CivilsIASPrep.comUPSC PYQs: Quantitative Aptitude
Review complete published questions grouped by topic: Quantitative Aptitude.
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Questions
- What is the least possible number of straight cuts needed to divide a cube into 64 identical smaller cubes?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- In 5 * 4 * 3 * 2 * 1, replace each * by +, − or ×, with each operator used at most twice. What is the smallest non-negative value obtainable?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- A group can finish a job in 6k days. By what percentage must the workforce increase to finish the same job in 5k days?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- X, Y and Z can individually complete a job in 6, 8 and 8 hours. Only one may work in each hour and nobody may work two consecutive hours. What is the minimum completion time?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- How many consecutive zeroes occur at the end of 1^2 × 2^4 × 3^6 × … × 25^50?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Starting 1 January 2023, a person saves ₹1 and then ₹2 more each day than on the previous day. At the end of which date does cumulative saving become both a perfect square and a perfect cube?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- 222^333 + 333^222 is divisible by which combination?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- What percentage of water, relative to the quantity of honey, must be added so that selling the mixture at the honey cost price yields a 20% gain?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the rightmost non-zero digit of 30^30?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- 421 and 427 leave remainder 1 when divided by the same divisor. How many divisors can satisfy this?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- 399 L of petrol and 532 L of diesel must be bottled separately in equal integer-litre bottle sizes with no remainder. How many bottle capacities are possible?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- For S=x+y+z, where x,y,z are distinct primes below 10, which are possible units digits: (1) 0; (2) 9; (3) 5?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- P and Q are business partners. P invests ₹14,000 more than Q; P invests for 8 months and Q for 10 months. From a ₹2,000 profit, P receives ₹400 more than Q. What is P’s capital?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- P’s salary is 20% below Q’s, and Q’s is 20% below R’s. By what percentage is R’s salary greater than P’s?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- A number is mistakenly divided by 4 instead of multiplied by 4. By what percentage does the obtained result differ from the correct result?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- In an exam, 80% pass English, 70% pass Hindi and 15% fail both. What percentage fail exactly one of the two subjects?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- A father tells his son: “n years ago I was as old as you are now. My present age is four times your age n years ago.” If their present ages total 130 years, what is the difference between their ages?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Which unit equivalences are correct: (1) 1,000 litres=1 cubic metre; (2) 1 metric tonne=1,000 kg; (3) 1 hectare=10,000 square metres?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Let X be a two-digit number and Y its digit-reversal. If X+Y=99, how many possible values can X take?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- The weight of 6 boys equals that of 7 girls, 3 men and 4 women. If the average woman weighs 63 kg, what is the average boy’s weight?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- How many times do the hour and minute hands coincide between 10:00 a.m. and 2:00 p.m. on the same day?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- The calendar for 2025 is identical to the calendar for which year?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the smaller angle between the hands of a clock at 4:25?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- How many times is the digit 5 used when numbering the pages of a 260-page book?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Find the sum of the first 28 terms of 1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,…2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- A person buys articles P,Q,R for ₹3,330. P costs 25% more than R and R costs 20% more than Q. What is the cost of P?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Two two-digit numbers AB and CD sum to the three-digit number 1CE, where A,B,C,D,E are distinct digits. What is A?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Three numbers x,y,z are selected from {1,2,3,4,5,6,7} such that x>2y>3z. How many ordered triplets satisfy this?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- The cost of 4 oranges, 6 mangoes and 8 apples equals twice the cost of 1 orange, 2 mangoes and 5 apples. Assess: (1) 3 oranges+5 mangoes+9 apples costs the same as the first basket; (2) one orange+one mango costs one apple.2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- For the expression 32^5 + 2^27, which number must divide it?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- Let positive integers p<q satisfy p+q=k. What is the smallest k for which p and q are not uniquely determined?2024 · Prelims CSAT · CSAT · Quantitative Aptitude
- A box has 10 red pairs, 9 white pairs and 8 black pairs of shoes. In the worst case, how many shoes may need to be picked before obtaining a wearable red pair?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- In how many unordered ways can a batsman make exactly 25 runs using only singles, fours and sixes?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the remainder when 85×87×89×91×95×96 is divided by 100?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the units digit of (57242) raised to the product 9×7×5×3×1?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- ABC and DEF are 3-digit numbers using six distinct non-zero digits and ABC+DEF=1111. Find A+B+C+D+E+F.2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- For a 3-digit number D, the ratio D/(sum of its digits) is minimal. What is the difference between its hundreds and units digits?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- For prime p and composite c, consider whether (p+c)/(p−c) can be even, p+c can be odd, and pc can be odd. Which statements can hold?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- A 3-digit number ABC multiplied by digit D gives 37DD; A,B,C,D are distinct non-zero digits. Find A+B+C.2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- For any 3-digit block XYZ, the 6-digit number XYZXYZ is always divisible by which numbers?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- 125 identical small cubes form a larger cube. How many are completely surrounded by other cubes?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- How many distinct arrangements of 11223344 have odd digits only in odd positions and even digits only in even positions?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- A, B and C can finish work alone in 8,16 and 12 days and work one day each cyclically from Monday. Consider: (1) work finishes on Thursday; (2) it finishes in 10 days. Which is correct?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- For positive integer x, 7x+96 is divisible by x. How many possible x values exist?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- For distinct positive single-digit p,q,r,s, what is the greatest value of (p+q)(r+s)?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- N consists of ninety-nine consecutive 9s. What remainder does N leave on division by 13?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- A nine-digit number consisting only of 1s is squared. What is the sum of digits of the square?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the sum of all digits appearing in every integer from 10 through 100 inclusive?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- Six marked points lie on the four sides of a square: one each on two opposite sides and two each on the other two. How many distinct triangles use three of these points?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- Principal P becomes Q in one year at nominal annual rate R compounded half-yearly, and also at annual rate S compounded once yearly. Which relation holds?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- How many natural-number divisors n make 1186 leave remainder 31 when divided by n?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- Let pp, qq and rr denote repeated-digit 2-digit numbers with p<q<r and pp+qq+rr=tt0. Consider: (1) p has 5 possible values; (2) q has 6 possible values. Which is correct?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the sum of all 4-digit numbers below 2000 formed from 1,2,3,4 without repetition?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- From 12 objects arranged on a circle, how many selections of 10 consecutive objects are possible when direction is clockwise?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- If today is Sunday, what weekday is the 10^10-th day from today?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- Three traffic lights take 25, 39 and 60 seconds respectively for each green-to-red or red-to-green change. All turn green at 2:00 p.m. When next do all turn green together?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- Four papers each carry 100 marks and scores are integers. In how many different ordered score combinations can a student obtain exactly 99% overall?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- A flag has four horizontal strips using red, green and yellow, with adjacent strips never the same colour. How many designs are possible?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- A 4 m × 2.2 m floor is tiled with non-overlapping 1.4 m × 0.6 m rectangles, edges parallel to floor edges and either orientation allowed. What maximum number fits?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- Unlimited coins weigh 2,5,10,25 and 50 g. Consider: (1) buying exactly 78 g requires at least 7 coins; (2) weighing 78 g can be done with fewer than 7 coins. Which is correct?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- What is the remainder when 2^192 is divided by 6?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- AB and CD are two-digit numbers; AB×CD=DEF and DEF+GHI=975. All nine letters are distinct digits, with E=0 and F=8. Find A+B+C.2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- A 7×5×3 cuboid is painted with a different colour on each pair of opposite faces and cut into 1 cm cubes. Statements: (1) exactly 15 cubes have no paint; (2) exactly 6 cubes have exactly a blue and green face. Which is correct?2023 · Prelims CSAT · CSAT · Quantitative Aptitude
- There is a milk sample with 50% water in it. If one-third of this milk is added to an equal amount of pure milk, then water in the new mixture will fall down to:2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- There are three pillars X, Y, and Z of different heights. Three spiders A, B, and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- Suppose the average weight of 9 persons is 50 kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the 5th person will be2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall, and 9 m from the point P. How many meters is the fly from the ceiling?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- The outer surface of a 4 cm × 4 cm × 4 cm cube is painted completely in red. It is sliced parallel to the faces to yield sixty-four 1 cm × 1 cm × 1 cm small cubes. How many small cubes do not have painted faces?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- A watch loses 2 minutes in every 24 hours while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if a 24-hour clock is followed?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- A clock strikes once at 1 o’clock, twice at 2 o’clock, and thrice at 3 o’clock, and so on. If it takes 12 seconds to strike at 5 o’clock, what is the time taken by it to strike at 10 o’clock?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- The monthly incomes of X and Y are in the ratio of 4 : 3, and their monthly expenses are in the ratio of 3 : 2. However, each saves Rs. 6,000 per month. What is their total monthly income?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- The average rainfall in a city for the first four days was recorded to be 0.40 inch. The rainfall on the last two days was in the ratio of 4 : 3. The average of six days was 0.50 inch. What was the rainfall on the fifth day?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- Certain 3-digit numbers have the following characteristics: 1. All the three digits are different. 2. The number is divisible by 7. 3. The number on reversing the digits is also divisible by 7. How many such 3-digit numbers are there?2017 · Prelims CSAT · CSAT · Quantitative Aptitude
- P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q, and R together work on a job, in what ratio should they share the earnings?2017 · Prelims CSAT · CSAT · Quantitative Aptitude