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.
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Product of ab
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j_shreyans
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binit
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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
but finally realized.
~Binit.
- - - - -
A thanks will be appreciated if u like my post.
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
but finally realized. ~Binit.
- - - - -
A thanks will be appreciated if u like my post.
