If a and b are positive integers, what is the digit at the units place

Question

If a and b are positive integers, what is the digit at the units place of  2^{4a+5b}

(1) b = 5

(2) a = 3

ak31 · Answer

(1) is sufficient so answer is A

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neha283 · Answer

2^(4a+5b)
Unit digit for 2^1 --> 2
Unit digit for 2^2 --> 4
Unit digit for 2^3 --> 8
Unit digit for 2^4 --> 6
Unit digit for 2^5 --> 2
So, unit digits are repeated after 4th power. 
we don't need to worry about 4a. 
unit digit for 2^4a = 6

Statement (1) b=5
2^(4a+25)
unit digit = 6 + 2 = 8
So, statement (1) is sufficient.

Statement (2) gives value for a but not b. Hence not sufficient.

(A)

mykrasovski · Answer

Bunuel , can you please suggest the solution? I believe the answer is B. Here is why

The unit digit of  2^{4a+5b}  depends on the power, so we need to know the value of  4a+5b .

1) tells us b, but we don't know anything about  4a . For instance, it could be that  4a = 4   (a = 1)  or  4a=8  if  (a = 2) .

2) tells us a, and this is sufficient because  5b  will always end in 5, so the power is  4*3+5b = 12+something5=something7 .

If a and b are positive integers, what is the digit at the units place

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GMAT Data Sufficiency (DS) Questions

If a and b are positive integers, what is the digit at the units place

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