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Positive integer Q gives a remainder of 5 when divided by 7. Find the

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Carcass
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Positive integer Q gives a remainder of 5 when divided by 7. Find the [#permalink] New post   09 Jul 2021, 08:42
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Positive integer Q gives a remainder of 5 when divided by 7. Find the remainder when 2Q is divided by 7.

(A) 2
(B) 3
(C) 5
(D) 7
(E) 9
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B
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Re: Positive integer Q gives a remainder of 5 when divided by 7. Find the [#permalink] New post   09 Jul 2021, 08:54
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Carcass wrote:
Positive integer Q gives a remainder of 5 when divided by 7. Find the remainder when 2Q is divided by 7.

(A) 2
(B) 3
(C) 5
(D) 7
(E) 9


-------------ASIDE------------------
When it comes to remainders, we have a nice property that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
--------------------------------------

Positive integer Q gives a remainder of 5 when divided by 7.
So, the possible values of Q are: 5, 12, 19, 26, 33, . . . etc

Find the remainder when 2Q is divided by 7.
Let's test one of the possible values of Q.
The easiest value to test is Q = 5
So, 2Q = 2(5) = 10, and 10 divided by 7 leaves remainder 3

Answer: B

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Positive integer Q gives a remainder of 5 when divided by 7. Find the [#permalink] New post   10 Jan 2022, 09:42
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Positive integer Q gives a remainder of 5 when divided by 7

Theory: Dividend = Divisor*Quotient + Remainder

Q -> Dividend
7 -> Divisor
a -> Quotient (Assume)
5 -> Remainders
=> Q = 7*a + 5 = 7a+5 ...(1)

Find the remainder when 2Q is divided by 7.

2Q = 2*(7a+5) [ From (1) ]
=> 2Q = 14a + 10 = 14a + 7 + 3 = 7*(2a + 1) + 3
=> 2Q when divided by 7 gives 2a+1 as quotient and 3 as remainder

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Positive integer Q gives a remainder of 5 when divided by 7. Find the [#permalink]
10 Jan 2022, 09:42
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