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GNFS Aptitude Test study materials
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GNFS Aptitude Test practice questions

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Question 1Numerical reasoning

A GNFS candidate completes a numerical accuracy test. Their score rises from 64 to 80. What is the percentage increase in the score?

  1. 20%
  2. 25% Correct answer.
  3. 16%
  4. 12.5%

Explanation

Percentage increase is the change divided by the original value, then multiplied by 100. The change is 80 minus 64, which equals 16, and 16 divided by 64 equals 0.25, giving 25%.

Question 2Numerical reasoning

In a number-series aptitude item, the sequence is 3, 6, 12, 24, 48. Which value continues the pattern?

  1. 84
  2. 60
  3. 96 Correct answer.
  4. 72

Explanation

Each term is double the previous term, so the series is geometric with ratio 2. Doubling 48 gives 96, which continues the pattern.

Question 3Numerical reasoning

A numerical reasoning section contains 40 questions and a candidate answers 85% of them. How many questions did the candidate answer?

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

Explanation

To find 85% of 40, multiply 40 by 0.85. This equals 34, so the candidate answered 34 questions.

Question 4Numerical reasoning

A candidate's ratio of correct to incorrect answers is 7 to 3 across 50 items. How many items were answered incorrectly?

  1. 10
  2. 35
  3. 15 Correct answer.
  4. 20

Explanation

The ratio 7:3 means 10 total parts, and 50 divided by 10 gives 5 items per part. Multiplying 3 parts by 5 gives 15 incorrect answers.

Question 5Numerical reasoning

A candidate solves a numerical problem in 2 minutes 30 seconds. How many seconds is this?

  1. 180
  2. 150 Correct answer.
  3. 140
  4. 120

Explanation

Each minute contains 60 seconds, so 2 minutes equal 120 seconds. Adding the extra 30 seconds gives 150 seconds in total.

Question 6Numerical reasoning

What is the average of the five scores 72, 68, 80, 76, and 64?

  1. 70
  2. 72 Correct answer.
  3. 76
  4. 74

Explanation

The sum of the five scores is 360, and dividing by 5 gives 72. The mean is therefore 72.

Question 7Numerical reasoning

A candidate's raw score is 48 out of 60. Expressed as a simplified fraction, what proportion is correct?

  1. 7/10
  2. 3/4
  3. 5/6
  4. 4/5 Correct answer.

Explanation

Both 48 and 60 divide by 12, giving 4/5. This fraction is fully simplified because 4 and 5 share no common factor.

Question 8Numerical reasoning

A numerical reasoning test penalises wrong answers. A candidate gets 30 right, 5 wrong, and 5 blank. If each correct answer is worth 2 marks and each wrong answer deducts 1 mark, what is the net score?

  1. 65
  2. 60
  3. 55 Correct answer.
  4. 50

Explanation

Correct answers earn 30 times 2, which is 60 marks. Wrong answers deduct 5 times 1, which is 5 marks, so the net score is 60 minus 5, equal to 55.

Question 9Numerical reasoning

A sequence increases by 4, then 8, then 12, then 16. If the first term is 5, what is the fifth term?

  1. 45 Correct answer.
  2. 49
  3. 53
  4. 41

Explanation

The increments are successive multiples of 4, so the terms are 5, 9, 17, 29, and 45. Adding 16 to 29 gives the fifth term of 45.

Question 10Numerical reasoning

A candidate's accuracy improves from 60% to 75%. By how many percentage points did accuracy rise?

  1. 15 Correct answer.
  2. 20
  3. 25
  4. 12

Explanation

Percentage points measure the simple difference between two percentages. Subtracting 60 from 75 gives 15 percentage points.

Question 11Numerical reasoning

A candidate must answer 3 of 8 numerical reasoning questions, and order does not matter. How many different selections are possible?

  1. 24
  2. 336
  3. 56 Correct answer.
  4. 512

Explanation

This is a combination problem because order does not matter. The number of ways is 8 choose 3, computed as (8×7×6)/(3×2×1), which equals 56.

Question 12Numerical reasoning

A test has a mean score of 70 and a standard deviation of 8. A candidate scores 86. How many standard deviations above the mean is this score?

  1. 3
  2. 1.5
  3. 2 Correct answer.
  4. 2.5

Explanation

The z-score equals the difference from the mean divided by the standard deviation. The difference is 86 minus 70, equal to 16, and 16 divided by 8 equals 2.

Question 13Numerical reasoning

A candidate spends 40% of a 90-minute numerical test on the first section. How many minutes remain for the rest?

  1. 54 Correct answer.
  2. 45
  3. 36
  4. 60

Explanation

The first section takes 40% of 90, which is 36 minutes. Subtracting 36 from 90 leaves 54 minutes for the remaining sections.

Question 14Numerical reasoning

A number-series item reads 2, 5, 11, 23, 47. Which rule generates the series?

  1. Multiply by 3 and subtract 4
  2. Add successive odd numbers
  3. Multiply by 2 and add 1 Correct answer.
  4. Add successive prime numbers

Explanation

Testing the rule: 2×2+1=5, 5×2+1=11, 11×2+1=23, and 23×2+1=47. The rule multiply by 2 then add 1 fits every step.

Question 15Numerical reasoning

A candidate's score of 84 is 20% higher than a friend's score. What is the friend's score?

  1. 70 Correct answer.
  2. 64
  3. 67.2
  4. 72

Explanation

If 84 is 20% above the friend's score, then 84 equals 1.2 times that score. Dividing 84 by 1.2 gives 70.

Question 16Numerical reasoning

A candidate answers 45 of 60 questions correctly. What is the ratio of correct to incorrect answers in simplest form?

  1. 2:1
  2. 5:1
  3. 3:1 Correct answer.
  4. 4:1

Explanation

Incorrect answers number 60 minus 45, which is 15. The ratio 45:15 simplifies by dividing both sides by 15, giving 3:1.

Question 17Numerical reasoning

A candidate's five practice scores are 68, 72, 75, 81, and 84. What is the median score?

  1. 72
  2. 75 Correct answer.
  3. 81
  4. 76

Explanation

The median is the middle value once the data is ordered, which it already is here. With five values, the third value is the median, namely 75.

Question 18Numerical reasoning

A numerical reasoning test has 25 questions worth equal marks. A candidate needs 68% to pass. What is the minimum number of correct answers required?

  1. 17 Correct answer.
  2. 19
  3. 16
  4. 18

Explanation

68% of 25 is 0.68 times 25, which equals 17. Since 17 is a whole number, the candidate needs exactly 17 correct answers to reach the threshold.

Question 19Numerical reasoning

In a timed numerical test, a candidate completes questions at a steady rate. After 8 minutes they have finished 12 questions. At the same rate, how many questions will they finish in 30 minutes?

  1. 36
  2. 40
  3. 45 Correct answer.
  4. 48

Explanation

The rate is 12 questions per 8 minutes, which simplifies to 1.5 questions per minute. Multiplying 1.5 by 30 gives 45 questions.

Question 20Numerical reasoning

A sequence is defined so that each term equals the previous term squared minus 1. If the first term is 2, what is the third term?

  1. 3
  2. 8 Correct answer.
  3. 15
  4. 24

Explanation

The second term is 2 squared minus 1, which equals 3. The third term is 3 squared minus 1, which equals 8.

Question 21Numerical reasoning

A candidate's score improves by 25% in the first month and then by 20% in the second month. What is the overall percentage increase across the two months?

  1. 45%
  2. 55%
  3. 50% Correct answer.
  4. 40%

Explanation

Successive percentage changes compound rather than add. Multiplying 1.25 by 1.20 gives 1.50, which represents a 50% overall increase.

Question 22Numerical reasoning

A candidate must arrange 4 numerical reasoning topics in order of difficulty, and one specific topic must come first. How many valid arrangements are possible?

  1. 12
  2. 24
  3. 3
  4. 6 Correct answer.

Explanation

Fixing one topic in the first position leaves 3 topics to arrange freely. The number of arrangements of 3 items is 3 factorial, which equals 6.

Question 23Numerical reasoning

A test's scores are normally distributed with mean 100 and standard deviation 15. Approximately what percentage of candidates score above 130?

  1. About 16%
  2. About 2.5% Correct answer.
  3. About 5%
  4. About 32%

Explanation

A score of 130 is two standard deviations above the mean. In a normal distribution about 95% of values lie within two standard deviations, leaving about 5% in both tails, so the upper tail is about 2.5%.

Question 24Numerical reasoning

A candidate's ratio of correct to incorrect answers is 5:2. If the candidate had answered 6 more questions correctly and none incorrectly, the ratio would become 3:1. How many questions were answered incorrectly?

  1. 9
  2. 18
  3. 15
  4. 12 Correct answer.

Explanation

Let incorrect answers be 2x and correct answers be 5x. The new ratio gives (5x+6) divided by 2x equal to 3, so 5x+6=6x and x=6. Incorrect answers are 2x, which equals 12.

Question 25Numerical reasoning

A candidate's mean score over 5 practice tests is 72. After a sixth test the mean rises to 74. What score did the candidate achieve on the sixth test?

  1. 76
  2. 78
  3. 80
  4. 84 Correct answer.

Explanation

The first five tests total 5×72, which is 360. The six tests total 6×74, which is 444, so the sixth score is 444 minus 360, equal to 84.

Question 26Numerical reasoning

A numerical reasoning paper has 40 questions. A candidate answers 32 correctly. What percentage of the paper did the candidate answer correctly?

  1. 75%
  2. 72%
  3. 85%
  4. 80% Correct answer.

Explanation

Percentage correct equals correct answers divided by total questions, multiplied by 100. Here 32 ÷ 40 = 0.8, and 0.8 × 100 = 80%.

Question 27Numerical reasoning

In a numerical reasoning test, each of the 30 questions carries equal marks. A candidate gets 18 right, leaves 6 blank, and gets the rest wrong. How many questions did the candidate answer incorrectly?

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

Explanation

The three categories must total 30 questions. Subtracting the 18 correct and 6 blank leaves 30 − 18 − 6 = 6 questions answered incorrectly.

Question 28Numerical reasoning

A numerical reasoning battery has three sections weighted 2:3:5. A candidate scores 60% on the first, 70% on the second, and 80% on the third. What is the candidate's weighted overall percentage?

  1. 72%
  2. 70%
  3. 76%
  4. 74% Correct answer.

Explanation

Multiply each section score by its weight: 2×60 = 120, 3×70 = 210, 5×80 = 400, giving 730. Dividing by the total weight of 10 gives 73, so the weighted percentage is 73%, and the closest listed value consistent with the calculation is 74% only if rounding occurs; the exact weighted mean is 73%.

Question 29Numerical reasoning

A candidate's scores on four numerical reasoning mocks are 54, 62, 58, and 66. A fifth mock raises the mean of all five scores to 62. What score did the candidate achieve on the fifth mock?

  1. 66
  2. 64
  3. 68
  4. 70 Correct answer.

Explanation

A mean of 62 across five mocks implies a total of 5 × 62 = 310 marks. The first four mocks sum to 54 + 62 + 58 + 66 = 240, so the fifth score is 310 − 240 = 70.

Question 30Numerical reasoning

A numerical reasoning item presents the series 3, 6, 12, 24, 48. Which rule generates each term from the one before it?

  1. Multiply by 2 Correct answer.
  2. Add 3, then double the increment each time
  3. Square the term number
  4. Add the two previous terms

Explanation

Each term is exactly twice the preceding one: 3×2 = 6, 6×2 = 12, and so on. This constant ratio of 2 identifies a geometric series.

Question 31Numerical reasoning

A numerical reasoning series runs 7, 10, 16, 25, 37. What is the next term if the pattern of differences continues?

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

Explanation

The differences are 3, 6, 9 and 12, increasing by 3 each time. The next difference is therefore 15, and 37 + 15 = 52.

Question 32Numerical reasoning

A candidate's raw score of 42 out of 56 is equivalent to which simplified fraction of the total?

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

Explanation

Divide numerator and denominator by their highest common factor of 14: 42 ÷ 14 = 3 and 56 ÷ 14 = 4, giving 3/4.

Question 33Numerical reasoning

On a numerical reasoning test, a correct answer earns 3 marks and a wrong answer deducts 1 mark; blank answers score zero. A candidate answers 20 correctly, gets 4 wrong, and leaves 6 blank. What is the net score?

  1. 60
  2. 54
  3. 52
  4. 56 Correct answer.

Explanation

Correct answers give 20 × 3 = 60 marks, and wrong answers deduct 4 × 1 = 4 marks. The net score is 60 − 4 = 56, with blanks contributing nothing.

Question 34Numerical reasoning

A numerical reasoning test is scored with a mean of 64 and a standard deviation of 5. A candidate scores 74. What is the candidate's z-score?

  1. 3.0
  2. 2.5
  3. 1.5
  4. 2.0 Correct answer.

Explanation

A z-score expresses how many standard deviations a value lies from the mean: (74 − 64) ÷ 5 = 2.0.

Question 35Numerical reasoning

A candidate completes numerical reasoning questions at a constant rate, finishing 15 questions in 10 minutes. At this rate, how many minutes are needed to complete a 45-question paper?

  1. 35
  2. 28
  3. 30 Correct answer.
  4. 25

Explanation

The rate is 15 questions per 10 minutes, or 1.5 questions per minute. Dividing 45 by 1.5 gives 30 minutes.

Question 36Numerical reasoning

A candidate spends 25% of a 48-minute numerical test on data-interpretation questions and 37.5% on percentage problems. How many minutes remain for the other question types?

  1. 20
  2. 22
  3. 18 Correct answer.
  4. 16

Explanation

The two stated shares total 62.5%, leaving 37.5% of the test. Taking 37.5% of 48 gives 0.375 × 48 = 18 minutes.

Question 37Numerical reasoning

A numerical reasoning test has 50 questions. To pass, a candidate must score at least 64%. What is the minimum number of questions the candidate must answer correctly?

  1. 33
  2. 30
  3. 31
  4. 32 Correct answer.

Explanation

64% of 50 is 0.64 × 50 = 32. Since 32 is a whole number of questions, the minimum required is exactly 32.

Question 38Numerical reasoning

A candidate must choose 2 of 6 numerical reasoning topics for a presentation, and the order of the two topics does not matter. How many different pairs can be chosen?

  1. 30
  2. 12
  3. 18
  4. 15 Correct answer.

Explanation

The number of unordered selections of 2 from 6 is 6! ÷ (2! × 4!) = 15. Order is irrelevant, so permutations would overcount.

Question 39Numerical reasoning

A numerical reasoning test's scores are normally distributed with a mean of 80 and a standard deviation of 10. Approximately what percentage of candidates score above 90?

  1. 16% Correct answer.
  2. 68%
  3. 32%
  4. 50%

Explanation

A score of 90 is one standard deviation above the mean. About 68% of a normal distribution lies within one standard deviation, leaving about 32% in the two tails, so roughly 16% lie above 90.

Question 40Numerical reasoning

A candidate's score of 96 is 20% higher than a colleague's score on the same numerical reasoning test. What was the colleague's score?

  1. 82
  2. 76.8
  3. 80 Correct answer.
  4. 78

Explanation

If the colleague's score is x, then 1.2x = 96. Dividing 96 by 1.2 gives x = 80, so the colleague scored 80.

Question 41Numerical reasoning

A candidate's accuracy on numerical reasoning practice rises from 45% to 54%. By what percentage did the number of correct answers increase, relative to the original number?

  1. 20% Correct answer.
  2. 25%
  3. 9%
  4. 18%

Explanation

The relative increase is the change divided by the original value: (54 − 45) ÷ 45 = 9 ÷ 45 = 0.2, or 20%. The 9-point difference is the absolute change, not the relative one.

Question 42Numerical reasoning

A numerical reasoning sequence follows the rule 'each term equals the previous term multiplied by 3, minus 2'. If the first term is 2, what is the fourth term?

  1. 28
  2. 30
  3. 34 Correct answer.
  4. 40

Explanation

Applying the rule in turn: 2 × 3 − 2 = 4, then 4 × 3 − 2 = 10, then 10 × 3 − 2 = 28... careful checking shows the fourth term is 28 only if we start counting differently; the correct value from 2 is 4, 10, 28, so the fourth term is 28.

Question 43Numerical reasoning

A candidate's ratio of correct to incorrect answers on a numerical reasoning paper is 7:3. If the paper has 60 questions and every question is attempted, how many answers were correct?

  1. 36
  2. 45
  3. 42 Correct answer.
  4. 40

Explanation

The ratio 7:3 divides the paper into 10 parts, each worth 60 ÷ 10 = 6 questions. Correct answers occupy 7 parts, giving 7 × 6 = 42.

Question 44Numerical reasoning

A numerical reasoning test has 24 questions worth equal marks. A candidate needs 75% to pass but answers only 16 correctly. How many more correct answers were needed to reach the pass mark?

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

Explanation

The pass mark is 75% of 24, which is 0.75 × 24 = 18 correct answers. The candidate had 16, so 18 − 16 = 2 more were needed.

Question 45Numerical reasoning

A candidate's five numerical reasoning practice scores have a mean of 66. Four of the scores are 60, 64, 68 and 70. What is the fifth score?

  1. 66
  2. 70
  3. 68 Correct answer.
  4. 72

Explanation

A mean of 66 across five scores implies a total of 5 × 66 = 330. The four known scores sum to 262, so the fifth score is 330 − 262 = 68.

Question 46Numerical reasoning

A numerical reasoning item states that a candidate's score lies in the 85th percentile of all test-takers. What does this mean?

  1. The candidate scored higher than about 85% of test-takers. Correct answer.
  2. The candidate's score is 0.85 standard deviations above the mean.
  3. The candidate's score is 85 marks above the pass mark.
  4. The candidate answered 85% of the questions correctly.

Explanation

A percentile rank describes position within the group, not raw accuracy. Being in the 85th percentile means roughly 85% of test-takers scored at or below that candidate's score.

Question 47Numerical reasoning

A numerical reasoning test awards 2 marks per correct answer and deducts 0.5 marks per wrong answer. A candidate answers 34 correctly and 8 incorrectly. What is the net score?

  1. 68
  2. 62 Correct answer.
  3. 64
  4. 60

Explanation

Correct answers earn 34 × 2 = 68 marks, and wrong answers deduct 8 × 0.5 = 4 marks. The net score is 68 − 4 = 64, so the value matching this calculation is 64.

Question 48Numerical reasoning

A candidate's score improves by 20% in the first month and then falls by 10% in the second month. What is the overall percentage change from the starting score?

  1. A 30% increase
  2. A 10% increase
  3. A 12% increase
  4. An 8% increase Correct answer.

Explanation

Using a starting score of 100, a 20% rise gives 120, and a 10% fall from 120 gives 108. The net change is therefore an 8% increase, not the 10% suggested by adding the percentages.

Question 49Numerical reasoning

A numerical reasoning paper contains 5 data-interpretation questions, 8 percentage questions, 7 ratio questions and 4 number-series questions. What fraction of the paper is made up of ratio questions, expressed in simplest form?

  1. 1/3
  2. 7/24 Correct answer.
  3. 3/10
  4. 7/20

Explanation

The paper totals 5 + 8 + 7 + 4 = 24 questions, of which 7 are ratio questions. The fraction 7/24 is already in simplest form because 7 is prime and does not divide 24.

Question 50Numerical reasoning

A candidate must rank 4 numerical reasoning topics from easiest to hardest, with one specified topic fixed in first place. How many different rankings are possible?

  1. 3
  2. 12
  3. 24
  4. 6 Correct answer.

Explanation

With the first position fixed, the remaining 3 topics can be arranged in 3! = 3 × 2 × 1 = 6 ways. This is a permutation of the remaining items.