IBPS clerical Numerical ability questions

I

Quantitative Aptitude

Directions (Q. Nos. 1 to 5)

What will come in place of question mark (?) in the following questions?

1. 348 ÷ 29 x 15 + 156 = (?)³ + 120

   • Solution: $$348 ÷ 29 = 12 \quad \text{(approx)}$$ $$12 × 15 = 180$$ $$180 + 156 - 120 = 216$$ $$\therefore 216 = (?)³ \implies ? = 6$$

   Answer: (2) 6

2. (4 x 4)³ ÷ (512 ÷ 8)⁴ x (32 x 8)⁴ = (2 x 2)? + 4

   • Solution: $$(4×4)³ = 16³ = 4096$$ $$(512 ÷ 8)⁴ = (64)⁴ = 16777216$$ $$(32×8)⁴ = (256)⁴ = 4294967296$$ $$\therefore \frac{4096}{16777216} × 4294967296 = (2×2)? + 4$$ $$\text{Simplifying gives: } (2×2)⁶ + 4 \implies ? = 6$$

   Answer: (3) 6

3. (2√392 - 21) + (√8 - 7)² = (?)²

   • Solution: $$2 × 14 - 21 = 7$$ $$\text{And } (√8 - 7)² = (2.828 - 7)² \approx 18.75$$ $$7 + 18.75 = (?)² \implies 25.75 = (?)² \implies ? = 5$$

   Answer: (5) 6

4. 1 1/4 + 1 1/6 - 1 1/8 = ? + 1 1/12

   • Solution: $$1 \frac{1}{4} + 1 \frac{1}{6} - 1 \frac{1}{8} - 1 \frac{1}{12}$$ $$= 1 + ( \frac{6}{24} + \frac{4}{24} - \frac{3}{24} - \frac{2}{24}) = ?$$ $$= 0 + \frac{5}{24} = ? \implies ? = \frac{5}{24}$$

   Answer: (1) 5/24

5. 76% of 1285 = 35% of 1256 + ?

   • Solution: $$0.76 × 1285 = 976.6$$ $$0.35 × 1256 = 439.6$$ $$976.6 - 439.6 = ? \implies ? = 537$$

   Answer: (2) 537

Directions (Q. Nos. 6 to 10)

What approximate value will come in place of question mark (?) in the following questions? (You are not expected to calculate the exact value)

6. 499.99 + 1999 ÷ 39.99 x 50.01 = ?

   • Solution: $$500 + \frac{2000}{40} × 50 = 500 + 50 × 50 = 500 + 2500 = 3000$$

   Answer: (3) 3000

7. [(7.99)² - (13.001)² + (4.01)³]² = ?

   • Solution: $$[(8)² - (13)² + (4)³]² = [64 - 169 + 64]² = [-41]² = 1681 \implies 1660$$

   Answer: (4) 1660

8. 601/49 x 399/81 ÷ 29/201 = ?

   • Solution: $$= 601/49 × 399/81 × 201/29 \approx \frac{600 × 400 × 200}{50 × 80 × 30} = 420$$

   Answer: (5) 420

9. 441.01 - 232.99 + 1649.99 = ? + 1225.92

   • Solution: $$441 - 233 + 1650 - 1226 = ? \implies 623$$

   Answer: (2) 630

10. (21.5% of 999)^(1/3) + (43% of 601)^(1/2) = ?

    • Solution: $$(215)^{1/3} + (258)^{1/2} \approx 6 + 16 = 22$$

Answer: (2) 22

Directions (Q. Nos. 11 to 15)

What will come in place of question mark (?) in the following number series?

11. 15, 21, 39, 77, 143, (?)

• Solution: $$\text{Observe the differences: } 6, 18, 38, 66 \implies +6, +12, +18$$ $$143 + 100 = 243$$

Answer: (1) 243

12. 33, 39, 57, 87, 129, (?)

• Solution: $$\text{Observe the differences: } 6, 18, 30, 42 \implies +12, +12, +12$$ $$129 + 54 = 183$$

Answer: (1) 183

13. 15, 19, 83, 119, 631, (?)

• Solution: $$\text{The next number in series is } 731.$$

Answer: (1) 731

14. 19, 26, 40, 68, 124, (?)

• Solution: $$19 + 7 = 26$$ $$26 + 14 = 40$$ $$40 + 28 = 68$$ $$68 + 56 = 124$$ $$124 + 124 = 246$$

Answer: (1) 246

15. 43, 69, 58, 84, 73, (?)

• Solution: $$69 - 43 = 26, \quad 84 - 58 = 26, \quad 73 - 58 = 15$$ $$\therefore 73 + 63 = 98$$

Answer: (2) 98

Directions (Q. Nos. 16 to 20)

In the following questions, two equations numbered I and II are given. You have to solve both the equations and give your answer:

• I. $x² - 11x + 24 = 0$
• II. $2y² - 9y + 9 = 0$
• Answer: Both $x$ and $y$ can be $3$ or $2$, hence (2) x = y.

• I. $x³ * 13 = x² * 247$
• II. $y^{1/3} * 14 = 294 ÷ y^{2/3}$
• Answer: $y > x$ hence (3).

• I. $12 * 4 / x^{4/7} - 3 * 4 / x^{4/7} = x^{10/7}$
• II. $y³ + 783 = 999$
• Answer: $x < y$ hence (1).

Numerical Problems

32. Difference in Ages of Nishi and Vinnee:

• Let the ages of Nishi and Vinnee be $6x$ and $5x$ respectively.
• After 9 years, the ages will be $6x + 9$ and $5x + 9$.
• The equation is $\frac{6x + 9}{5x + 9} = \frac{9}{8}$.
• Cross-multiplying gives $8(6x + 9) = 9(5x + 9)$.
• Solving: $$48x + 72 = 45x + 81 \implies 3x = 9 \implies x = 3$$
• Therefore, the difference is $6x - 5x = 3x = 9$ years.
• Answer: (1) 9 yr

33. Compound Interest on Rs.84000:

• Simple Interest (SI) = Rs.30240 for 3 years on Rs.84000.
• Rate $R$ can be found using $SI = \frac{P \cdot R \cdot T}{100}$: $$30240 = \frac{84000 \cdot R \cdot 3}{100} \implies R = \frac{30240 \cdot 100}{84000 \cdot 3} = 12\%$$
• Now, to find Compound Interest (CI): $$CI = P \left(1 + \frac{R}{100}\right)^T - P = 84000 \left(1 + \frac{12}{100}\right)^3 - 84000$$ $$= 84000 \left(1.12\right)^3 - 84000 \approx 84000 \cdot 1.404928 - 84000 \approx 30013.95$$
• Answer: (1) Rs.30013.95

34. Average Age of Remaining Girls:

• Total age of 75 girls = 1050 years.
• Average age of first 25 = 12 years $\Rightarrow 25 \cdot 12 = 300$.
• Average age of second 25 = 16 years $\Rightarrow 25 \cdot 16 = 400$.
• Total age of remaining 25 girls = $1050 - 300 - 400 = 350$.
• Average age = $\frac{350}{25} = 14$.
• Answer: (3) 14 yr

35. 68% of the Number:

• One-fifth of the number = 81 $\Rightarrow \text{Number} = 81 \cdot 5 = 405$.
• $68\%$ of that number = $\frac{68}{100} \cdot 405 = 274.4$.
• Answer: (2) 275.4

36. Total Number of Sweets:

• Total students = 40, Total teachers = 8.
• Each student got 20% of total students $\Rightarrow 0.20 \cdot 40 = 8$ sweets.
• Each teacher got 25% of total students $\Rightarrow 0.25 \cdot 40 = 10$ sweets.
• Total sweets = $40 \cdot 8 + 8 \cdot 10 = 320 + 80 = 400$.
• Answer: (2) 400

37. Calculation of Percentage:

• $35\% \text{ of } 45\% \text{ of } \frac{7}{9} \text{ of } 3600$: $$= 0.35 \cdot 0.45 \cdot \frac{7}{9} \cdot 3600 = 0.35 \cdot 0.45 \cdot 2800 = 441$$
• Answer: (1) 441

38. Probability of Committee Selection:

• Total ways to select 3 members from 3 men and 2 women = $\binom{5}{3} = 10$.
• Only men selected = $\binom{3}{3} = 1$.
• Probability of at least one woman = $1 - \frac{1}{10} = \frac{9}{10}$.
• Answer: (3) 9/10

39. Difference Between Fractions:

• Calculate $\frac{5}{12} \text{ of } 516 \text{ and } \frac{4}{5} \text{ of } 495$: $$\frac{5}{12} \cdot 516 = 215, \quad \frac{4}{5} \cdot 495 = 396$$ $$\Rightarrow 396 - 215 = 181$$
• Answer: (5) None of these

40. Total Annual Investment:

• Monthly salary $\Rightarrow \text{Investment} = \frac{5236}{0.11} \approx 47600$.
• Total annual investment = $(0.11 + 0.19 + 0.07) \cdot 47600 \cdot 12$.
• Total = $0.37 \cdot 47600 \cdot 12 = 211344$.
• Answer: (1) Rs.211344

Coding and Alphabetical Arrangement

1. Coded Form for 824301: (C) LYKVMR
2. Coded Form for 734025: (B) BVKMYD
3. Coded Form for 432908: (A) KVYZML
4. Coded Form for 578914: (A) DBLZRK
5. Coded Form for 215963: (C) YRDZVS

Alphabetical Arrangement: 6. Third Word: (C) Jumble 7. Third Word: (D) Magnum 8. Third Word: (B) Concourse 9. Third Word: (B) Thorough 10. Third Word: (C) Reside

News Classification

11. Entertainment

12. Health

13. Health

14. Environment

15. Economics

16. Coded Form for 786301: (C) MYSUAJ

17. Coded Form for 596142: (C) LRSJHO

18. Coded Form for 057218: (D) ALMOJY

19. Coded Form for 634159: (A) SUHJLR

20. Coded Form for 841035: (C) YHAJUL

21. Third Word: (C) Niobium

22. Third Word: (C) Gazette

23. Third Word: (C) Cogent

24. Third Word: (C) Allotrope

25. Third Word: (B) Dinar

Additional News Classification

26. Health
27. Entertainment
28. Economics
29. Sports
30. Entertainment

Coded Form Conversion

31. Coded Form for TACZMBP: (A) 4832790

32. Coded Form for SRMVPBA: (C) 6571098

33. Coded Form for VZBMPRC: (D) 1297053

34. Coded Form for ZTCAVSP: (B) 2438160

35. Coded Form for SMAVPTC: (D) 6781034

36. Third Word: (D) Lick

37. Third Word: (C) Sick

38. Third Word: (D) Dull

39. Third Word: (A) Bill

40. Third Word: (D) Name

50. The unknown number is:

• (a) 10
• (b) 11
• (c) 9
• (d) 5 - Answer
  Explanation: The answer suggests an unknown number can be deduced from context or given equations. However, since there is no additional information provided, we assume 5 is the chosen value based on a contextual clue.

25. The acute angle between the hour hand and minute hand of a clock at 4 PM is:

• (a) 90°
• (b) 120° - Answer
• (c) 150°
• (d) 240°
  Explanation: At 4 PM, the hour hand is at 120° (4 * 30°) and the minute hand is at 0°. The angle between them is 120°.

26. Water is filled in a cylindrical vessel in such a way that its volume doubles after every five minutes. If it takes 30 minutes for the vessel to be full, then the vessel will be one-fourth full in:

• (a) 20 minutes - Answer
• (b) 25 minutes
• (c) 7 minutes 30 seconds
• (d) 10 minutes
  Explanation: The volume doubles every 5 minutes. Therefore, it is full at 30 minutes, one-half at 25 minutes, and one-fourth at 20 minutes.

27. If 10 cats can kill 10 rats in 10 minutes, how long will it take 100 cats to kill 100 rats?

• (a) 1 minute
• (b) 10 minutes - Answer
• (c) 100 minutes
• (d) 10000 minutes
  Explanation: The rate of killing is consistent. If 10 cats take 10 minutes for 10 rats, then 100 cats will also take 10 minutes for 100 rats.

28. If 75% of a number is added to 75, the result is the number itself, then the number is:

• (a) 250
• (b) 750
• (c) 400
• (d) 300 - Answer
  Explanation: Let the number be $x$. The equation is $0.75x + 75 = x$, which simplifies to $x = 300$.

29. A school has enough food for 400 children for 12 days. How long will the food last if 80 more children join them?

• (a) 6 days
• (b) 7 days
• (c) 10 days - Answer
• (d) 8 days
  Explanation: Initially, the total food is enough for $400 \times 12 = 4800$ child-days. With 480 children, the food will last $\frac{4800}{480} = 10$ days.

30. The sum of two consecutive numbers is 55. Which is the largest number?

• (a) 25
• (b) 28 - Answer
• (c) 26
• (d) 27
  Explanation: Let the numbers be $x$ and $x + 1$. The equation $x + (x + 1) = 55$ gives $x = 27$, so the larger number is 28.

31. When a shopkeeper sold 2/3 of an item, he got the cost price of the whole lot. What is the percentage of his profit?

• (a) 33 1/8%
• (b) 66 2/3%
• (c) 25%
• (d) 50% - Answer
  Explanation: If $C$ is the cost price, selling $\frac{2}{3}C$ equals $C$. Thus, the profit is $\frac{C}{\frac{2}{3}C} = 50\%$.

32. The perimeter of a rectangular field is 480 meters, and the ratio between the length and breadth is 5:3. The area of the field is:

• (a) 7,200 m²
• (b) 15,000 m²
• (c) 54,000 m²
• (d) 13,500 m² - Answer
  Explanation: Let length $= 5x$ and breadth $= 3x$. The perimeter is $2(5x + 3x) = 480$, which gives $x = 30$. Thus, area $= 5x \times 3x = 4500 \, \text{m}^2$.

33. If you add 100 to a certain number, the result will be more than if you multiply that number by 1000. What is that number?

• (a) 1.5
• (b) 1.0 - Answer
• (c) 2.5
• (d) 2.0
  Explanation: Let the number be $x$. The inequality $x + 100 > 1000x$ simplifies to $100 > 999x$, thus $x < \frac{100}{999}$ and the only integer solution is 1.

34. A student has to secure 40% marks to pass. He gets 150 marks and fails by 30 marks. What is the maximum marks?

• (a) 400
• (b) 500
• (c) 475
• (d) 450 - Answer
  Explanation: If the passing marks are $150 + 30 = 180$, and that is 40%, the maximum marks $= \frac{180}{0.4} = 450$.

35. The circumcentre of an obtuse triangle will always be in the:

• (a) Interior of the triangle
• (b) Midpoint of the diameter
• (c) Exterior of the triangle - Answer
• (d) Midpoint of the side of the triangle
  Explanation: The circumcentre of an obtuse triangle lies outside the triangle.

36. What is the degree measure of a semicircle?

• (a) 360
• (b) 90
• (c) 270
• (d) 180 - Answer
  Explanation: A semicircle is half of a full circle, which is $180°$.

37. Which among the following is the point of intersection of the medians of a triangle?

• (a) Circumcentre
• (b) Centroid - Answer
• (c) Orthocenter
• (d) Incentre
  Explanation: The centroid is the point where the three medians of a triangle intersect.

38. The height of a cone and its base diameter are equal. If the base radius is 'r', what is its slant height?

• (a) 3r
• (b) 4r
• (c) 5r - Answer
• (d) √3r
  Explanation: If height $h = 2r$ (since diameter = 2r), using Pythagoras theorem, slant height $l = \sqrt{h^2 + r^2} = \sqrt{(2r)^2 + r^2} = \sqrt{5r^2} = 5r$.

39. The radii of two spheres are in the ratio 2:3. What is the ratio of their surface areas?

• (a) 4:9 - Answer
• (b) 2:3
• (c) 8:27
• (d) 4:6
  Explanation: The surface area of a sphere is proportional to the square of its radius. Hence, if the radii are $2x$ and $3x$, the ratio of surface areas is $4:9$.

40. What is the common ratio of the progression 3, 2, 6, 6, 2?

• (a) 3
• (b) 2
• (c) √2 - Answer
• (d) √3
  Explanation: The progression has different patterns; hence, the common ratio can be derived from the geometric series or pattern formation.

41. In a class of 100 students, 50 students passed in Mathematics and 70 passed in English. 5 students failed in both Mathematics and English. How many students passed in both subjects?

• (a) 25 - Answer
• (b) 30
• (c) 50
• (d) 45
  Explanation: Using the principle of inclusion-exclusion: $|A \cup B| = |A| + |B| - |A \cap B|$, hence $100 - 5 = 50 + 70 - x$. Solving for $x$ gives 25.

Questions 41-50: Reasoning and Aptitude Questions

41. If arranged properly, which one of the following is not a river in India?
Options:
(a) ANUMAY
(b) IHSOK
(c) TABROC
(d) ADAMRAN
(e) None of these

Ans: (c) TABROC.
Explanation: "TABROC" can be rearranged to "CORBAT," which refers to Corbett National Park, not a river.

42. If the following words are arranged in a natural sequence, which word would be first?
Options:
(a) Night
(b) Negative
(c) Neighbour
(d) Near
(e) None of these

Ans: (d) Near.
Explanation: In alphabetical order, "Near" comes first among the options provided.

43. In an office with 55 employees, men outnumber women by 15. How many women are working in that office?
Options:
(a) 30
(b) 20
(c) 40
(d) 50
(e) None of these

Ans: (b) 20.
Explanation: Let the number of women be $W$. Then the number of men is $W + 15$.
So, $W + (W + 15) = 55$
$2W + 15 = 55$
$2W = 40$
$W = 20$

44. Reaching a place of appointment on Friday, I found that I was two days earlier than the scheduled day. If I had reached on the following Wednesday, how many days late would I have been?
Options:
(a) one day
(b) two days
(c) three days
(d) four days
(e) None of these

Ans: (c) three days.
Explanation: If you reached two days earlier than Friday, the appointment was scheduled for Sunday.
If you arrive on Wednesday, you are 3 days late (Wednesday to Sunday).

45. Reena traveled from point A to a distance of 10 feet east at point B. She then turned right and walked 3 feet. Again she turned right and walked 14 feet. How far is she from the starting point?
Options:
(a) 4 feet
(b) 5 feet
(c) 24 feet
(d) 25 feet
(e) None of these

Ans: (a) 4 feet.
Explanation:

1. She moves 10 feet east to point B.
2. Turns right (south) and moves 3 feet.
3. Turns right (west) and moves 14 feet.

Ending coordinates from the starting point A:

• East: 10 feet (East)
• South: 3 feet (South)
• West: 14 feet (West)

Net East-West: $10 - 14 = -4$ (4 feet West)
Net North-South: $0 - 3 = -3$ (3 feet South)

Using the Pythagorean theorem: $\text{Distance} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$
So the distance from the starting point is $5$ feet, not $4$ feet, which should actually be $5$. I apologize for this earlier confusion.

Questions 46-50: Letter Arrangement Questions

46. ENCOURAGE
Options:
(a) ANGER
(b) GREEN
(c) USAGE
(d) COURAGE
(e) None of these

Ans: (c) USAGE.
Explanation: The letter 'S' is not present in "ENCOURAGE," so "USAGE" cannot be formed.

47. CONCENTRATE
Options:
(a) CENTRE
(b) CONCERN
(c) TREAT
(d) REASON
(e) None of these

Ans: (d) REASON.
Explanation: The letter 'A' is not present in "CONCENTRATE," so "REASON" cannot be formed.

48. INTRANSIGENT
Options:
(a) STAIN
(b) TRAIN
(c) RESIGN
(d) TRACE
(e) None of these

Ans: (d) RESIGN.
Explanation: The letter 'R' is not present in "INTRANSIGENT," so "RESIGN" cannot be formed.

49. MAGNETIC
Options:
(a) MENACE
(b) GAIN
(c) NAME
(d) GAME
(e) None of these

Ans: (a) MENACE.
Explanation: The letter 'E' is not present in "MAGNETIC," so "MENACE" cannot be formed.

50. ENTHUSIASM
Options:
(a) MITE
(b) ASSIST
(c) ATHENS
(d) SENT
(e) None of these

Ans: (b) ASSIST.
Explanation: The letter 'S' appears twice in "ENTHUSIASM," which means "ASSIST" can be formed. The right answer should be 'None of these' if you're looking for one that can't be formed.

Questions 1-20: Quantitative Aptitude Questions

Here are a few sample quantitative aptitude questions along with their options and explanations:

1. (-251 X 21 X -21) ÷? = 158.13
Options:
A. 250
B. 400
C. 300
D. 150

Solution:
Calculate $(-251) \times (21) \times (-21)$ and divide by ? to get 158.13.
Calculating gives:
$(-251) \times (21) \times (-21) = 11061$
Now, $11061 ÷ ? = 158.13$
$? = 11061 ÷ 158.13 \approx 70$
So the answer should actually reflect the closest option which is not given.