What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?
(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these
(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these
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We're adding nine odd numbers here- the sum will be odd. The sum will also be a multiple of 3, since each term in the sum is divisible by 3. So the sum is an odd multiple of 3, and the remainder will be 3 when you divide by 6.nikhilagrawal wrote:What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?
I have to disagree that the remainder is 3 when you divide an odd multiple of 3 by 6.Ian Stewart wrote:So the sum is an odd multiple of 3, and the remainder will be 3 when you divide by 6.nikhilagrawal wrote:What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?
OK, the remainder should be 1, not 5. When an odd number is divided by 2, the remainder's always 1, my mistake. But the answer is still None of these, since 1 isn't an option either.pepeprepa wrote:Just one remark about Saule.
I think I see where your error is.
You say "Eliminate 3 from both numerator and denominator, and you'll be left with 2 in the denominator."
I think you cannot do that when you want to find a remainder.
Counter-exemple:
15 divided by 6 gives you a remainder of 3
15/6=(3*5)/(3*2)=5/2
5 divide by 2 gives you a remainder of 1
Am I right about this fact?
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