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# When positive integer x is divided by 5, the quotient is q and the rem

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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink]
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GMATPrepNow wrote:
When positive integer x is divided by 5, the quotient is q and the remainder is 1. When x is divided by 7, the quotient is k and the remainder is 1. What is the remainder when q is divided by 7?

A) 0
B) 1
C) 2
D) 3
E) 4

*Kudos for all correct solutions

we know that x=5q+1 and x=7k+1

in other words, x is a multiple of 5 and 7 +1 for example 35 or 70 or 105 .....
in each case q is a multiple of 7 ====>7 or 14 or 21....

therefore $$\frac{q}{7}$$ is equal to an integer. (remainder=0)

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When positive integer x is divided by 5, the quotient is q and the rem [#permalink]
1
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When positive integer x is divided by 5, the quotient is q and the remainder is 1. When x is divided by 7, the quotient is k and the remainder is 1. What is the remainder when q is divided by 7?

A) 0
B) 1
C) 2
D) 3
E) 4

x=1+5*7=36
q=7
7/7 gives a remainder of 0
A
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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink]
2
Kudos
GMATPrepNow wrote:
When positive integer x is divided by 5, the quotient is q and the remainder is 1. When x is divided by 7, the quotient is k and the remainder is 1. What is the remainder when q is divided by 7?

A) 0
B) 1
C) 2
D) 3
E) 4

*Kudos for all correct solutions

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Hi,
We get two equations..
1) x=5q+1
2) x=7k+1...

This means 5q+1=7k+1......
Or 5q=7k..
This tells us that q is multiple of 7 and k is multiple of 5..
SO if you divide q by 7 or k by 5, remainder will be 0

A
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When positive integer x is divided by 5, the quotient is q and the rem [#permalink]
GMATPrepNow wrote:
When positive integer x is divided by 5, the quotient is q and the remainder is 1. When x is divided by 7, the quotient is k and the remainder is 1. What is the remainder when q is divided by 7?

A) 0
B) 1
C) 2
D) 3
E) 4

least value of x=1
q=0
0/7 leaves remainder of 0
A
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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink]
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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink]
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