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a = 1. Does not tell anything about b --therefore is insufficient on its own to answer the question.

Statement 2

b = 2

2a + 1 + b becomes

2a (even) + 1 (odd) + b (even) = ODD. So the exponent to 4 is ODD. So I understand that if we put 3, 5 etc I get the remainder 4, but why can't I put exponent as 1 as 1 is ODD too. Can you please help?

Re: Remainder when divided by 10 [#permalink]
26 Feb 2012, 15:39

5

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powers of 4 go like this:

The unit place is: 1 = 4 2 = 6 3 = 4 4 = 6

So all even exponents have 6 in unit place, and all off exponents have 4 in unit place. To solve the problem we need to find whether the 2a + 1 + b is even or odd

As a is +ve integer, 2a is always even. 2a + 1 will be odd. Now to determine whether (2a + 1 + b) is even or odd, we need to know only b.

Re: Remainder when divided by 10 [#permalink]
26 Feb 2012, 15:58

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Expert's post

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This post was BOOKMARKED

If a and b are positive integers, what is the remainder when \(4^{2a+1+b}\) is divided by 10?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

Back to the question: 4 in positive integer power can have only 2 last digits: 4, when the power is odd or 6 when the power is even. Hence, to get the remainder of 4^x/10 we should know whether the power is odd or even: if it's odd the remainder will be 4 and if it's even the remainder will be 6.

(1) a = 1 --> \(4^{2a+1+b}=4^{3+b}\) depending on b the power can be even or odd. Not sufficient.

(2) b = 2 --> \(4^{2a+1+b}=4^{2a+3}=4^{even+odd}=4^{odd}\) --> the remainder upon division of \(4^{odd}\) by 10 is 4. Sufficient.

Answer: B.

enigma123 wrote:

2a (even) + 1 (odd) + b (even) = ODD. So the exponent to 4 is ODD. So I understand that if we put 3, 5 etc I get the remainder 4, but why can't I put exponent as 1 as 1 is ODD too. Can you please help?

The power of 4 is \(2a+3\) and since \(a\) is a positive integer then the lowest value of \(2a+3\) is 5, for \(a=1\). Next, even if the power were 1 then 4^1=4 and the remainder upon division of 4 by 10 would still be 4.

Re: If a and b are positive integers, what is the remainder when [#permalink]
11 Aug 2013, 08:20

REM(4^(2a+1+b))/10

Means we have to find last digit of the expression.So rephrasing the question

What is the last digit of 4^(2a+1+b)

(1). a=1

Break the expression as 4^2a * 4^1 * 4^b.

b is unknown hence INSUFFICIENT

(2).

b=2

4^2a * 4^1 * 4^b.

If you can observe the expression 4^2a, you will see that this will always give last digit as '6' you can try out numbers if you want.

So knowing the expression and value of b last digit can be calculated and hence the remainder can also be calculated.

Hence (B) it is !! _________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: If a and b are positive integers, what is the remainder when [#permalink]
30 Aug 2014, 04:22

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