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

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Difficulty:   45% (medium)

Question Stats: 56% (01:02) correct 44% (01:20) wrong based on 315 sessions

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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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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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2
$$(48+1)(60+4)=48*60+48*4+60+4$$=> 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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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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Joined: 02 Aug 2009
Posts: 7959
Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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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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1
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

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.

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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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
$$1^2 * 2^2 = 4$$
D
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GRE 1: Q169 V154 Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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Great Question.
Here is what i did=>
7=6k+1
and 8=6k+2
so 7^2=> 6k+1
8^2=> 6k+4
Hence there product would leave the remainder 4

Hence D

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

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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

$$\frac{7^2}{6}$$ = 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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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?
Intern  B
Joined: 28 Dec 2010
Posts: 21
What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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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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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?  [#permalink]

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(7^2*8^2)/6=
(56^2)/6=
((54+2)^2)/6=
(2^2)/6=4

D = 4

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Intern  B
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Posts: 28
Location: India
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Re: What is the remainder when 7^2 * 8^2 is divided by 6?  [#permalink]

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Zoser wrote:
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?

6/3= 2 so reminder will be
2*(reminder of 1568/3 ) = 4

Posted from my mobile device Re: What is the remainder when 7^2 * 8^2 is divided by 6?   [#permalink] 20 Jul 2019, 01:29
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