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GATE 2022: General Aptitude (Divisibility & Remainder)

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Question 1

By which smallest number should 20184 be multiplied so that it becomes a perfect square?

Question 2

If two numbers are each divided by the same divisor, the remainder are respectively 3 and 4. If the sum of the two numbers is divided by the same divisor, the remainder is 2. The divisor is ?

Question 3

The 2nd smallest number which when divided successively by 2, 3 and 5 leaves remainder 1, 2, and 4, is?

Question 4

Find the smallest number which leaves the same remainder 13 when divided by 24, 18 and 32.

Question 5

Find the remainder if (6458201)563421 is divided by 250.

Question 6

Find the smallest 6-digit number which is exactly divisible by 111.
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May 16ESE & GATE EE