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# What is the remainder?

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Intern
Joined: 17 Oct 2019
Posts: 3

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17 Nov 2019, 21:08
2
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:09) correct 45% (01:32) wrong based on 42 sessions

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What is the remainder for the following:

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

A 1
B 2
C 3
D 4
E 5
Intern
Joined: 10 Oct 2019
Posts: 11
GMAT 1: 400 Q35 V12

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17 Nov 2019, 23:57
=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
Senior Manager
Joined: 15 Feb 2018
Posts: 411
Re: What is the remainder?  [#permalink]

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18 Nov 2019, 04:19
What is the question source?
Intern
Joined: 27 Nov 2018
Posts: 48
Re: What is the remainder?  [#permalink]

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18 Nov 2019, 08:36
1
(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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Joined: 03 Jun 2019
Posts: 1882
Location: India
Re: What is the remainder?  [#permalink]

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18 Nov 2019, 08:39
henilshaht wrote:
What is the remainder for the following:

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

A 1
B 2
C 3
D 4
E 5

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

IMO D
Senior Manager
Joined: 30 Sep 2017
Posts: 463
GMAT 1: 720 Q49 V40
GPA: 3.8

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18 Nov 2019, 09:03
3
$$=\frac{6^{35}}{6}−\frac{6^{25}}{6}−\frac{2}{6}$$

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.

Intern
Joined: 27 Nov 2018
Posts: 48
Re: What is the remainder?  [#permalink]

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18 Nov 2019, 10:05
Kinshook wrote:
henilshaht wrote:
What is the remainder for the following:

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

A 1
B 2
C 3
D 4
E 5

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

IMO D

Can you please elaborate on term "6k+6" used in your solution ? How did you get that
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Re: What is the remainder?  [#permalink]

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22 Nov 2019, 12:39
henilshaht wrote:
What is the remainder for the following:

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

A 1
B 2
C 3
D 4
E 5

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.

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Re: What is the remainder?   [#permalink] 22 Nov 2019, 12:39
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