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

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BrentGMATPrepNow
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When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   31 Oct 2016, 07:58
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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

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A
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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   31 Oct 2016, 19:08
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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

Show Spoiler
Here's our video solution: https://www.gmatprepnow.com/module/gmat ... /video/856


RELATED VIDEO


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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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   31 Oct 2016, 08:04
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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


x = 5q + 1

x = 7k + 1

Think of a number which when divided by both 5 & 7 leaves a remainder of 1

Trick : Do LCM of 5 & 7 and add 1 to it...

x = 36

So, x = 5q + 1

Or, 36 = 5*7 + 1

7/7 will leave remainder of 0

Hence correct answer will be (A) 0
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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   31 Oct 2016, 08:29
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1,6,11,16,21,26,31,36

1,8,15,22,29,36


So x=35z+1

When x is divided by 5, then q will always be a multiple of 7.

So the reminder when q is divided by 7 will always be 0.

A


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Re: When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   31 Oct 2016, 11:51
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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)

answer A
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When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   31 Oct 2016, 13:42
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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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gracie
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When positive integer x is divided by 5, the quotient is q and the rem [#permalink] New post   11 Jan 2020, 21:16
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] New post   03 Feb 2023, 09:40
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