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11 May 2022, 02:45
Kudos
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E
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Difficulty:
55%
(hard)
Question Stats:
62% (01:29) correct
38%
(02:01)
wrong
based on 369
sessions
History
Date
Time
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Not Attempted Yet
What is the remainder when \((24^3*38^5) + 17^7\) is divided by 6 ?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
19 May 2022, 09:58
Kudos
Bookmarks
Bunuel
\((24^3)\) is divisible by 6 so term \((24^3*38^5)\) will generate reminder 0.
\((17^7)\) is divisible by 6 so term
\(17^7/6\\
=5^7/6\\
=(6-1)^7/6\\
=(-1)^7/6\) will generate reminder -1 or 5.
[Applied Euler's Rule for reminder]
remainder when \((24^3*38^5) + 17^7\) is divided by 6 is 0+5=5
Answer E
17 Sep 2024, 09:27
Kudos
Bookmarks
We need to find the remainder when \(24^3*38^5 + 17^7\) is divided by 6?
Remainder of \(24^3*38^5 + 17^7\) by 6 = Remainder of \(24^3*38^5\) by 6 + Remainder of \(17^7\) by 6
= 0 + Remainder of \(17^7\) by 6 [ as 24 is divisible by 6 ]
We solve these problems by using Binomial Theorem, where we split the number into two parts, one part is a multiple of the divisor(6) and a big number, other part is a small number.
=> \(17^{7}\) = \((18-1)^{7}\)
Watch this video to MASTER BINOMIAL Theorem
Now, if we use Binomial Theorem to expand this then all the terms except the last term will be a multiple of 6
=> All terms except the last term will give remainder of 0 when divided by 6
=> Problem is reduced to what is the remainder when the last term (i.e. 7C7 * 18^0 * (-1)^7) is divided by 6
=> Remainder of -1 is divided by 6
=> Remainder of -1 + 6 = 5
So, Answer will be E
Hope it Helps!
Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem
Remainder of \(24^3*38^5 + 17^7\) by 6 = Remainder of \(24^3*38^5\) by 6 + Remainder of \(17^7\) by 6
= 0 + Remainder of \(17^7\) by 6 [ as 24 is divisible by 6 ]
We solve these problems by using Binomial Theorem, where we split the number into two parts, one part is a multiple of the divisor(6) and a big number, other part is a small number.
=> \(17^{7}\) = \((18-1)^{7}\)
Watch this video to MASTER BINOMIAL Theorem
Now, if we use Binomial Theorem to expand this then all the terms except the last term will be a multiple of 6
=> All terms except the last term will give remainder of 0 when divided by 6
=> Problem is reduced to what is the remainder when the last term (i.e. 7C7 * 18^0 * (-1)^7) is divided by 6
=> Remainder of -1 is divided by 6
=> Remainder of -1 + 6 = 5
So, Answer will be E
Hope it Helps!
Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem
