CivilsIASPrep.comUPSC PYQs: Numeracy
Review complete published questions grouped by subject: Numeracy.
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Questions
- Weights satisfy A+B+C+D=17, A+C=6, P+Q+S+D=15, P+Q+R+B=17, with P=R and Q=S. Which statement must be correct?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Linear equations
- X, Y and Z jump in steps of 4, 6 and 5 feet respectively. At 8 AM all are at mark 199. How many marks between 195 and 1000 can all three land on, not necessarily at the same time?2026 · Prelims CSAT · Basic Numeracy, Numeracy · LCM
- A toy moves 5 feet forward for each forward jump and 2 feet backward for each backward jump. In 31 jumps it ends 15 feet ahead. What is the absolute difference between the numbers of forward and backward jumps?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Linear equations
- If 10^m ×1000×n = 75^25 ×25^32 ×32^75 and n is not divisible by 10, find m.2026 · Prelims CSAT · Basic Numeracy, Numeracy · Prime factorization
- A 100 km/h train passes a person walking at 4 km/h in the same direction in 15 seconds. Approximately how long would it take to pass the person if the person walked in the opposite direction?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Relative speed
- For 1/3 < x < y < 2, which is always true? I. x+1/x < y+1/y. II. √(1+y²)/y < √(1+x²)/x.2026 · Prelims CSAT · Basic Numeracy, Numeracy · Inequalities and functions
- Using measuring vessels of 1, 6, 25 and 100 litres, what is the minimum number of measurements needed to obtain a net 298 litres, allowing a measured quantity to be returned to the tank?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Measurement optimization
- Weights of 1, 2, 5 and 10 kg are available. In how many different ways can exactly 20 kg be measured if at least 8 but not more than 11 one-kilogram weights must be used?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Integer combinations
- A class average x rises by 4 when a score is corrected from 0 to100. Later another score is corrected from81 down to56. If the final average is y, find y−x.2026 · Prelims CSAT · Basic Numeracy, Numeracy · Average
- x,y,z are distinct values chosen from 2,3,4,5. If M and N are the maximum and minimum of xy+z, what is M−N?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Optimization
- Positive variables satisfy y∝x² and x∝1/z. When z=7/25, x=5 and y=50. If y=98, find z.2026 · Prelims CSAT · Basic Numeracy, Numeracy · Variation
- Runners X and Y have speed ratio 7:5 and start together in the same direction. After Y finishes5 laps it reverses and doubles speed; X continues until completing21 laps. How many meetings occur after start and before the final stopping instant?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Circular motion
- An exam awards +5 for correct and −2 for wrong. A student attempts all questions and scores69. Under an alternative +4/−1 scheme the same responses would score84. How many questions were there?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Linear equations
- An explosion occurs some distance from an army camp. When its sound reaches the camp, drone 1 flies to the site and sends a picture instantly on arrival. On receipt, drone 2 immediately flies to the same site and sends another picture. Pictures arrive at 5:02 PM and 5:05 PM. Drone speed is 30 m/s and sound speed 300 m/s. When did the explosion occur?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Time speed distance
- What is the units digit of 6^129 × 7^307?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Units digit
- A person saves 10% of salary. Salary rises by12% while expenditure rises by10%. What happens to monthly saving?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Percentage
- How many three-digit positive integers are integral powers of 2?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Powers
- Across all two-digit positive integers, how many times does the digit 5 occur?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Counting digits
- X cycles 6 km: first1 km at5 km/h, next2 km at10, last3 km at4. Y covers the same legs at4,10,5 km/h respectively. How many minutes earlier does Y finish?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Speed and time
- A sequence starts 4,7 and every later term is the sum of the two preceding terms. What is the sixth term?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Number sequence
- Male:female worker ratios in companies A and B are13:10 and7:5. If both companies have the same number of female workers, what is the ratio of their total workforces A:B?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Ratio
- For two distinct natural numbers, suppose HCF×LCM equals the cube of one of the numbers. I. Their difference must be even. II. One of the numbers must be a perfect square. Which are correct?2026 · Prelims CSAT · Basic Numeracy, Numeracy · HCF and LCM
- Digits x and y make the number 4x5y790 divisible by11. What remainder does x+y leave on division by11?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Divisibility by 11
- Alloy P is20% copper and80% zinc; Q is60% copper and40% zinc. In what ratio P:Q should they be mixed to obtain an alloy with equal copper and zinc?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Alligation
- A is a two-digit number with distinct non-zero reversal B, also two-digit. If A>B and A−B is a multiple of27, how many possible values of A exist?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Digits and divisibility
- A 3×100 rectangular strip must be tiled exactly with 3×3, 3×7 and 3×11 tiles. If x and y are the maximum and minimum possible numbers of tiles, what is x−y?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Integer optimization
- A train must cover800 km. After200 km a minor accident halves its speed; 400 km later a mechanical defect reduces the then-current speed to one-fourth. If reversing the order of accident and defect at those same distances would add4 hours, what was the original speed?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Speed changes
- Five candidates are scored in three components with weights0.2,0.3,0.5. Their component scores are: C1=(5,4,6), C2=(4,6,5), C3=(3,2,8), C4=(9,4,3), C5=(8,8,2). What cutoff selects exactly the top three?2026 · Prelims CSAT · Data Interpretation, Numeracy · Weighted score
- Partners A,B,C share profit proportional to capital×time. A invests one-third of total capital for one-third of the duration; B one-fourth for one-fourth; C the remaining capital for the full duration. From ₹17,000 profit, how much does C receive?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Partnership
- A 10-litre container initially holds only chemical A. Three times, 1 litre of the mixture is removed and replaced with 1 litre of B. Approximately what percentage of the final mixture is B?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Replacement mixtures
- A delivery worker earns ₹5 per delivery plus ₹2 per kilometre, wants more than ₹500 per day, and refuses to travel more than100 km. Which number of deliveries definitely guarantees the target without knowing total distance?2026 · Prelims CSAT · Basic Numeracy, Numeracy · Linear constraints
- A cube is painted on all faces and cut into 60 equal smaller pieces using the minimum number of planar cuts. Consider: I. The minimum number of cuts is 9. II. Six smaller pieces have no painted face. Which is correct?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Mensuration
- If the operation satisfies 7 × 24 = 25 and 12 × 16 = 20, what is 16 × 63?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Number patterns
- Petrol rises by 10% from ₹90/litre. A person normally drives 2200 km per month in a car giving 16 km/litre. By how many kilometres must monthly travel be reduced to keep petrol spending unchanged?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Percentage
- A four-digit number N leaves remainders 1, 3, 4 and 7 when divided by 3, 5, 6 and 9 respectively. What is the smallest possible N?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Remainders
- What is the units digit of 1×3×5×7×9×…×999?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Units digit
- What is the greatest n for which 7×343×385×1000×2401×77777 is divisible by 35^n?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Prime factorization
- Find X in the sequence 24, X, 12, 18, 36, 90.2025 · Prelims CSAT · Numeracy, Basic Numeracy · Number series
- P and Q start together at 5:00 a.m. on a circular track in opposite directions, moving at 5 and 3 rounds per hour. How many times do they cross between 5:20 a.m. and 7:00 a.m.?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Time and speed
- A tram moving in the same direction overtakes walkers X and Y, who move at 3 km/h and 4 km/h. It completely passes them in 8 s and 9 s respectively. What is the tram's length?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Relative speed
- If N² = 12345678987654321, how many digits does N contain?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Squares
- A natural number N can be written as N=p+q+r, where p, q and r are distinct factors of N. How many such N below 50 exist?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Factors
- Three prime numbers p, q and r, each below 20, satisfy p−q=q−r. How many distinct values can p+q+r take?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Prime numbers
- How many distinct values of p+q+r are possible for natural numbers p, q and r satisfying 1/p + 1/q + 1/r = 1?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Diophantine fractions
- Team X scores N runs in 20 overs. Team Y ties the score in 10% fewer overs. The question also says that with a 50% higher average run rate, Y would tie the score in 12 overs. How many runs did X score?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Rates
- A commodity price p is increased by k%, decreased by k%, then again increased by k% and decreased by k%. If the final price is q, which relation is correct?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Percentage
- Among the first 100 natural numbers, how many are not divisible by any of 2, 3, 5, 7 or 9?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Divisibility
- If 4≤x≤8 and 2≤y≤7, what is the ratio of the maximum value of (x+y) to the minimum value of (x−y)?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Optimization
- Let p and k be prime numbers such that p²+k is also prime and less than 30. How many possible values can k take?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Prime numbers
- There are n distinct sets, each containing three positive integers, whose LCM is 1001 and HCF is 1. What can be said about n?2025 · Prelims CSAT · Numeracy, Basic Numeracy · HCF and LCM
- X completes one-third of a work in 6 days, Y one-third in 8 days, and Z three-fourths in 12 days. They work together for n days; then X and Z stop, and Y finishes the remaining work in 8⅔ days. Find n.2025 · Prelims CSAT · Numeracy, Basic Numeracy · Time and work
- Find X in 1, 3, 6, 11, 18, X, 42.2025 · Prelims CSAT · Numeracy, Basic Numeracy · Number series
- Three T20 players X,Y,Z score 37 runs in total and X/Y=Y/Z. Compare their individual runs. Which ordering must hold?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Ratio and proportion
- Let p+q=10. Value I is the maximum pq for positive integers p,q. Value II is the maximum pq when integers satisfy p≥−6 and q≥−4. Compare the values.2025 · Prelims CSAT · Numeracy, Basic Numeracy · Optimization
- For a set of 11 numbers, Value I is the minimum average when they are consecutive integers each ≥−5. Value II is the minimum product when they are consecutive non-negative integers. Compare.2025 · Prelims CSAT · Numeracy, Basic Numeracy · Sequences
- The average of p,q,r is k. The amount by which p exceeds the average equals the amount by which q falls below the average. What is r?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Averages
- For a real number 0 x³. II. x>√x. Which is correct?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Inequalities
- Two natural numbers differ by 10. What can be said about natural numbers divisible by 5 that lie strictly between them?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Divisibility
- Twenty pipes of set X can fill 70% of a tank in 14 minutes. Ten pipes of set Y fill 3/8 of it in 6 minutes. Sixteen pipes of set Z can empty half the tank in 20 minutes. If only 10 X pipes and 5 Y pipes work while all Z pipes are open, how long is required to fill half the tank?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Pipes and cisterns
- For natural number n, how many distinct remainders can 1^n + 2^n leave when divided by 4?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Remainders
- Let P = QQQ denote a three-digit number with all digits equal to Q. What is HCF(P, 481)?2025 · Prelims CSAT · Numeracy, Basic Numeracy · HCF
- In the concatenated sequence 12345678910111213..., what is the 489th digit?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Number sequence
- Consider: I. There exists a natural number whose number of factors remains unchanged after a 50% increase. II. There exists a natural number whose number of factors remains unchanged after a 150% increase. Which statements are correct?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Factors
- What is the remainder when 9^3 + 9^4 + ... + 9^100 is divided by 6?2025 · Prelims CSAT · Numeracy, Basic Numeracy · Modular arithmetic