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Manhattan Question Set # 1

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Manhattan Question Set # 1

by richachampion » Sun Oct 09, 2016 5:53 pm
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

OA: D
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by [email protected] » Sun Oct 09, 2016 7:28 pm
Hi richachamption,

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

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by GMATGuruNY » Mon Oct 10, 2016 2:19 am
richachampion 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
Alternate approach:

When x is divided by 4, the quotient is y and the remainder is 1.
Implication:
x = 4y + 1, where y is a nonzero integer.
Options for x:
1, 5, 9, 13...

When x is divided by 7, the quotient is z and the remainder is 6.
Implication:
x = 7z + 6, where z is a nonzero integer.
Options for x:
6, 13, 20...

The smallest value common to both lists is 13.
If x=13, then y=3 and z=1.
The question stem asks for the value of y=3. This is our target.
Now plug z=1 into the answer choices to see which yields our target of 3.
Only D works:
(7z + 5) / 4 = (7*1 + 5)/4 = 3.

The correct answer is D.
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