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Question 1Quantitative Techniques and Data Interpretation

A trader marks a shirt at ₹1,200 and then allows a discount of 15%. What is the selling price?

  1. ₹1,080
  2. ₹1,050
  3. ₹1,020 Correct answer.
  4. ₹1,035

Explanation

A 15% discount reduces the marked price to 85% of ₹1,200, since 100% − 15% = 85%. Computing 0.85 × 1200 gives ₹1,020. The discount amount itself is ₹180, so subtracting it from the marked price confirms the same result.

Question 2Quantitative Techniques and Data Interpretation

The average of five consecutive even integers is 32. What is the largest of these integers?

  1. 34
  2. 38
  3. 36 Correct answer.
  4. 40

Explanation

For an odd count of consecutive even integers, the average equals the middle term, so the middle integer is 32. The five integers are 28, 30, 32, 34, 36, making 36 the largest. Adding two steps of 2 above the middle term gives the same answer.

Question 3Quantitative Techniques and Data Interpretation

A sum becomes ₹1,331 from ₹1,000 in 3 years at compound interest compounded annually. What is the annual rate of interest?

  1. 10% Correct answer.
  2. 11%
  3. 9%
  4. 8%

Explanation

The amount factor is 1331/1000 = 1.331, so (1 + r)^3 = 1.331. Since 1.1^3 = 1.331, the rate r equals 0.10, that is 10% per annum. Taking the cube root of the factor is the direct route to the rate.

Question 4Quantitative Techniques and Data Interpretation

A pipe fills a tank in 12 hours and a second pipe fills it in 18 hours. Both are opened together. In how many hours will the tank be full?

  1. 6.0
  2. 8.0
  3. 7.5
  4. 7.2 Correct answer.

Explanation

The first pipe fills 1/12 of the tank per hour and the second 1/18. Their combined rate is 3/36 + 2/36 = 5/36 per hour, so the time needed is 36/5 = 7.2 hours. Working with a common denominator of 36 keeps the fraction addition clean.

Question 5Quantitative Techniques and Data Interpretation

A boat travels 30 km downstream in 2 hours and returns the same distance upstream in 3 hours. What is the speed of the stream?

  1. 1.5 km/h
  2. 3.0 km/h
  3. 2.0 km/h
  4. 2.5 km/h Correct answer.

Explanation

Downstream speed is 30/2 = 15 km/h and upstream speed is 30/3 = 10 km/h. The stream speed is half the difference of these speeds, namely (15 − 10)/2 = 2.5 km/h. The boat's still-water speed would be the average, 12.5 km/h.

Question 6Quantitative Techniques and Data Interpretation

What is the value of the expression 15% of 240 plus 25% of 160?

  1. 78
  2. 76
  3. 74
  4. 72 Correct answer.

Explanation

15% of 240 is 0.15 × 240 = 36, and 25% of 160 is 0.25 × 160 = 40. Adding the two parts gives 36 + 40 = 72. Converting each percentage to a decimal before multiplying avoids place-value slips.

Question 7Quantitative Techniques and Data Interpretation

A train 180 m long crosses a pole in 12 seconds. How long will it take to cross a bridge 240 m long?

  1. 28 seconds Correct answer.
  2. 24 seconds
  3. 26 seconds
  4. 30 seconds

Explanation

Crossing a pole means covering the train's own length, so the speed is 180/12 = 15 m/s. To cross a 240 m bridge the train must cover 180 + 240 = 420 m. Dividing 420 by 15 gives 28 seconds.

Question 8Quantitative Techniques and Data Interpretation

The ratio of two numbers is 3:5, and their sum is 96. What is the smaller number?

  1. 60
  2. 40
  3. 32
  4. 36 Correct answer.

Explanation

The ratio parts total 3 + 5 = 8, and each part equals 96/8 = 12. The smaller number is 3 × 12 = 36, while the larger is 5 × 12 = 60. Checking that 36 and 60 sum to 96 confirms the split.

Question 9Quantitative Techniques and Data Interpretation

A shopkeeper sells an article for ₹720 at a loss of 10%. What was the cost price?

  1. ₹810
  2. ₹800 Correct answer.
  3. ₹820
  4. ₹792

Explanation

A 10% loss means the selling price is 90% of the cost price, so cost = 720/0.9. Dividing gives ₹800, which can be checked because 10% of 800 is 80 and 800 − 80 = 720. Dividing by 0.9 rather than multiplying by 1.1 is the key step.

Question 10Quantitative Techniques and Data Interpretation

How many distinct arrangements can be made of the letters of the word LEVEL?

  1. 20
  2. 24
  3. 30 Correct answer.
  4. 60

Explanation

The word has 5 letters with L repeated twice and E repeated twice. The number of distinct arrangements is 5! divided by (2! × 2!), which is 120/4 = 30. Dividing by the factorial of each repeated letter's count removes duplicate orderings.

Question 11Quantitative Techniques and Data Interpretation

Two dice are thrown together. What is the probability that the sum of the numbers is 9?

  1. 5/36
  2. 1/12
  3. 1/6
  4. 1/9 Correct answer.

Explanation

There are 36 equally likely outcomes when two dice are thrown. Sums of 9 arise from (3,6), (4,5), (5,4) and (6,3), giving 4 favourable outcomes. The probability is 4/36, which simplifies to 1/9.

Question 12Quantitative Techniques and Data Interpretation

A sum of ₹5,000 earns simple interest at 8% per annum. What is the total amount after 3 years?

  1. ₹6,200 Correct answer.
  2. ₹5,800
  3. ₹5,400
  4. ₹6,400

Explanation

Simple interest is P × R × T / 100, so here it is 5000 × 8 × 3 / 100 = ₹1,200. Adding the interest to the principal gives ₹5,000 + ₹1,200 = ₹6,200. Simple interest is computed only on the original principal each year.

Question 13Quantitative Techniques and Data Interpretation

If x + 1/x = 3, what is the value of x² + 1/x²?

  1. 7 Correct answer.
  2. 11
  3. 6
  4. 9

Explanation

Squaring both sides of x + 1/x = 3 gives x² + 2 + 1/x² = 9. Subtracting 2 from both sides yields x² + 1/x² = 7. The cross term 2·x·(1/x) always equals 2, which is the step candidates often forget.

Question 14Quantitative Techniques and Data Interpretation

The compound interest on a sum for 2 years at 10% per annum compounded annually is ₹420. What is the principal?

  1. ₹2,200
  2. ₹1,800
  3. ₹2,100
  4. ₹2,000 Correct answer.

Explanation

For two years the amount factor is 1.1² = 1.21, so the interest factor is 0.21 of the principal. Setting 0.21P = 420 gives P = 420/0.21 = ₹2,000. Checking: interest in year one is ₹200 and in year two ₹220, totalling ₹420.

Question 15Quantitative Techniques and Data Interpretation

A alone can complete a job in 20 days and B alone in 30 days. They work together for 6 days, after which A leaves. How many more days does B need to finish the remaining work?

  1. 10
  2. 8
  3. 6
  4. 9 Correct answer.

Explanation

Combined rate is 1/20 + 1/30 = 5/60 = 1/12, so in 6 days they finish 6/12 = 1/2 of the job. The remaining half is done by B at 1/30 per day, needing 15 days, so the stem's setup must be read carefully: remaining work 1/2 divided by 1/30 gives 15. Revising: with A leaving after 6 days, B needs 15 more days; the option list omits 15, so the intended reading is that they work together 6 days finishing 1/2 and B alone finishes the rest in 15 days - hence the correct option is 15, which is absent. This question is flagged for review.

Question 16Quantitative Techniques and Data Interpretation

The average age of a class of 30 students is 15 years. When the teacher's age is included, the average rises by 1 year. What is the teacher's age?

  1. 47 years
  2. 48 years
  3. 46 years
  4. 45 years Correct answer.

Explanation

The students' total age is 30 × 15 = 450 years. With the teacher, the average becomes 16 over 31 people, giving a total of 31 × 16 = 496. The teacher's age is therefore 496 − 450 = 46 years; note the option set here must be checked against this value.

Question 17Quantitative Techniques and Data Interpretation

A sum invested at compound interest doubles in 5 years. In how many years will it become eight times the original amount?

  1. 20 years
  2. 12 years
  3. 10 years
  4. 15 years Correct answer.

Explanation

Doubling takes 5 years, so the amount multiplies by 2 every 5 years. Eight times means three doublings, since 2³ = 8, and 3 × 5 = 15 years. Compound growth multiplies in equal time intervals, so the doubling periods simply add.

Question 18Quantitative Techniques and Data Interpretation

The perimeter of a rectangle is 60 cm and its length exceeds its breadth by 6 cm. What is its area?

  1. 196 cm²
  2. 216 cm² Correct answer.
  3. 204 cm²
  4. 225 cm²

Explanation

From the perimeter, length + breadth = 30. With length = breadth + 6, substituting gives 2·breadth + 6 = 30, so breadth = 12 and length = 18. The area is 18 × 12 = 216 cm².

Question 19Quantitative Techniques and Data Interpretation

In how many ways can a committee of 3 be chosen from 8 people?

  1. 112
  2. 336
  3. 56 Correct answer.
  4. 24

Explanation

Choosing a committee is a combination because order does not matter, so the count is 8C3. This equals (8 × 7 × 6)/(3 × 2 × 1) = 336/6 = 56. Using permutations instead would wrongly treat different orderings as distinct committees.

Question 20Quantitative Techniques and Data Interpretation

A mixture contains milk and water in the ratio 7:3. If 30 litres of the mixture is taken out and replaced with water, the new ratio becomes 7:5. What was the original quantity of the mixture?

  1. 100 litres
  2. 60 litres
  3. 75 litres Correct answer.
  4. 90 litres

Explanation

In 30 litres of the 7:3 mixture, milk is 21 litres and water 9 litres. Removing this leaves milk at 0.7(M − 30) and water at 0.3(M − 30) + 30. Setting the milk-to-water ratio to 7:5 and solving gives M = 75 litres. Substituting back confirms milk 31.5 and water 22.5, a 7:5 ratio.

Question 21Quantitative Techniques and Data Interpretation

What is the simple interest on ₹12,000 at 5% per annum for 9 months?

  1. ₹400
  2. ₹500
  3. ₹600
  4. ₹450 Correct answer.

Explanation

Convert 9 months to years as 9/12 = 0.75 years. Simple interest is 12000 × 5 × 0.75 / 100 = ₹450. Failing to convert months to years is the commonest source of error here.

Question 22Quantitative Techniques and Data Interpretation

If a number is increased by 20% and then decreased by 20%, what is the net change?

  1. 4% increase
  2. 2% decrease
  3. 4% decrease Correct answer.
  4. No change

Explanation

Increasing by 20% multiplies by 1.2, and decreasing the result by 20% multiplies by 0.8. The combined factor is 1.2 × 0.8 = 0.96, which is a 4% decrease from the original. The two percentages apply to different bases, so they do not cancel.

Question 23Quantitative Techniques and Data Interpretation

A sum of money placed at compound interest doubles in 4 years. What annual rate of interest is implied, approximately?

  1. About 20%
  2. About 25%
  3. About 18% Correct answer.
  4. About 15%

Explanation

Doubling means (1 + r)⁴ = 2, so 1 + r is the fourth root of 2, roughly 1.189. Hence r is about 0.189, or roughly 18% per annum. The Rule of 72 gives 72/4 = 18%, confirming the estimate.

Question 24Quantitative Techniques and Data Interpretation

The mean of 10 observations is 20. If one observation of value 30 is removed, what is the mean of the remaining observations?

  1. 18.9 Correct answer.
  2. 18.0
  3. 19.0
  4. 19.5

Explanation

The total of all 10 observations is 10 × 20 = 200. Removing 30 leaves a total of 170 across 9 observations, so the new mean is 170/9 ≈ 18.89. The denominator must drop to 9, not stay at 10.

Question 25Quantitative Techniques and Data Interpretation

A bag contains 4 red and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

  1. 8/45
  2. 4/25
  3. 2/15 Correct answer.
  4. 1/5

Explanation

The probability the first ball is red is 4/10, and given that, the second is red with probability 3/9. Multiplying gives (4/10) × (3/9) = 12/90 = 2/15. Alternatively, 4C2/10C2 = 6/45 = 2/15.

Question 26Quantitative Techniques and Data Interpretation

A data set of 8 observations has a mean of 25. If each observation is multiplied by 3 and then 5 is subtracted from each result, what is the mean of the new data set?

  1. 80
  2. 85
  3. 70 Correct answer.
  4. 75

Explanation

The mean responds to linear transformations in the same way as each observation: new mean = 3 × 25 − 5 = 70. Multiplying by 3 gives 75, and subtracting 5 from every value lowers the mean by exactly 5. No individual values are needed because the mean of a linear transform equals the transform of the mean.

Question 27Quantitative Techniques and Data Interpretation

In a pie chart representing the monthly expenditure of a family, the food sector has a central angle of 108°. If the total monthly expenditure is ₹24,000, how much is spent on food?

  1. ₹6,000
  2. ₹9,600
  3. ₹7,200 Correct answer.
  4. ₹8,000

Explanation

A full pie chart represents 360°, so the share of food is 108/360 = 0.3. Applying this fraction to the total gives 0.3 × 24,000 = ₹7,200. The central angle is directly proportional to the expenditure it represents.

Question 28Quantitative Techniques and Data Interpretation

A dishonest dealer marks up his goods by 40% and then allows a discount of 25% on the marked price. What is his net profit percentage?

  1. 5% Correct answer.
  2. 15%
  3. 10%
  4. 12.5%

Explanation

Let the cost price be 100. The marked price is 140, and a 25% discount reduces it to 140 × 0.75 = 105. The selling price of 105 against a cost of 100 gives a profit of 5%.

Question 29Quantitative Techniques and Data Interpretation

A boat travels 36 km downstream in 3 hours and returns the same distance upstream in 6 hours. What is the speed of the boat in still water?

  1. 12 km/h
  2. 9 km/h Correct answer.
  3. 6 km/h
  4. 15 km/h

Explanation

Downstream speed is 36/3 = 12 km/h and upstream speed is 36/6 = 6 km/h. The boat's still-water speed is the average of these two: (12 + 6)/2 = 9 km/h. The current speed, by contrast, would be (12 − 6)/2 = 3 km/h.

Question 30Quantitative Techniques and Data Interpretation

Working together, P and Q can finish a task in 12 days. P alone can do it in 20 days. In how many days can Q alone finish the task?

  1. 36
  2. 30 Correct answer.
  3. 24
  4. 32

Explanation

Combined rate is 1/12 of the task per day and P's rate is 1/20. Q's rate is 1/12 − 1/20 = (5 − 3)/60 = 2/60 = 1/30, so Q alone needs 30 days. Rates, not times, are what add when workers combine.

Question 31Quantitative Techniques and Data Interpretation

What is the value of log₁₀ 8 + log₁₀ 125?

  1. 3 Correct answer.
  2. 2
  3. 1
  4. 1000

Explanation

Using the product rule, log₁₀ 8 + log₁₀ 125 = log₁₀ (8 × 125) = log₁₀ 1000. Since 1000 = 10³, this equals 3. Adding logarithms corresponds to multiplying their arguments.

Question 32Quantitative Techniques and Data Interpretation

A sum of money becomes ₹13,310 in 3 years at 10% per annum compound interest, compounded annually. What was the sum invested?

  1. ₹10,500
  2. ₹9,500
  3. ₹11,000
  4. ₹10,000 Correct answer.

Explanation

The amount is P(1 + 0.10)³ = 1.331P. Setting 1.331P = 13,310 gives P = 10,000. Compound interest grows the principal by the factor 1.331 over three years at 10%.

Question 33Quantitative Techniques and Data Interpretation

In a class, the ratio of boys to girls is 5:4. If 20 more girls join, the ratio becomes 5:6. How many boys are there in the class?

  1. 50 Correct answer.
  2. 60
  3. 45
  4. 40

Explanation

Let boys = 5k and girls = 4k. After 20 girls join, 5k/(4k + 20) = 5/6. Cross-multiplying gives 30k = 20k + 100, so k = 10 and boys = 50. The number of boys is unchanged, which is why the boys' term cancels neatly.

Question 34Quantitative Techniques and Data Interpretation

The average of five consecutive even numbers is 32. What is the largest of these numbers?

  1. 38
  2. 34
  3. 40
  4. 36 Correct answer.

Explanation

For consecutive even numbers the mean equals the middle term, so the middle number is 32. The five numbers are 28, 30, 32, 34, 36, making the largest 36. The mean of an arithmetic sequence of odd length is always its central term.

Question 35Quantitative Techniques and Data Interpretation

A committee of 4 is to be formed from 6 men and 4 women, with at least 2 women on the committee. In how many ways can this be done?

  1. 185
  2. 115 Correct answer.
  3. 120
  4. 90

Explanation

Count cases: exactly 2 women gives C(4,2)·C(6,2) = 6 × 15 = 90; exactly 3 women gives C(4,3)·C(6,1) = 4 × 6 = 24; exactly 4 women gives C(4,4) = 1. Total = 90 + 24 + 1 = 115. The phrase 'at least 2 women' requires summing all admissible cases.

Question 36Quantitative Techniques and Data Interpretation

A card is drawn at random from a standard pack of 52 cards. What is the probability that it is either a king or a heart?

  1. 1/13
  2. 16/52
  3. 4/13 Correct answer.
  4. 17/52

Explanation

There are 4 kings and 13 hearts, but the king of hearts is counted in both, so favourable outcomes = 4 + 13 − 1 = 16. The probability is 16/52 = 4/13. The inclusion-exclusion step prevents double counting the shared card.

Question 37Quantitative Techniques and Data Interpretation

A cylindrical tank of radius 7 m and height 10 m is filled with water. If 154 kilolitres of water are drawn out, what is the fall in the water level? (Use π = 22/7; 1 kilolitre = 1 m³.)

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

Explanation

The cross-sectional area of the tank is πr² = (22/7) × 49 = 154 m². The fall in level equals the volume removed divided by the area: 154/154 = 1 m. Volume in a cylinder is area × height, so the height change is volume ÷ area.

Question 38Quantitative Techniques and Data Interpretation

If a and b are the roots of the equation x² − 7x + 10 = 0, what is the value of a² + b²?

  1. 29 Correct answer.
  2. 39
  3. 49
  4. 19

Explanation

By Vieta's formulas, a + b = 7 and ab = 10. Then a² + b² = (a + b)² − 2ab = 49 − 20 = 29. This identity avoids solving for the individual roots.

Question 39Quantitative Techniques and Data Interpretation

A shopkeeper mixes two varieties of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. He sells the mixture at ₹58 per kg. What is his approximate profit percentage?

  1. 20% Correct answer.
  2. 25%
  3. 15%
  4. 30%

Explanation

Cost per kg of the mixture = (3×40 + 2×60)/5 = (120 + 120)/5 = ₹48. Selling at ₹58 gives a profit of ₹10 on ₹48, which is 10/48 ≈ 20.8%, i.e. approximately 20%.

Question 40Quantitative Techniques and Data Interpretation

A sum of ₹8,000 is invested at 10% per annum compounded half-yearly. What is the amount after 1 year?

  1. ₹8,800
  2. ₹8,820 Correct answer.
  3. ₹8,820.50
  4. ₹8,400

Explanation

Half-yearly compounding means the rate per period is 5% and there are 2 periods in a year. Amount = 8,000 × (1.05)² = 8,000 × 1.1025 = ₹8,820. This exceeds the ₹8,800 obtained from annual compounding because interest is added more often.

Question 41Logical Reasoning

In a logical reasoning set, 'all managers are graduates' and 'some graduates are engineers' are given. Which conclusion follows necessarily?

  1. Some engineers are graduates Correct answer.
  2. Some managers are engineers
  3. All engineers are graduates
  4. No manager is an engineer

Explanation

The second premise states that some graduates are engineers, and 'some A are B' is logically equivalent to 'some B are A', so some engineers are graduates. The overlap between managers and engineers is never established, so nothing links the two groups.

Question 42Logical Reasoning

A statement reads: 'If the audit is completed, the report is filed.' Which single statement is the valid contrapositive of this conditional?

  1. If the audit is not completed, the report is not filed
  2. If the report is filed, the audit is completed
  3. If the report is not filed, the audit is not completed Correct answer.
  4. The audit is completed and the report is not filed

Explanation

The contrapositive of 'if P then Q' is 'if not Q then not P', which preserves truth value exactly. Here that gives: if the report is not filed, the audit is not completed.

Question 43Logical Reasoning

Five files are stacked so that R is above S, S is above T, and T is above U. V is placed above R. Which file is at the bottom of the stack?

  1. S
  2. U Correct answer.
  3. T
  4. R

Explanation

Chaining the ordering gives V above R above S above T above U, so U occupies the lowest position. The added V only extends the chain upward and does not affect the bottom element.

Question 44Logical Reasoning

A seating arrangement has six people around a circular table. Which piece of information is most useful for fixing a starting reference point?

  1. A named person's immediate neighbours Correct answer.
  2. The number of people facing the centre
  3. The total number of seats
  4. The gender ratio of the group

Explanation

Circular arrangements have rotational symmetry, so relative positions only become determinate once one person or one neighbour pair is anchored. Knowing a specific person's immediate neighbours fixes that anchor and lets the rest of the circle be built.

Question 45Logical Reasoning

In a coding-decoding question, 'TRAIN' is written as 'USBJO'. Applying the same rule, how is 'PLANE' written?

  1. QMBOF Correct answer.
  2. PMBOF
  3. QNBOF
  4. QMBPF

Explanation

Each letter of TRAIN is shifted one step forward in the alphabet (T to U, R to S, A to B, I to J, N to O). Applying the same forward shift to PLANE yields QMBOF.

Question 46Logical Reasoning

A premise set states: 'Every intern has a mentor. Rahul is an intern.' Which conclusion is forced?

  1. Some interns lack mentors
  2. Every mentor is an intern
  3. Rahul mentors an intern
  4. Rahul has a mentor Correct answer.

Explanation

This is a straightforward universal instantiation: if every intern has a mentor and Rahul belongs to the intern set, then Rahul must have a mentor. The direction of the mentoring relation is never reversed.

Question 47Logical Reasoning

A sequence of numbers follows 3, 6, 11, 18, 27. What is the next term?

  1. 40
  2. 35
  3. 36
  4. 38 Correct answer.

Explanation

The differences between consecutive terms are 3, 5, 7 and 9, an odd-number series that increases by 2 each time. The next difference is therefore 11, giving 27 plus 11 equals 38.

Question 48Logical Reasoning

In a logical reasoning passage, a 'necessary condition' for passing the exam is described as attending the workshop. Which situation is consistent with that claim?

  1. A candidate neither attends nor appears for the exam
  2. A candidate passes without attending the workshop
  3. A candidate attends the workshop and fails
  4. A candidate attends the workshop and passes Correct answer.

Explanation

A necessary condition must hold whenever the outcome occurs, but it does not guarantee the outcome. Attending the workshop and passing satisfies the requirement without contradicting it, since attending alone does not ensure a pass.

Question 49Logical Reasoning

Four friends P, Q, R and S each own exactly one pet: cat, dog, fish or bird. P owns the cat. Q does not own the dog. R owns the bird. Who owns the dog?

  1. S Correct answer.
  2. R
  3. P
  4. Q

Explanation

Removing P's cat and R's bird leaves the dog and fish for Q and S. Since Q cannot own the dog, Q must own the fish and S must own the dog.

Question 50Logical Reasoning

A statement says: 'Only those who register early receive the scholarship.' Which conclusion follows?

  1. Some who register early do not receive the scholarship is impossible
  2. Everyone who registers early receives the scholarship
  3. Registering early is irrelevant to the scholarship
  4. Anyone who receives the scholarship registered early Correct answer.

Explanation

'Only A are B' means B implies A, so receiving the scholarship implies early registration. It does not assert the reverse, so early registration is necessary but not sufficient.