Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

4

This post received KUDOS

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

3

This post received KUDOS

Expert's post

1

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 ais 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 _____________________________________________________________________________