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Product of ab

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by j_shreyans » Tue May 19, 2015 8:58 am
If a and b are two integers such that a is even, b is odd and neither of them leaves a remainder of 1 when divided by 10, what is the units digit of the product ab?

1) The units digit of a^3 is the same as the units digit of a.
2) The units digit of b^4 is the same as the units digit of b.

OAB
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Source: — Data Sufficiency |

by binit » Wed May 20, 2015 1:21 am
My take:

a is even. b is odd. a or b not equals 1, 11, 21, 31 etc.

St 1: Units digit of a^3 = Units digit of a.
So, a can be 4, 5, 6 or 9. But a is even. So, a = 4 or 6.
But we have no idea about b, hence we can't say anything about units digit of ab. INSUFFICIENT.

St 2: Units digit of b^4 = Units digit of b.
So, b can be 1, 5 or 6. b is odd so 6 is out. b can't be 1, as the problem states. So, b = 5.
If b is 5 and a is even, the units digit of ab has to be ZERO. SUFFICIENT.
Note: This is very mistake prone to choose C after doing all this, I did :wink: but finally realized.

~Binit.
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