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Bunuel
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Pre-think:
5^(3n) always has unit digit of 5.
For 9^(5m), its unit digit will be 9 if m is odd, or its unit digit will be 1 if m is even.
We just need to know whether m is odd.

(1)Only
m is odd.
Sufficient

(2) Only
We do not know whether m is odd.
Insufficient

The answer is thus (A).
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Bunuel
If m and n are positive integers, what is the units digit of \(5^{3n} + 9^{5m}\) ?

(1) m is an odd integer.
(2) n is an even integer.




Question -> units digit of \(5^{3n} + 9^{5m}\)?

We don't care what n is as for any power of 5, Unit digit is 5
Whereas For Odd Power of 9, Unit Digit is 9, for even power it is 1
So, we need to know if m is odd or even

(1) m is an odd integer. -> This answers our pre-thinking! Sufficient
(2) n is an even integer. -> We don't care about nature of n as mentioned earlier, Not sufficient

Answer is A
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In 9^5m does it matter what the value of m is as it will always be odd ?



zhanbo
Pre-think:
5^(3n) always has unit digit of 5.
For 9^(5m), its unit digit will be 9 if m is odd, or its unit digit will be 1 if m is even.
We just need to know whether m is odd.

(1)Only
m is odd.
Sufficient

(2) Only
We do not know whether m is odd.
Insufficient

The answer is thus (A).
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