PAF Officer GDP / GD (Initial Test) Mathematics Fractions — Set 2

1. Question 1

   Q1. Solve the equation: -8/20 + 9/2 - 1/2 = ?

   • A) 20-Mar
   • B) 21-Aug
   • C) 18-May
   • D) 23-Sep

   Answer: 18-May

   Explanation: −8/20 + 9/2 − 1/2 = −2/5 + 4 = 18/5, which equals 3 and 3/5.

2. Question 2

   Q2. What is probability of drawing two clubs from a well shuffled pack of 52 cards?

   • A) 13/51
   • B) Jan-17
   • C) Jan-26
   • D) 13/17

   Answer: Jan-17

   Explanation: Probability of drawing two clubs = C(13,2)/C(52,2) = 78/1326 = 1/17. Show the calculation clearly when solving similar quantitative items.

3. Question 3

   Q3. 2/3 * 5 1/2 * 2 * 7 5/6 * 9/11 = ______________?

   • A) 4.81
   • B) 37
   • C) 47
   • D) 74

   Answer: 47

   Explanation: Converting to improper fractions and multiplying: 2/3 × 11/2 × 2 × 47/6 × 9/11 = 1692/36 = 47.

4. Question 4

   Q4. ³√?/9261 = 11/21

   • A) 121
   • B) 1331
   • C) 14641
   • D) 2662

   Answer: 1331

   Explanation: ∛(x/9261) = 11/21 → x/9261 = (11/21)³ = 1331/9261 → x = 1331.

5. Question 5

   Q5. What fraction is equal to 3.275?

   • A) 13/35
   • B) 3 11/40
   • C) 2 2/7
   • D) None of these

   Answer: 3 11/40

   Explanation: The correct value is 3 11/40. Apply the formula or arithmetic step shown in the question and

6. Question 6

   Q6. What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?

   • A) Rs. 2.04
   • B) Rs. 3.06
   • C) Rs. 4.80
   • D) Rs. 8.30

   Answer: Rs. 2.04

   Explanation: Yearly CI for 1.5 years on Rs. 5000 at 4% = Rs. 304; half-yearly CI = Rs. 306.04. The difference is Rs. 2.04.

7. Question 7

   Q7. The probability that a man will be alive for 25 years is 3/5 and the probability that his wife will be alive for 25 years is 2/3. Find the probability that only the man will be alive for 25 years. Probability

   • A) 02-May
   • B) 01-May
   • C) 03-May
   • D) 04-May

   Answer: 01-May

   Explanation: P(only man alive) = P(man alive) × P(wife not alive) = 3/5 × (1 − 2/3) = 3/5 × 1/3 = 1/5.

8. Question 8

   Q8. The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is_________?

   • A) 30-Jul
   • B) 30/98
   • C) 60/147
   • D) 50/294

   Answer: 30-Jul

   Explanation: The smallest fraction divisible by 6/7, 5/14, and 10/21 is LCM of numerators over GCD of denominators = LCM(6,5,10)/GCD(7,14,21) = 30/7.

9. Question 9

   Q9. [10 + {4 * ({2/3 + 1/4} * √144/121 + 23) ÷ 12 + 5} - 3] = _______?

   • A) 20
   • B) 8
   • C) 10
   • D) 15

   Answer: 20

   Explanation: Evaluating from the innermost brackets outward using BODMAS, the expression simplifies step-by-step to 20.

10. Question 10

    Q10. 5/8 % is equal to what?

    • A) 0.5/8
    • B) 1/160
    • C) 1/200
    • D) 1/800

    Answer: 1/160

    Explanation: 5/8% = 5/(8 × 100) = 5/800 = 1/160. Show the calculation clearly when solving similar quantitative items.

11. Question 11

    Q11. If a man's 1 day work = 1/20 then time required to finish the job(in days):

    • A) 20
    • B) 10
    • C) 25
    • D) 30

    Answer: 20

    Explanation: If 1/20 of the work is done in one day, the total time to finish the entire job is 20 days.

12. Question 12

    Q12. 33/4 of 4500 + ? = 118500

    • A) 8.1375 * 104
    • B) 2.4123 * 104
    • C) 5.124 * 104
    • D) 6.125 * 104

    Answer: 8.1375 * 104

    Explanation: 33/4 of 4500 = 8.25 × 4500 = 37125; ? = 118500 − 37125 = 81375 = 8.1375 × 10⁴.

13. Question 13

    Q13. Which of the following fractions is the largest?

    • A) 19/24
    • B) 13/16
    • C) 31/40
    • D) 63/80

    Answer: 13/16

    Explanation: Converting to decimals: 19/24 ≈ 0.792, 13/16 = 0.8125, 31/40 = 0.775, 63/80 = 0.7875; the largest is 13/16.

14. Question 14

    Q14. A garrison has provisions for a certain number of men for 30 days. If 2/3 of the men do not attend the mess, for how many days will the food last for the remaining men?

    • A) 50 days
    • B) 65 days
    • C) 90 days
    • D) None of these

    Answer: 90 days

    Explanation: The correct value is 90 days. Apply the formula or arithmetic step shown in the question and

15. Question 15

    Q15. If the numerator of a fraction is increased by 140 % and the denominator is increased by 150 % the resultant fraction is 4/15 what is the original fraction?

    • A) 03-May
    • B) May-16
    • C) 02-Sep
    • D) None of these

    Answer: None of these

    Explanation: The correct value is None of these. Apply the formula or arithmetic step shown in the question and

16. Question 16

    Q16. If 15% of 30% of 50% of a number is 90, then what is the number?

    • A) 4000
    • B) 3050
    • C) 4400
    • D) 4500

    Answer: 4000

    Explanation: 0.15 × 0.30 × 0.50 × N = 90 → 0.0225N = 90 → N = 4000.

17. Question 17

    Q17. When 20% of a number is added to the number itself, the result is 102. Find the number. Algebra

    • A) 85
    • B) 90
    • C) 75
    • D) 185

    Answer: 85

    Explanation: 20% of x added to x gives 1.2x = 102; solving gives x = 85.

18. Question 18

    Q18. By converting 75% into a fraction, the answer will be:

    • A) 03-Apr
    • B) 02-Mar
    • C) 01-Mar
    • D) 01-Apr

    Answer: 03-Apr

    Explanation: To convert a percentage to a fraction: 75% = 75/100 = 3/4.

19. Question 19

    Q19. An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?

    • A) 04-Sep
    • B) 02-Mar
    • C) 04-Jul
    • D) 01-Jun

    Answer: 04-Sep

    Explanation: The pipe empties 2/3 of the cistern in 12 minutes, so rate = 1/18 per minute; in 8 minutes it empties 8/18 = 4/9.

20. Question 20

    Q20. On a map, 1/2 inch is equal to 12 kilometers. The distance between two points is 5 2/3 inches. What is the actual distance in kilometers?

    • A) 122 km
    • B) 130 km
    • C) 136 km
    • D) 140 km

    Answer: 136 km

    Explanation: Scale: 1 inch = 24 km; 5⅔ inches = 17/3 inches; distance = 17/3 × 24 = 136 km.