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When x is divided by 4, the quotient is y and the remainder is 1.

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goodyear2013
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When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   29 Aug 2014, 13:01
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When x is divided by 4, the quotient is y and the remainder is 1. When x is divided by 7, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

(A) 4z/7 + 5
(B) (7z + 5)/6
(C) (6z + 7)/4
(D) (7z + 5)/4
(E) (4z + 6)/7
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D
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   29 Aug 2014, 14:39
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goodyear2013 wrote:
When x is divided by 4, the quotient is y and the remainder is 1. When x is divided by 7, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

A) 4z/7 + 5
B) (7z + 5) / 6
C) (6z + 7) / 4
D) (7z + 5) / 4
E) (4z + 6) / 7

This is easy one.


When x is divided by 4, the quotient is y and the remainder is 1: x = 4y + 1.
When x is divided by 7, the quotient is z and the remainder is 6: x = 7z + 6.

Equate those two:
4y + 1 = 7z + 6;
y = (7z + 5)/4.

Answer: D.
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   01 Oct 2014, 21:56
x = 4y + 1

x = 7z + 6

4y = 7z + 5

\(y = \frac{7z+5}{4}\)

Answer = D
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   10 Dec 2015, 07:32
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goodyear2013 wrote:
When x is divided by 4, the quotient is y and the remainder is 1. When x is divided by 7, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

A) 4z/7 + 5
B) (7z + 5) / 6
C) (6z + 7) / 4
D) (7z + 5) / 4
E) (4z + 6) / 7

This is easy one.


Number = Quotient*Divisor + Remainder

x = 4y + 1 (i)
x = 7z + 6 (ii)

Equating (i) and (ii)
4y + 1 = 7z + 6
y = (7z + 5)/4

Option D
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   27 Jun 2017, 15:27
goodyear2013 wrote:
When x is divided by 4, the quotient is y and the remainder is 1. When x is divided by 7, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

A) 4z/7 + 5
B) (7z + 5) / 6
C) (6z + 7) / 4
D) (7z + 5) / 4
E) (4z + 6) / 7

This is easy one.


X is 13- one way to come with the number is just through trial and error- if x is 13 then z is 1 and y is 3- only D solves for Y

Thus
"D"
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   26 Jan 2018, 14:47
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Hi All,

This question can be solved in a couple of different ways, but you would likely find the algebra to be fairly straight-forward. From the first two sentences, we can create the following 2 equations:

X/4 = Y remainder 1
X = 4Y + 1

X/7 = Z remainder 6
X = 7Z + 6

Now we can set the two equations equal to one another:

4Y + 1 = 7Z + 6
4Y = 7Z + 5
Y = (7X+5)/4

Final Answer:
Show Spoiler
D


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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   25 Sep 2022, 09:15
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When x is divided by 4, the quotient is y and the remainder is 1

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
4 -> Divisor
y -> Quotient
1 -> Remainder

=> x = 4*y + 1 = 4y + 1 ...(1)

When x is divided by 7, the quotient is z and the remainder is 6

=> x = 7*z + 6 = 7z + 6 ...(2)

Equating (1) and (2) we get

x = 4y + 1 = 7z + 6
=> 4y = 7z + 6 - 1 = 7z + 5
=> y = \(\frac{7z + 5}{4}\)

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   28 Sep 2022, 05:08
goodyear2013 wrote:
When x is divided by 4, the quotient is y and the remainder is 1. When x is divided by 7, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

A) 4z/7 + 5
B) (7z + 5) / 6
C) (6z + 7) / 4
D) (7z + 5) / 4
E) (4z + 6) / 7

This is easy one.


The statement can be written in the form of following equations:

x=4y+1.......(i)
x=7z+6.......(ii)

Equating (i) & (ii)

4y+1=7z+6
4y= 7z+5
y=(7z+5)/4

Hence, answer is option D.
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink] New post   04 Oct 2023, 01:41
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Re: When x is divided by 4, the quotient is y and the remainder is 1. [#permalink]
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