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AFM Enlistment (Maths) study materials
AFM Enlistment (Maths) study resources

AFM Enlistment (Maths) practice questions

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Question 1Arithmetic and Number Operations

A recruit records a ration pack weight as 2.5 kg. How many grams is that?

  1. 25,000 g
  2. 250 g
  3. 0.25 g
  4. 2,500 g Correct answer.

Explanation

One kilogram equals 1,000 grams, so converting kilograms to grams means multiplying by 1,000. Therefore 2.5 × 1,000 = 2,500 grams.

Question 2Arithmetic and Number Operations

What is the value of the digit 7 in the number 4,703?

  1. 7 units
  2. 7 thousands
  3. 7 hundreds Correct answer.
  4. 7 tens

Explanation

Place value increases by a factor of ten as you move left from the units column. In 4,703 the digits occupy thousands, hundreds, tens and units columns, so the 7 sits in the hundreds column and is worth 700.

Question 3Arithmetic and Number Operations

A section of 48 recruits is split into squads of 6. How many squads are formed?

  1. 8 Correct answer.
  2. 9
  3. 6
  4. 7

Explanation

Splitting a total into equal groups is division, so compute 48 ÷ 6. Since 6 × 8 = 48, the answer is 8 squads with none left over.

Question 4Arithmetic and Number Operations

Which number is even?

  1. 9,871
  2. 5,239
  3. 6,584 Correct answer.
  4. 3,417

Explanation

A whole number is even exactly when its final digit is 0, 2, 4, 6 or 8, because only then is it divisible by 2. The number 6,584 ends in 4, so it is even.

Question 5Arithmetic and Number Operations

A stores ledger records an issue of 350 rounds followed by a return of 120 rounds. What is the net movement?

  1. An increase of 230 rounds
  2. A decrease of 230 rounds Correct answer.
  3. An increase of 470 rounds
  4. A decrease of 470 rounds

Explanation

Issuing stores reduces the holding while returning stores increases it, so the net effect is 350 − 120 = 230. Because the issue is larger, the holding falls by 230 rounds.

Question 6Arithmetic and Number Operations

Round 6,847 to the nearest hundred.

  1. 7,000
  2. 6,900
  3. 6,850
  4. 6,800 Correct answer.

Explanation

The hundreds digit is 8 and the deciding digit in the tens column is 4. Since 4 is less than 5, the hundreds digit stays the same and the remaining digits become zeros, giving 6,800.

Question 7Arithmetic and Number Operations

A training run is timed at 3 minutes 45 seconds. What is this time in seconds only?

  1. 185 seconds
  2. 345 seconds
  3. 245 seconds
  4. 225 seconds Correct answer.

Explanation

Each minute contains 60 seconds, so 3 minutes is 3 × 60 = 180 seconds. Adding the remaining 45 seconds gives 180 + 45 = 225 seconds.

Question 8Arithmetic and Number Operations

Which list shows the numbers in ascending order?

  1. 0.5, 0.4, 0.35, 0.09
  2. 0.35, 0.4, 0.09, 0.5
  3. 0.09, 0.35, 0.4, 0.5 Correct answer.
  4. 0.4, 0.09, 0.35, 0.5

Explanation

To compare decimals of different lengths, align them on the decimal point and compare place by place: 0.09, 0.35, 0.40 and 0.50. Ascending order runs from smallest to largest, giving 0.09, 0.35, 0.4, 0.5.

Question 9Arithmetic and Number Operations

A range day issues 3 boxes of 24 rounds each, then a further 2 boxes of 24. How many rounds are issued in total?

  1. 96
  2. 72
  3. 144
  4. 120 Correct answer.

Explanation

There are 3 + 2 = 5 boxes in total, each holding 24 rounds. Multiplying gives 5 × 24 = 120 rounds, which can be checked as 72 + 48 = 120.

Question 10Arithmetic and Number Operations

A stores total of 1,250 items is shared equally between 5 detachments. How many items does each detachment receive?

  1. 240
  2. 275
  3. 205
  4. 250 Correct answer.

Explanation

Sharing equally means dividing the total by the number of groups, so compute 1,250 ÷ 5. Since 5 × 250 = 1,250, each detachment receives 250 items.

Question 11Arithmetic and Number Operations

What is 3/8 expressed as a decimal?

  1. 0.625
  2. 0.267
  3. 0.125
  4. 0.375 Correct answer.

Explanation

A fraction is converted to a decimal by dividing the numerator by the denominator. Dividing 3 by 8 gives 0.375 exactly, since 8 × 0.375 = 3.

Question 12Arithmetic and Number Operations

A fuel drum holds 240 litres when full. If it is currently 65% full, how many litres does it contain?

  1. 144 litres
  2. 84 litres
  3. 156 litres Correct answer.
  4. 120 litres

Explanation

To find a percentage of a quantity, convert the percentage to a decimal and multiply: 0.65 × 240. This gives 156 litres, which is more than half the drum as expected for 65%.

Question 13Arithmetic and Number Operations

A convoy travels 84 km in 1 hour 30 minutes. What is its average speed in kilometres per hour?

  1. 63 km/h
  2. 56 km/h Correct answer.
  3. 48 km/h
  4. 84 km/h

Explanation

Average speed is distance divided by time, and the time must be in hours. Since 1 hour 30 minutes is 1.5 hours, the speed is 84 ÷ 1.5 = 56 km/h.

Question 14Arithmetic and Number Operations

A crate of 1,500 ration packs is split in the ratio 2 : 3 between two units. How many packs does the larger share contain?

  1. 900 Correct answer.
  2. 1,000
  3. 750
  4. 600

Explanation

The ratio 2 : 3 creates 2 + 3 = 5 equal parts, so one part is 1,500 ÷ 5 = 300 packs. The larger share is 3 parts, giving 3 × 300 = 900 packs.

Question 15Arithmetic and Number Operations

What is the highest common factor of 36 and 60?

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

Explanation

The highest common factor is the largest number dividing both values exactly. Listing factors of 36 and 60 shows the largest shared value is 12, and indeed 36 = 3 × 12 and 60 = 5 × 12.

Question 16Arithmetic and Number Operations

A stores balance of −45 items is adjusted by adding 60 items. What is the new balance?

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

Explanation

Adding a positive number to a negative number moves the value to the right on the number line. So −45 + 60 = 15, meaning the balance becomes positive by 15 items.

Question 17Arithmetic and Number Operations

A vehicle covers 3/5 of a 250 km route before refuelling. How many kilometres remain?

  1. 200 km
  2. 100 km Correct answer.
  3. 50 km
  4. 150 km

Explanation

The fraction covered is 3/5, so the fraction remaining is 1 − 3/5 = 2/5. Two fifths of 250 km is 250 ÷ 5 × 2 = 100 km remaining.

Question 18Arithmetic and Number Operations

A recruit's run times over four sessions are 12.4 s, 11.9 s, 12.6 s and 11.5 s. What is the mean time?

  1. 11.9 s
  2. 12.0 s
  3. 12.1 s Correct answer.
  4. 12.4 s

Explanation

The mean is the total of the values divided by how many there are. The four times total 48.4 s, and 48.4 ÷ 4 = 12.1 s.

Question 19Arithmetic and Number Operations

A fuel allowance of 480 litres is reduced by 15%. How many litres remain?

  1. 408 litres Correct answer.
  2. 465 litres
  3. 415 litres
  4. 72 litres

Explanation

A reduction of 15% leaves 85% of the original allowance. Multiplying 480 by 0.85 gives 408 litres, which can be checked as 480 − 72 = 408.

Question 20Arithmetic and Number Operations

Which number is divisible by 9?

  1. 5,217
  2. 6,346
  3. 7,128 Correct answer.
  4. 4,812

Explanation

A whole number is divisible by 9 exactly when the sum of its digits is a multiple of 9. The digits of 7,128 sum to 18, which is 2 × 9, so 7,128 is divisible by 9.

Question 21Arithmetic and Number Operations

A signal lamp flashes every 12 seconds and a second lamp every 18 seconds. If both flash together now, after how many seconds will they next flash together?

  1. 36 seconds Correct answer.
  2. 30 seconds
  3. 6 seconds
  4. 72 seconds

Explanation

The next simultaneous flash occurs after the lowest common multiple of the two intervals. The multiples of 12 and 18 first coincide at 36, so both lamps flash together again after 36 seconds.

Question 22Arithmetic and Number Operations

A stores issue is recorded as 4.5 × 10³ rounds. What is this in ordinary form?

  1. 4,500 Correct answer.
  2. 45,000
  3. 450
  4. 450,000

Explanation

The factor 10³ equals 1,000, so the value is 4.5 × 1,000. Multiplying by 1,000 moves the decimal point three places to the right, giving 4,500.

Question 23Arithmetic and Number Operations

A convoy of 3 vehicles carries 14 crates each, and each crate holds 25 packs. If 150 packs are then removed, how many packs remain?

  1. 1,000
  2. 950
  3. 900 Correct answer.
  4. 1,050

Explanation

First find the total load: 3 × 14 = 42 crates, and 42 × 25 = 1,050 packs. Removing 150 packs leaves 1,050 − 150 = 900 packs.

Question 24Arithmetic and Number Operations

A recruit's pay of 2,400 units rises by 5% and the following year the new amount rises by a further 5%. What is the final amount?

  1. 2,520 units
  2. 2,640 units
  3. 2,700 units
  4. 2,646 units Correct answer.

Explanation

Successive percentage increases compound rather than simply adding. After two rises the amount is 2,400 × 1.05 × 1.05 = 2,400 × 1.1025 = 2,646 units.

Question 25Arithmetic and Number Operations

What is 0.6 ÷ 0.04?

  1. 150
  2. 15 Correct answer.
  3. 0.15
  4. 1.5

Explanation

Dividing by a decimal is simplified by multiplying both numbers by 100, giving 60 ÷ 4. That equals 15, and the estimate 0.6 ÷ 0.04 ≈ 0.6 ÷ 0.05 = 12 confirms the order of magnitude.

Question 26Arithmetic and Number Operations

A range register records 5,208 rounds fired. What is 5,208 written in words?

  1. Five hundred and twenty-eight
  2. Fifty-two thousand and eight
  3. Five thousand two hundred and eight Correct answer.
  4. Five thousand and twenty-eight

Explanation

Place value splits 5,208 into 5 thousands, 2 hundreds, 0 tens and 8 units, giving 'five thousand two hundred and eight'. The zero tens place is not spoken as a separate word group.

Question 27Arithmetic and Number Operations

A stores tally reads 4,706. What is the value of the digit 7 in this number?

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

Explanation

In 4,706 the digits sit in thousands, hundreds, tens and units columns. The 7 occupies the hundreds column, so its value is 7 × 100 = 700.

Question 28Arithmetic and Number Operations

What is 647 + 285?

  1. 922
  2. 942
  3. 832
  4. 932 Correct answer.

Explanation

Adding the units gives 7 + 5 = 12, so write 2 and carry 1. The tens give 4 + 8 + 1 = 13, so write 3 and carry 1. The hundreds give 6 + 2 + 1 = 9, giving 932.

Question 29Arithmetic and Number Operations

A stores account holds 803 items and 476 are issued. How many items remain?

  1. 327 Correct answer.
  2. 373
  3. 427
  4. 337

Explanation

Subtracting column by column requires borrowing: 3 − 6 needs a ten, giving 13 − 6 = 7. The tens become 9 − 7 = 2 and the hundreds 8 − 4 = 4, so 803 − 476 = 327.

Question 30Arithmetic and Number Operations

A vehicle holds 6 pallets and each pallet carries 48 boxes. How many boxes does the vehicle carry?

  1. 248
  2. 288 Correct answer.
  3. 268
  4. 328

Explanation

Multiply 48 by 6: 40 × 6 = 240 and 8 × 6 = 48, and 240 + 48 = 288. The product is 288 boxes.

Question 31Arithmetic and Number Operations

A stores total of 936 items is packed into boxes of 8. How many boxes are needed?

  1. 107
  2. 117 Correct answer.
  3. 112
  4. 127

Explanation

Dividing 936 by 8: 8 into 9 gives 1 remainder 1; 8 into 13 gives 1 remainder 5; 8 into 56 gives 7. The quotient is 117 with no remainder.

Question 32Arithmetic and Number Operations

Which of these numbers is a prime number?

  1. 63
  2. 59 Correct answer.
  3. 51
  4. 57

Explanation

A prime has exactly two factors, 1 and itself. The number 59 is not divisible by 2, 3, 5 or 7, so it is prime.

Question 33Arithmetic and Number Operations

What is the lowest common multiple of 6 and 8?

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

Explanation

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

Question 34Arithmetic and Number Operations

A rifle range is 300 metres long. What is this distance in centimetres?

  1. 3,000 cm
  2. 30,000 cm Correct answer.
  3. 300,000 cm
  4. 30 cm

Explanation

One metre equals 100 centimetres, so multiply by 100. 300 × 100 = 30,000 centimetres.

Question 35Arithmetic and Number Operations

A stores item is listed at 84.60 units and a discount of 15.75 units applies. What is the reduced price?

  1. 68.95
  2. 69.85
  3. 68.85 Correct answer.
  4. 70.35

Explanation

Align the decimal points and subtract: 84.60 − 15.75. Borrowing gives 0 − 5 → 10 − 5 = 5, then 5 − 7 → 15 − 7 = 8, then 3 − 5 → 13 − 5 = 8, and 7 − 1 = 6, giving 68.85.

Question 36Arithmetic and Number Operations

What is 0.35 written as a fraction in its simplest form?

  1. 7/20 Correct answer.
  2. 3/5
  3. 7/50
  4. 35/100

Explanation

0.35 means 35 hundredths, so write 35/100. Dividing numerator and denominator by their highest common factor of 5 gives 7/20.

Question 37Arithmetic and Number Operations

A stores ledger records an issue of 2/3 of a 540-item stock, then a further 1/6 of the original stock. How many items have been issued in total?

  1. 480
  2. 360
  3. 90
  4. 450 Correct answer.

Explanation

Two-thirds of 540 is 360, and one-sixth of 540 is 90. Adding the two issues gives 360 + 90 = 450 items.

Question 38Arithmetic and Number Operations

A recruit completes a 2.4 km march in 18 minutes. What is the average speed in metres per minute?

  1. 1,333 m/min
  2. 133.3 m/min Correct answer.
  3. 240 m/min
  4. 120 m/min

Explanation

Convert 2.4 km to 2,400 metres, then divide by the 18 minutes: 2,400 ÷ 18 = 133.3 metres per minute (to one decimal place).

Question 39Arithmetic and Number Operations

A stores balance of 1,200 items rises by 5% and the new total then rises by a further 10%. What is the final total?

  1. 1,380
  2. 1,320
  3. 1,260
  4. 1,386 Correct answer.

Explanation

A 5% rise gives 1,200 × 1.05 = 1,260. A further 10% rise gives 1,260 × 1.10 = 1,386, because the second rise applies to the increased total.

Question 40Arithmetic and Number Operations

A stores figure is recorded as 6.2 × 10⁴ items. What is this in ordinary form?

  1. 620,000
  2. 620
  3. 62,000 Correct answer.
  4. 6,200

Explanation

Multiplying by 10⁴ moves the decimal point four places to the right. Starting from 6.2 this gives 62,000.

Question 41Arithmetic and Number Operations

What is the value of 3 + 2 × (8 − 5)²?

  1. 45
  2. 27
  3. 21 Correct answer.
  4. 81

Explanation

Work through the order of operations: brackets first give 8 − 5 = 3, then the square gives 9, then 2 × 9 = 18, and finally 3 + 18 = 21.

Question 42Arithmetic and Number Operations

A convoy of 4 vehicles each carries 12 crates, and each crate holds 15 packs. If 80 packs are unloaded, how many packs remain on the vehicles?

  1. 560
  2. 800
  3. 720
  4. 640 Correct answer.

Explanation

First find the total load: 4 × 12 = 48 crates, and 48 × 15 = 720 packs. Subtracting the 80 unloaded packs gives 720 − 80 = 640.

Question 43Arithmetic and Number Operations

A stores total of 2,100 items is shared between three units in the ratio 1 : 2 : 4. How many items does the largest share contain?

  1. 600
  2. 1,500
  3. 1,200 Correct answer.
  4. 300

Explanation

The ratio has 1 + 2 + 4 = 7 parts, so one part is 2,100 ÷ 7 = 300 items. The largest share is 4 parts, giving 4 × 300 = 1,200 items.

Question 44Arithmetic and Number Operations

A signal is sent every 45 seconds and a second signal every 60 seconds. If both are sent together now, after how many minutes will they next be sent together?

  1. 15 minutes
  2. 3 minutes Correct answer.
  3. 9 minutes
  4. 12 minutes

Explanation

The next simultaneous sending occurs at the lowest common multiple of 45 and 60. Prime factors give 2² × 3² × 5 = 180 seconds, which is 3 minutes.

Question 45Arithmetic and Number Operations

A stores item costs 96 units before a 12.5% surcharge is added. What is the total cost after the surcharge?

  1. 106
  2. 108 Correct answer.
  3. 120
  4. 112

Explanation

A 12.5% surcharge is one-eighth of the price: 96 ÷ 8 = 12. Adding the surcharge to the original price gives 96 + 12 = 108 units.

Question 46Arithmetic and Number Operations

A fuel depot holds 7,500 litres, of which 2/5 is used in the first week and 1/3 of the original total in the second week. How many litres are left?

  1. 4,500
  2. 2,000 Correct answer.
  3. 2,500
  4. 3,000

Explanation

First week: 2/5 × 7,500 = 3,000 litres. Second week: 1/3 × 7,500 = 2,500 litres. Total used is 5,500, so 7,500 − 5,500 = 2,000 litres remain.

Question 47Arithmetic and Number Operations

What is 0.075 ÷ 0.25?

  1. 0.03
  2. 0.003
  3. 0.3 Correct answer.
  4. 3

Explanation

Multiply both numbers by 1,000 to remove the decimals: 75 ÷ 250. Dividing gives 0.3, since 250 × 0.3 = 75.

Question 48Arithmetic and Number Operations

A stores figure of 0.000462 is written in standard form. Which option is correct?

  1. 4.62 × 10⁻³
  2. 4.62 × 10⁻⁴ Correct answer.
  3. 4.62 × 10⁴
  4. 46.2 × 10⁻⁵

Explanation

Standard form requires a number between 1 and 10 multiplied by a power of 10. Moving the decimal point four places right from 0.000462 gives 4.62, so the exponent is −4.

Question 49Arithmetic and Number Operations

A recruit's times over five sessions are 11.8 s, 12.4 s, 11.6 s, 12.2 s and 12.0 s. What is the mean time?

  1. 12.4 s
  2. 11.8 s
  3. 12.2 s
  4. 12.0 s Correct answer.

Explanation

Sum the five times: 11.8 + 12.4 + 11.6 + 12.2 + 12.0 = 60.0 seconds. Dividing by 5 gives a mean of 12.0 seconds.

Question 50Arithmetic and Number Operations

Two stores totals are 3.6 × 10³ items and 4.8 × 10² items. What is their combined total in standard form?

  1. 4.08 × 10²
  2. 8.4 × 10³
  3. 4.08 × 10⁴
  4. 4.08 × 10³ Correct answer.

Explanation

Convert to the same power of ten: 3.6 × 10³ = 3,600 and 4.8 × 10² = 480. The sum is 4,080, which in standard form is 4.08 × 10³.