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For positive integers x and y, x/y=94.35. Which of the follo

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by hazelnut01 » Sat May 06, 2017 4:28 pm
For positive integers x and y, x/y=94.35. Which of the following could not be the remainder when x is divided by y?

A. 14
B. 15
C. 35
D. 70
E. 105

Source : Veritas Prep
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by [email protected] » Sat May 06, 2017 5:26 pm
Hi ziyuenlau,

From we wording of the prompt, we know that 4 of the answers COULD be the remainder, so one way to approach this prompt is to find the 4 answers that are possible remainders - and the fifth one is the one that is not. I'm going to start you off on this question so that you can finish it on your own:

We're told that X and Y are POSITIVE INTEGERS and that X/Y = 94.35

Thus, X and Y could be...

X = 9435
Y = 100

In this example, 9435/100 = 94 remainder 35... so 35 could be the remainder.

By increasing/decreasing the relative values of X and Y, you should be able to find the other 3 possible remainders. What would happen if you divided those two values by 5? What would happen if you multiplied those two values by 2? Etc.

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by Jay@ManhattanReview » Sat May 06, 2017 9:13 pm
ziyuenlau wrote:For positive integers x and y, x/y=94.35. Which of the following could not be the remainder when x is divided by y?

A. 14
B. 15
C. 35
D. 70
E. 105

Source : Veritas Prep
We are given that x/y = 94.35. Thus, we have,

x/y = 95.35

x/y = 9535/100

x/y = 99 + 7/20

We see that the remainder must be a multiple of 7. The only option that is not a multiple of 7 is 15.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

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by GMATGuruNY » Sun May 07, 2017 2:39 am
ziyuenlau wrote:For positive integers x and y, x/y=94.35. Which of the following could not be the remainder when x is divided by y?

A. 14
B. 15
C. 35
D. 70
E. 105

Source : Veritas Prep
When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.

Strategy:
Rephrase the decimal AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = r.
Divisor = y.
Decimal = 0.35 = 35/100 = 7/20.
Plugging these values into remainder/divisor = decimal, we get:
r/y = 7/20.

The resulting ratio indicates that r must be a MULTIPLE OF 7 and that y must be a multiple of 20.
Of the five answer choices, only B is not a multiple of 7.

The correct answer is B.
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by Jeff@TargetTestPrep » Fri May 12, 2017 12:24 pm
ziyuenlau wrote:For positive integers x and y, x/y=94.35. Which of the following could not be the remainder when x is divided by y?

A. 14
B. 15
C. 35
D. 70
E. 105
This problem will be best solved using the remainder formula. Let's first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

We are given that x/y = 94.35. Using the remainder formula, we can say:

x/y = 94.35

x/y = 94 + 35/100

x/y = 94 + 7/20

We see that we now can equate 7/20 to r/y:

7/20 = r/y

We see that the remainder must be a multiple of 7. The only answer choice that is not a multiple of 7 is 15.

Answer: B

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