CAT 2016 Quantitative Ability

Question : 22 of 34

Marks: +1, -0

Find the smallest number which when divided by 3, 5 and 7 leaves remainders 2,4 and 6 respectively.

104
105
209
None of these

Solution:

The form of a number which when divided by 3,5 and 7 leaves remainders 2,4 and 6 respectively
= k * (LCM of 3.5 and 7) -1, where k is a natural number
= 105k - 1
For the number to be the smallest, k has to be 1.
Hence, the smallest such number

= 105 × 1 -1 = 104

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