A is a set of positive integers such that when divided by 2 3 4 5 and 6 leaves the remainder 1 2 3 4...........

Quantitative Aptitude (CDS) Number System

A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integer between 0 and 100 belong to the set A?

No integer

One

Two

Three

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Explanation:

Number = LCM of (2, 3, 4, 5, 6) – (Difference of divisors and remainder) = 60 − Differences of divisors and remainder ………… (i)
As number when divided by 2, 3, 4, 5, 6 gives remainder 1, 2, 3, 4,5 respectively
Then,
2−1=1
3−2=1
4−3=1
5−4=1
6−5=1
From (i)
Number =60−1=59
Other number =59×2=118
Clearly, there is one number of set A which is below 100
Hence option (2)