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Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number :
p×q can be an odd number. q÷p can be a prime number. p+q can be…
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If 15 × 14 × 13 ×…………× 3 × 2 × 1 = 3^m × n, where m and n are positive integers, then what is the maximum value of m?
(UPSC CSAT - 2022) 7 6 5 4 Solution: Ans.(b) Power of 3 in 15!…
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The sum of three consecutive integers is equal to their product. How many such possibilities are there?
(UPSC CSAT - 2022) Only one Only two Only three No such possibility is there…
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What is the number of numbers of the form 0.XY, where X and Y are distinct nonzero digits?
(UPSC CSAT - 2022) 72 81 90 100 Solution: Ans.(a) X,Y ϵ {1, 2, 3,…
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Let A, B and C represent distinct non zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.
Consider the following statements : The 4-digit least value of x is 1332. The 3-digit…
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There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously ?
(UPSC CSAT - 2023) 4:00 p.m. 4:10 p.m. 4:20 p.m. 4:30 p.m. Solution: Ans.(2) Time…
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Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements:
1. The number of possible values of p is 5. 2. The number of possible…
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How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers ?
(UPSC CSAT - 2023) 6 7 8 9 Solution: Ans.(4) All the factors of 1155…
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AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8 then what is A + B + C equal to ?
(UPSC CSAT - 2023) 6 7 8 9 Solution: Ans.(1) So D & G should…
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What is the remainder if 2^192 is divided by 6 ?
(UPSC CSAT - 2023) 0 1 2 4 Solution: Ans.(4) 2192 / 6 = (2×2191) / 6…