What is the remainder?

Question

What is the remainder for the following:

\frac{6^{35} - 6^{25} - 2}{6} ?

A 1
B 2
C 3
D 4
E 5

freedom128 · Accepted Answer

=\frac{6^{35}}{6}−\frac{6^{25}}{6}−\frac{2}{6}

Both  \frac{6^{35}}{6}  and  \frac{6^{25}}{6}  leave NO reminder.  \frac{-2}{6}  has a reminder of -2 or (6-2)=4.

Answer is (D)

kawal27 · Answer

QUESTION IS ASKING  REMAINDER  
=6^35-6^25-2/6
=6^10-2/6
=6^9*6-2/6
=1*1*1*1*1*1*1*1*1*6-2/6
=6-2/4 =4/6 
which is reminder 4
ANS:D

dont need to do all this if you can get direct ans

philipssonicare · Answer

What is the question source?

pandajee · Answer

(6^35 - 6^25 )..whatever will be the value of this ..it will be a multiple of 6 or it will be divisible by 6. Example- 6^2-6 = 30 which is divisible by 6. It follows from the rule "If two multiples of a number are subtracted then the result would be another multiple of that number. Example 49-14=35..49 and 14 are multiple of 7 and the resultant is also a multiple of 7. 
Now, in the question.. 6^35-6^25 will result in a multiple of 6. Subtracting 2 from a multiple of 6 will leave remainder as 4.Example- 18 is divisible by 6 and if we subtract 2 from 18 we get 16. 16÷6 will leave remainder as 4. Hence, for the question under discussion, 4 will be the remainder.

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Kinshook · Answer

6^{25}(6^{10} -1) -2 = 6k + 6 -2 = 6k +4 
Remainder when  6^{35} - 6^{25} - 2  is divided by 6 is 4.

IMO D

pandajee · Answer

Can you please elaborate on term "6k+6" used in your solution ? How did you get that

ScottTargetTestPrep · Answer

Recall that 6 raised to any positive integer power is always divisible by 6. Thus, we see that the first two terms are divisible by 6. Therefore, the remainder is the last term “-2.” Since -2 can’t be remainder (remainder can’t be negative), we can add 6 to -2 to obtain 4 as the actual remainder.

Answer: D

BrentGMATPrepNow · Answer

\frac{6^{35} - 6^{25} - 2}{6}=\frac{6^{35} - 6^{25} - 6 +4}{6}

=\frac{6(6^{34} - 6^{24} - 1) +4}{6}

At this point, we can see that the numerator is  4 greater than   some multiple of 6, 
So when we divide the numerator by 6, the remainder must be 4.

Answer: D

RELATED VIDEO 
 https://www.youtube.com/watch?v=XCxgIR042tE

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What is the remainder?

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What is the remainder?

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