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

Question

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

Bunuel · Answer

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.

PareshGmat · Answer

x = 4y + 1

x = 7z + 6

4y = 7z + 5

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

Answer = D

TeamGMATIFY · Answer

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

Nunuboy1994 · Answer

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"

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made, 
Rich

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=P0S6j2uTaj4

tanyas311 · Answer

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.

bumpbot · Answer

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

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

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