Practice UPSC CSAT previous year questions from 2011–2026 classified underAlgebra. Review the original question, four options, correct answer and explanation for every PYQ.
13 questions • 2011–2026
The weight of X, in kg, is denoted by X. The weights of A, B, C, D, P, Q, R and S are measured. Given: A + B + C + D = 17 A + C = 6 P + Q + S + D = 15 P + Q + R + B = 17 P = R and Q = S Which one of the following statements is correct?
From the equations, P+Q=7 while A+C=6. Therefore P and Q together weigh more than A and C together. Hence B.
For 1/3 < x < y < 2, which of the following statements is/are always correct? I. x + 1/x < y + 1/y II. √(1 + y²)/y < √(1 + x²)/x Select the answer using the code given below.
The function √(1+t²)/t is strictly decreasing for t>0, so II is always true. The function t+1/t is not monotonic over the whole interval (1/3,2), so I is not always true. Hence B.
Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}, then M − N is
Maximum is 5×4+3=23; minimum is 2×3+4=10. Therefore M−N=13. Hence C.
Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
Since y∝x² and y=50 when x=5, y=2x². For y=98, x=7. Since xz is constant, xz=5×7/25=7/5, so z=(7/5)/7=1/5. Hence B.
If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?
Maximum x+y=15 and minimum x−y=−3, so the ratio is −5, not listed.
Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers. Value-II = Maximum value of p × q when p ≥ −6, q ≥ −4. Which one of the following is correct?
Both maxima occur at p=q=5, giving 25.
The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?
Let p=k+d and q=k−d; then r=k.
Let x be a real number between 0 and 1. Which of the following statements is/are correct? I. x² > x³. II. x > √x. Select the correct answer using the code given below:
For 0<x<1, x²>x³ but x<√x, so I only.
A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now is the smallest two-digit number. How many coins does A have in the beginning?
Work backwards from D=10: C/2+2=10 gives C=16; B/2+2=16 gives B=36; A/2+2=36 gives A=68.
Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below: 1. Z purchased 8 notebooks more than X did. 2. P and Q together purchased 21 notebooks. 3. Q purchased 5 notebooks less than P did. 4. X and Y together purchased 28 notebooks. 5. P purchased 5 notebooks more than X did. If each notebook is priced Rs. 40, then what is the total cost of all the notebooks?
Let X=x. Then P=x+5, Q=P-5=x, Z=x+8 and Y=28-x. From P+Q=21, 2x+5=21, so x=8. Total notebooks = 13+8+8+20+16=65; at Rs.40 each, cost = Rs.2,600.
A person P asks one of his three friends X as to how much money he had. X replied, “If Y gives me Rs. 40, then Y will have half of as much as Z, but if Z gives me Rs. 40, then three of us will have equal amount.” What is the total amount of money that X, Y and Z have?
Let amounts be x,y,z. The conditions give y−40=z/2 and x+40=y=z−40, yielding y=120, x=80, z=160; total Rs.360.
Four persons, Alok, Bhupesh, Chander and Dinesh have a total of ₹100 among themselves. Alok and Bhupesh between them have as much money as Chander and Dinesh between them, but Alok has more money than Bhupesh; and Chander has only half the money that Dinesh has. Alok has in fact ₹5 more than Dinesh has. Who has the maximum amount of money?
Let Dinesh=x, Chander=x/2, Alok=x+5, and Bhupesh=x−5. The totals give x=30, so Alok has ₹35 and is maximum.
A person has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively
Let x be ₹1 coins and y be ₹2 coins. x+y=50 and x+2y=75; subtracting gives y=25 and x=25.
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