4. 9 days

Explanation

The job takes 4 × 9 = 36 worker-days in total. Sharing 36 worker-days among 6 workers gives 36 ÷ 6 = 6 days.

Question 45Number and algebra

Calculate 2/3 ÷ 4/9.

  1. 1 1/2 Correct answer.
  2. 8/27
  3. 1/6
  4. 2/3

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal: 2/3 × 9/4 = 18/12. Simplified, this is 3/2, or 1 1/2.

Question 46Number and algebra

Factorise x² − 5x − 24.

  1. (x − 6)(x + 4)
  2. (x + 8)(x − 3)
  3. (x − 12)(x + 2)
  4. (x − 8)(x + 3) Correct answer.

Explanation

Two numbers must multiply to −24 and add to −5; these are −8 and 3. Hence x² − 5x − 24 = (x − 8)(x + 3).

Question 47Number and algebra

A 40 L container holds an acid solution that is 15% acid. How much pure water must be added to make the solution 10% acid?

  1. 60 L
  2. 26.7 L
  3. 10 L
  4. 20 L Correct answer.

Explanation

The amount of acid is 15% of 40 L = 6 L, and adding water does not change it. For 6 L to be 10% of the new solution, the total must be 6 ÷ 0.10 = 60 L, so 60 − 40 = 20 L of water is added.

Question 48Number and algebra

Solve for x: (x + 1)/2 − (x − 3)/3 = 2.

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

Explanation

Multiply every term by the common denominator 6: 3(x + 1) − 2(x − 3) = 12. Expanding gives 3x + 3 − 2x + 6 = 12, so x + 9 = 12 and x = 3.

Question 49Number and algebra

The formula A = P(1 + rt) gives the amount A when a principal P is invested at simple interest rate r for t years. Which expression gives r in terms of the other variables?

  1. r = (A/P − 1)t
  2. r = (A − P)/(Pt) Correct answer.
  3. r = (A − P)/t
  4. r = A/(Pt) − 1

Explanation

Expand to A = P + Prt, then subtract P to get A − P = Prt. Dividing both sides by Pt isolates r, giving r = (A − P)/(Pt).

Question 50Number and algebra

Simplify (2x²y)³ ÷ (4xy²).

  1. 8x⁵y
  2. 2x⁵y Correct answer.
  3. 2x⁶y³
  4. 2x⁴y²

Explanation

Cube the numerator: 2³ = 8, (x²)³ = x⁶ and y³. Dividing by 4xy² gives 8 ÷ 4 = 2, x⁶ ÷ x = x⁵ and y³ ÷ y² = y, so the result is 2x⁵y.