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CAT 1994 — QA Question 29

Number TheoryEasy

Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.

Answer & solution

Correct answer: 172

  • A

    137

  • B

    1361

  • C

    140

  • 172

Solution

The LCM of 7, 12 and 16 is 336. The closest multiple of 336 to 1856 is 1680. So 1684 when divided by 7, 12 and 16 leaves a remainder of 4. This is the closest such number, less than 1856.
Hence the number to be subtracted from 1856 to get 1684, must be the least such number. So the answer is (1856 – 1684) = 172.
 

Alternate method:
Subtract options from 1856 and check.

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CAT 1994 QA Q29: Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and — Solution | TheCATExam