What is the value of the two-digit positive integer n?

(1) When n is divided by 5, the remainder is equal to the tens digit of n.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.



Any help on this one would be much appreciated! Thanks

Let's take each statement at a time.

(1) When n is divided by 5, the remainder is equal to the tens digit of n.
Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16.
Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27
There will be more such numbers so we can see that this is certainly not sufficient.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19.
Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29
There will be more such numbers so we can see that this is certainly not sufficient.

What do we do when we consider both statements together?
We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49
Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99.
Hence, there is only one such two digit number i.e. n = 49.

Answer (C)
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