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What is the remainder when 7^2 * 8^2 is divided by 6?

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What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 06 Feb 2016, 13:16
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What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 06 Feb 2016, 13:28
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BrainLab wrote:
What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible


(7²)(8²) = (49)(64)
= (48 + 1)(64)
= (48)(64) + (1)(64)
Since 48 is a multiple of 6, we can conclude that (48)(64) is a multiple of 6, so we get:
= (some multiple of 6) + (1)(64)
= (some multiple of 6) + 64
= (some multiple of 6) + 60 + 4
Since 60 is a multiple of 6, we can write:
= (some multiple of 6) + (another multiple of 6) + 4
= (A MULTIPLE OF 6) + 4

So, when we divide the above by 6, we get a remainder of 4

Cheers,
Brent
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What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 06 Feb 2016, 13:50
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\((48+1)(60+4)=48*60+48*4+60+4\)=> All of them except 4 are divisible by 6, so the answer is 4 (D)
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 06 Feb 2016, 13:35
3
BrainLab wrote:
What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible


7^2*8^2 = (56)^2 = (54+2)^2 = 54^2+2*2*54+2^2 = multiple of 6+multiple of 6 + 4 and this will give you a remainder of 4.

D is the correct answer.

Hope this helps.
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 07 Feb 2016, 03:21
3
4
BrainLab wrote:
What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible


a method different from above could be..

\(7^2 * 8^2\)= (6+1)^2*(6+2)^2..
(6+1)^2 will leave 1 as remainder and (6+2)^2 will leave 4 as remainder..
so overall remainder=1*4=4
D
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 07 Feb 2016, 08:25
2
BrainLab wrote:
What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible


the solution from chetan2u was mind blowing and most simplifying.

However I have a remainder rule I know.
"Multiply the remainders of the dividends and divide the product by the divisor"

49/6 is remainder 1. 64/6 is remainder 4.
Therefore 4 * 1 equals 4.
4/6 is 0 remainder 4.
Answer is D

you know this rule, you do this math in 4 seconds.
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What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 25 Feb 2016, 03:14
1
BrainLab wrote:
What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

\(\frac{(49 * 64)}{6}\) gives remainer x
49 is remainder 1. 64 is remainder 4. 4*1 = 4. So x = 4
OR
7 is remainer 1. 8 is remainder 2
\(1^2 * 2^2 = 4\)
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 03 Dec 2016, 23:28
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 04 Dec 2016, 00:12
BrainLab wrote:
What is the remainder when \(7^2 * 8^2\) is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible


\(\frac{7^2}{6}\) = Remainder 1
\(\frac{8^2}{6}\) = Remainder 4

Thus, remainder of \(\frac{7^2 * 8^2}{6}\) will be 1*4 , ie 4

Hence remainder will be (D) 4

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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 07 Apr 2017, 04:24
I had come to an answer of 2.

This was my approach:
7^2*8^2
Simplify: 7*7*8*8
Then divide by 6: (7*7*8*8)/6
We get: (7*7*8*4)/3
We get 1568/3
Which gives a quotient of 522 and remainder of 2

What did I do incorrectly here?
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What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 27 Jun 2017, 15:06
Another way of looking at the problem:

(7^2 * 8^2)/6 = (56^2)/6

Now, since the remainder of 56/6 is 2 remainder of 56^2/6 will be 4.

Example: M/7 we get remainder r. What will be the remainder of M^2/7?

M = 7a+r. where a is a quotient and r is remainder.

M^2= (7a + r)(7a +r)
= 49a^2 + 7ar + 7ar + r^2
M^2/7 = 49a^2/7 + 7ar/7 +7ar/7 + r^2 => Remainder is r^2.
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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New post 16 Jul 2018, 02:17
1
Why is it wrong to transform 49*64/6 into 49*32/3 (divide numerator and denominator by 2)
Then remainder would be 2..
(48+1)(30+2)/3, 48 and 30 are multiples of 3, remainder=2
Why is it not possible to simplify the equation?

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Re: What is the remainder when 7^2 * 8^2 is divided by 6? &nbs [#permalink] 16 Jul 2018, 02:17
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