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

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

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New post 31 Oct 2016, 06:58
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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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Re: When positive integer x is divided by 5, the quotient is q and the rem  [#permalink]

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New post 31 Oct 2016, 07:04
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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]

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New post 31 Oct 2016, 07:29
1
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]

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New post 31 Oct 2016, 10:51
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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]

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New post 31 Oct 2016, 12:42
1
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]

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New post 31 Oct 2016, 18:08
2
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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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 &nbs [#permalink] 05 Dec 2017, 05:54
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