CSAT 2020

Q. What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?

(a) 1012
(b) 1022
(c) 1122
(d) 1222
Correct Answer: (b) 1022

Question from UPSC Prelims 2020 CSAT Paper

Explanation :

Number divided by 3,4,5,6

Let’s solve this problem step by step. The least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case can be found using the following method:

First we need to find the least common multiple (LCM) of 3, 4, 5 and 6. The LCM of these numbers is 60.

Now we need to find the smallest four-digit number that is divisible by this LCM. The smallest four-digit number that is divisible by 60 is 1020.

Since we want a remainder of 2 when this number is divided by any of these numbers (3,4,5 and 6), we add 2 to this number.

So the least four-digit number when divided by 3,4,5 and 6 leaves a remainder of 2 in each case is 1020 + 2 =1022.

Check Demo Video

More Questions:

Q. Two Statements are given followed by two Conclusions: Statements: All numbers are divisible by 2. All numbers are divisible by 3.

Q. A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?

Q. Question: Is (p+q-r) greater than (p-q+r), where p, q and r are integers ? Statement-1: (p-q) is positive. Statement-2: (p-r) is negative.

Q. Researchers were able to use stem cells to gauge the neurotoxic effects of the environmental pollutants Bisphenol A (BPA).

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8. 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5.