agdimple333 wrote:
If \(N = 1234@\) and \(@\) represents the units digit, is \(N\) a multiple of 5?
\(@!\) is not divisible by 5
\(@\) is divisible by 9
This is how you would analyze this question:
N = 1234@
Question: Is N a multiple of 5?
How do you figure whether a number is a multiple of 5 or not? You see the last digit to decide. If the last digit is 0/5, the number is divisible by 5, else it is not.
1. @! is not divisible by 5.
If @ = 0, 0! is 1 which is not divisible by 5. In this case N (12340) is divisible by 5.
If @ = 1, 1! is 1 which is not divisible by 5. In this case N (12341) is not divisible by 5.
So satisfying statement 1 is not sufficient to know whether N is divisible by 5.
2. @ is divisible by 9.
There are only 2 digits that are divisible by 9: 0 and 9
If @ = 0, N (12340) is divisible by 5.
If @ = 9, N (12349) is not divisible by 5.
So satisfying statement 2 is not sufficient to know whether N is divisible by 5.
Using both, The only value of @ that satisfies both statements is 0. (9! is divisible by 5 hence @=9 doesn't satisfy statement 1.)
If @ = 0, N (12340) is divisible by 5.
Hence, using both together, we know that N is divisible by 5. Sufficient.
Answer (C).
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