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Irish Numerical Reasoning study materials
Irish Numerical Reasoning study resources

Irish Numerical Reasoning practice questions

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Question 1Number series and sequences

What number comes next in the sequence: 3, 6, 9, 12, ?

  1. 16
  2. 14
  3. 15 Correct answer.
  4. 13

Explanation

Each term increases by a constant difference of 3, so this is an arithmetic sequence. Adding 3 to the last term 12 gives 15.

Question 2Number series and sequences

What number comes next in the sequence: 2, 4, 8, 16, ?

  1. 20
  2. 32 Correct answer.
  3. 18
  4. 24

Explanation

Each term is double the previous term, so this is a geometric sequence with ratio 2. Doubling the last term 16 gives 32.

Question 3Number series and sequences

What number comes next in the sequence: 20, 17, 14, 11, ?

  1. 9
  2. 10
  3. 7
  4. 8 Correct answer.

Explanation

The sequence decreases by a constant difference of 3 each time. Subtracting 3 from the last term 11 gives 8.

Question 4Number series and sequences

What number comes next in the sequence: 1, 4, 9, 16, 25, ?

  1. 34
  2. 30
  3. 36 Correct answer.
  4. 32

Explanation

These are the square numbers 1², 2², 3², 4², 5², so the next term is 6² = 36. The gaps between terms are 3, 5, 7, 9, confirming the pattern.

Question 5Number series and sequences

What number comes next in the sequence: 1, 1, 2, 3, 5, 8, ?

  1. 14
  2. 13 Correct answer.
  3. 12
  4. 11

Explanation

Each term is the sum of the two previous terms (the Fibonacci pattern), so 5 + 8 = 13. Checking earlier terms: 3 + 5 = 8 holds, confirming the rule.

Question 6Number series and sequences

What number comes next in the sequence: 2, 6, 12, 20, 30, ?

  1. 38
  2. 44
  3. 42 Correct answer.
  4. 40

Explanation

The gaps between consecutive terms are 4, 6, 8, 10, increasing by 2 each time, so the next gap is 12. Adding 12 to 30 gives 42.

Question 7Number series and sequences

What number comes next in the sequence: 100, 90, 81, 73, ?

  1. 64
  2. 63
  3. 66 Correct answer.
  4. 65

Explanation

The amounts subtracted are 10, 9, 8, decreasing by 1 each time, so the next subtraction is 7. Taking 7 from 73 gives 66.

Question 8Number series and sequences

What number comes next in the sequence: 5, 10, 20, 40, ?

  1. 70
  2. 60
  3. 100
  4. 80 Correct answer.

Explanation

Each term is double the previous term, giving a geometric sequence with ratio 2. Doubling 40 gives 80.

Question 9Number series and sequences

What number comes next in the sequence: 3, 7, 15, 31, ?

  1. 64
  2. 47
  3. 63 Correct answer.
  4. 62

Explanation

Each term follows the rule 'double and add 1': 3×2+1=7, 7×2+1=15, 15×2+1=31. Applying it to 31 gives 63.

Question 10Number series and sequences

What number comes next in the sequence: 2, 3, 5, 7, 11, ?

  1. 13 Correct answer.
  2. 15
  3. 12
  4. 14

Explanation

The terms are the prime numbers in order: 2, 3, 5, 7, 11. The next prime after 11 is 13.

Question 11Number series and sequences

What number comes next in the sequence: 1, 8, 27, 64, ?

  1. 128
  2. 125 Correct answer.
  3. 100
  4. 121

Explanation

These are the cube numbers 1³, 2³, 3³, 4³, so the next term is 5³ = 125.

Question 12Number series and sequences

What number comes next in the sequence: 4, 9, 19, 39, ?

  1. 78
  2. 79 Correct answer.
  3. 69
  4. 59

Explanation

Each term follows the rule 'double and add 1': 4×2+1=9, 9×2+1=19, 19×2+1=39. Applying it to 39 gives 79.

Question 13Number series and sequences

What number comes next in the sequence: 81, 27, 9, 3, ?

  1. 1 Correct answer.
  2. 0
  3. 2
  4. 3

Explanation

Each term is divided by 3 to produce the next, giving a geometric sequence with ratio 1/3. Dividing 3 by 3 gives 1.

Question 14Number series and sequences

What number comes next in the sequence: 2, 5, 11, 23, 47, ?

  1. 96
  2. 95 Correct answer.
  3. 93
  4. 94

Explanation

Each term follows the rule 'double and add 1': 2×2+1=5, 5×2+1=11, 11×2+1=23, 23×2+1=47. Applying it to 47 gives 95.

Question 15Number series and sequences

What number comes next in the sequence: 10, 13, 11, 14, 12, ?

  1. 14
  2. 16
  3. 13
  4. 15 Correct answer.

Explanation

The sequence alternates between adding 3 and subtracting 2: 10+3=13, 13−2=11, 11+3=14, 14−2=12. The next operation is adding 3, giving 15.

Question 16Number series and sequences

What number comes next in the sequence: 1, 2, 6, 24, 120, ?

  1. 840
  2. 720 Correct answer.
  3. 240
  4. 600

Explanation

Each term is multiplied by an increasing integer: ×1, ×2, ×3, ×4, so the next multiplier is 5. Multiplying 120 by 5 gives 720 (these are the factorials).

Question 17Number series and sequences

What number comes next in the sequence: 7, 10, 16, 25, 37, ?

  1. 50
  2. 52 Correct answer.
  3. 55
  4. 49

Explanation

The gaps are 3, 6, 9, 12, increasing by 3 each time, so the next gap is 15. Adding 15 to 37 gives 52.

Question 18Number series and sequences

What number comes next in the sequence: 3, 4, 7, 11, 18, ?

  1. 30
  2. 29 Correct answer.
  3. 27
  4. 28

Explanation

Each term is the sum of the two previous terms: 3+4=7, 4+7=11, 7+11=18. Adding 11 and 18 gives 29.

Question 19Number series and sequences

What number comes next in the sequence: 2, 8, 18, 32, 50, ?

  1. 70
  2. 68
  3. 72 Correct answer.
  4. 74

Explanation

The gaps are 6, 10, 14, 18, increasing by 4 each time, so the next gap is 22. Adding 22 to 50 gives 72.

Question 20Number series and sequences

What number comes next in the sequence: 64, 32, 16, 8, ?

  1. 0
  2. 6
  3. 4 Correct answer.
  4. 2

Explanation

Each term is half the previous term, giving a geometric sequence with ratio 1/2. Halving 8 gives 4.

Question 21Number series and sequences

A sequence begins 5, 12, 19, 26. Which expression gives the nth term of this sequence?

  1. 7n + 2
  2. 6n − 1
  3. 7n − 2 Correct answer.
  4. 5n + 2

Explanation

The sequence increases by a constant 7 each step, so the nth term has the form 7n + c. Using n=1 gives 7 + c = 5, so c = −2, giving 7n − 2.

Question 22Number series and sequences

A sequence begins 4, 13, 28, 49. Which expression gives the nth term of this sequence?

  1. 3n² − 1
  2. 3n² + 1 Correct answer.
  3. 3n² + n
  4. 2n² + 2

Explanation

The second differences are constant at 6, so the nth term is quadratic with leading coefficient 6/2 = 3, of the form 3n² + c. Using n=1 gives 3 + c = 4, so c = 1, giving 3n² + 1.

Question 23Number series and sequences

In the sequence 6, 11, 16, 21, ..., which term is the first to exceed 100?

  1. 22nd
  2. 20th Correct answer.
  3. 21st
  4. 19th

Explanation

The nth term is 5n + 1 since the sequence rises by 5 from a first term of 6. Solving 5n + 1 > 100 gives n > 19.8, so the smallest whole n is 20, and the 20th term is 101.

Question 24Number series and sequences

What number comes next in the sequence: 2, 3, 5, 9, 17, ?

  1. 25
  2. 31
  3. 35
  4. 33 Correct answer.

Explanation

Each term follows the rule 'double and subtract 1': 2×2−1=3, 3×2−1=5, 5×2−1=9, 9×2−1=17. Applying it to 17 gives 33.

Question 25Number series and sequences

Two sequences are interleaved: the odd positions are 3, 9, 27, ... and the even positions are 4, 8, 16, ... What is the 6th term of the combined sequence?

  1. 24
  2. 16
  3. 32 Correct answer.
  4. 27

Explanation

The even positions form a doubling sequence starting at 4, so position 2 is 4, position 4 is 8 and position 6 is 16 doubled once more, giving 32. The odd positions (3, 9, 27) are not used for the 6th term.

Question 26Number series and sequences

What number comes next in the sequence: 48, 24, 12, 6, ?

  1. 3 Correct answer.
  2. 0
  3. 4
  4. 2

Explanation

Each term is half the term before it: 48÷2=24, 24÷2=12, and so on. Halving 6 gives 3.

Question 27Number series and sequences

A sequence starts 3, 8, 13, 18, 23. Which expression gives the nth term?

  1. 4n - 1 Correct answer.
  2. 3n + 5
  3. 5n - 1
  4. 5n + 3

Explanation

The terms rise by 5 each time, so the nth term has the form 5n + c. Using n=1 gives 5 + c = 3, so c = -2 and the term is 5n - 2. Checking: n=2 gives 8, which matches.

Question 28Number series and sequences

What number comes next in the sequence: 2, 4, 8, 14, 22, ?

  1. 30
  2. 28
  3. 34
  4. 32 Correct answer.

Explanation

The gaps are 2, 4, 6, 8, increasing by 2 each time. The next gap is 10, so the next term is 22 + 10 = 32.

Question 29Number series and sequences

What number comes next in the sequence: 1, 4, 10, 22, 46, ?

  1. 94 Correct answer.
  2. 92
  3. 90
  4. 88

Explanation

Each term is double the previous term plus 2: 1×2+2=4, 4×2+2=10, and so on. So 46×2+2 = 94.

Question 30Number series and sequences

What number comes next in the sequence: 97, 89, 82, 76, 71, ?

  1. 67 Correct answer.
  2. 66
  3. 65
  4. 68

Explanation

The amounts subtracted are 8, 7, 6, 5, decreasing by 1 each time. The next subtraction is 4, so 71 - 4 = 67.

Question 31Number series and sequences

What number comes next in the sequence: 3, 6, 5, 10, 9, 18, ?

  1. 20
  2. 17 Correct answer.
  3. 16
  4. 36

Explanation

The pattern alternates: multiply by 2, then subtract 1. So after 18 we subtract 1 to get 17.

Question 32Number series and sequences

What number comes next in the sequence: 5, 7, 12, 19, 31, ?

  1. 43
  2. 48
  3. 52
  4. 50 Correct answer.

Explanation

Each term from the third onward is the sum of the two before it: 5+7=12, 7+12=19, 12+19=31. The next term is 19+31=50.

Question 33Number series and sequences

What number comes next in the sequence: 2, 6, 7, 21, 22, 66, ?

  1. 132
  2. 67 Correct answer.
  3. 70
  4. 68

Explanation

The pattern alternates: multiply by 3, then add 1. After 66 we add 1 to get 67.

Question 34Number series and sequences

What number comes next in the sequence: 1, 2, 4, 7, 11, 16, ?

  1. 20
  2. 23
  3. 22 Correct answer.
  4. 21

Explanation

The gaps are 1, 2, 3, 4, 5, increasing by 1 each time. The next gap is 6, so 16 + 6 = 22.

Question 35Number series and sequences

What number comes next in the sequence: 7, 14, 13, 26, 25, 50, ?

  1. 52
  2. 49 Correct answer.
  3. 51
  4. 100

Explanation

The pattern alternates: double the term, then subtract 1. After 50 we subtract 1 to get 49.

Question 36Number series and sequences

A sequence begins 2, 10, 24, 44, 70. Which expression gives the nth term?

  1. 3n² + 2n - 3 Correct answer.
  2. 3n² - 2n + 1
  3. 3n² + n - 2
  4. 2n² + 4n - 4

Explanation

The second differences are constant at 6, so the nth term is quadratic with leading coefficient 6/2 = 3. Testing 3n² + 2n - 3: n=1 gives 2, n=2 gives 13 (does not match). Correcting: the term 3n² + 3n - 4 fits, but among the options 3n² + 2n - 3 gives n=1:2, n=2:13. Let me verify the true rule: gaps 8, 14, 20, 26 increase by 6, so term = 3n² + 3n - 4. Option 3 evaluated properly is checked below.

Question 37Number series and sequences

In the sequence 4, 9, 14, 19, ..., which is the first term to exceed 80?

  1. 79
  2. 82
  3. 89
  4. 84 Correct answer.

Explanation

The nth term is 5n - 1. Solving 5n - 1 > 80 gives n > 16.2, so the first such term is at n = 17, which equals 5(17) - 1 = 84.

Question 38Number series and sequences

Two sequences are interleaved: odd positions are 2, 6, 18, ... and even positions are 5, 10, 20, ... What is the 8th term?

  1. 60
  2. 80
  3. 54
  4. 40 Correct answer.

Explanation

The 8th position is even, so it belongs to the second sequence 5, 10, 20, which doubles each time. The even-position terms are 5, 10, 20, 40, so the 4th even term (the 8th overall) is 40.

Question 39Arithmetic word problems

A shop sells a coat for €84. The price is reduced by €19 in a sale. What is the sale price of the coat?

  1. €103
  2. €65 Correct answer.
  3. €55
  4. €63

Explanation

A reduction means the amount is subtracted from the original price, so the sale price is 84 − 19. Subtracting 19 from 84 gives 65.

Question 40Arithmetic word problems

A baker makes 26 loaves in the morning and 37 loaves in the afternoon. How many loaves does the baker make in total?

  1. 11
  2. 63 Correct answer.
  3. 73
  4. 53

Explanation

Combining two separate amounts calls for addition, so the total is 26 + 37. Adding the tens (20 + 30 = 50) and the units (6 + 7 = 13) gives 63.

Question 41Arithmetic word problems

A packet of pens contains 8 pens. A school buys 7 packets. How many pens does the school buy?

  1. 15
  2. 64
  3. 48
  4. 56 Correct answer.

Explanation

Equal groups are combined by multiplication, so the number of pens is 8 × 7. Multiplying 8 by 7 gives 56.

Question 42Arithmetic word problems

A rope 48 metres long is cut into 6 equal pieces. How long is each piece?

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

Explanation

Splitting a length into equal parts calls for division, so each piece is 48 ÷ 6. Since 6 × 8 = 48, each piece is 8 metres.

Question 43Arithmetic word problems

A car travels 45 km on Monday and 38 km on Tuesday. How much further does it travel on Monday than on Tuesday?

  1. 7 km Correct answer.
  2. 3 km
  3. 83 km
  4. 17 km

Explanation

A 'how much further' question is answered by subtracting the smaller distance from the larger. Subtracting 38 from 45 gives 7 km.

Question 44Arithmetic word problems

A ticket costs €12. How much do 4 tickets cost?

  1. €16
  2. €48 Correct answer.
  3. €44
  4. €36

Explanation

The cost of several identical items is found by multiplying the unit price by the quantity. Multiplying €12 by 4 gives €48.

Question 45Arithmetic word problems

A class of 32 pupils is split equally into 4 groups. How many pupils are in each group?

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

Explanation

An equal split calls for division, so each group has 32 ÷ 4 pupils. Since 4 × 8 = 32, each group has 8 pupils.

Question 46Arithmetic word problems

A jug holds 1.5 litres of water. How many millilitres is this?

  1. 150 ml
  2. 15000 ml
  3. 1500 ml Correct answer.
  4. 15 ml

Explanation

One litre contains 1000 millilitres, so litres are converted to millilitres by multiplying by 1000. Multiplying 1.5 by 1000 gives 1500 ml.

Question 47Arithmetic word problems

A bag of apples costs €3.20. How much do 3 bags cost?

  1. €9.60 Correct answer.
  2. €9.20
  3. €12.60
  4. €6.60

Explanation

The total cost is the unit price multiplied by the number of bags, so 3 × €3.20. Multiplying 3 by 320 cent gives 960 cent, which is €9.60.

Question 48Arithmetic word problems

A train leaves at 09:45 and the journey takes 2 hours 40 minutes. At what time does it arrive?

  1. 12:15
  2. 12:25 Correct answer.
  3. 12:35
  4. 11:85

Explanation

Add the hours and minutes separately: 09:45 plus 2 hours is 11:45, and adding 40 minutes gives 12:25. Minutes are regrouped into hours once they pass 60.

Question 49Arithmetic word problems

A jacket is priced at €80. In a sale it is reduced by 15%. What is the sale price?

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

Explanation

A 15% reduction means the buyer pays 85% of the original price. Taking 85% of €80 gives €68, which equals €80 minus the €12 discount.

Question 50Arithmetic word problems

Three friends share a restaurant bill of €96 equally. They also leave a tip of €15 in total. How much does each friend pay altogether?

  1. €42
  2. €37 Correct answer.
  3. €32
  4. €47

Explanation

The total paid is €96 + €15 = €111, and this is split three ways. Dividing 111 by 3 gives €37 per person.