remainder problem/trick/confusion

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remainder problem/trick/confusion

by Cally627 » Sun May 20, 2012 11:28 am
This is from chapter 10 of manhattan gmat prep, book 1. pg 29

When positive integer A is divided by positive integer B, the result is 4.35.
Which of the following could be the remainder when A is divided by b?

I see that .35 is part of the remainder, so solve the decimal: 35/100 = 7/20 (by reducing)
and since we know that a remainder = R/B (the divisor)

7/20 = R/B

in the book, they suggest cross multiplying - leaving us with 7B = 20R...

the answer states, that since both b and r are integers, we can see that r MUST contain a 7 in its prime factorization, otherwise there is no way for 7 to appear on the left side.

this may be silly of me to ask for some, but does this mean that b must be a multiple of 20 also? (or 2^2 and 5?) since they are equal?

a little lost...on how you figure out that the remainder must be a multiple of 7...

if anyone has any advice, input - i would really appreciate it! thanks.
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by aneesh.kg » Sun May 20, 2012 11:45 am
Cally627 wrote:This is from chapter 10 of manhattan gmat prep, book 1. pg 29

When positive integer A is divided by positive integer B, the result is 4.35.
Which of the following could be the remainder when A is divided by b?

I see that .35 is part of the remainder, so solve the decimal: 35/100 = 7/20 (by reducing)
and since we know that a remainder = R/B (the divisor)

7/20 = R/B

in the book, they suggest cross multiplying - leaving us with 7B = 20R...

the answer states, that since both b and r are integers, we can see that r MUST contain a 7 in its prime factorization, otherwise there is no way for 7 to appear on the left side.

this may be silly of me to ask for some, but does this mean that b must be a multiple of 20 also? (or 2^2 and 5?) since they are equal?

a little lost...on how you figure out that the remainder must be a multiple of 7...

if anyone has any advice, input - i would really appreciate it! thanks.
Hi,

Let me run you through the basics of a Number being divided by another number(called a 'divisor').

Any Number N can be represented by the following equation:
N = Quotient*Divisor + Remainder, or
(N/Divisor) = Quotient + (Remainder/Divisor) = Integral Part + Decimal Part

The equation above tells us that when you divide a number by another number, the decimal part = (Remainder/Divisor)

For
A/B = 4.35
0.35 = Remainder/B
Remainder = 0.35B = (7/20)B

So far, So good.

First things first: Since Remainder is an integer and (7/20) is the most reduced of the fraction, B has to be a multiple of 20. You're right. Let B = 20k, where k is an integer.
The Remainder = (7/20)(20k) = 7k

The remainder is, thus, a multiple of 7.

Please let me know it this makes sense.
Aneesh Bangia
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by ihatemaths » Mon May 21, 2012 12:57 am
@aneesh will the Gmat twist like giving 2 answers with multiple of 7? i.e only with the above info in the question stem ?

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by aneesh.kg » Mon May 21, 2012 1:20 am
ihatemaths wrote:@aneesh will the Gmat twist like giving 2 answers with multiple of 7? i.e only with the above info in the question stem ?
If this were a GMAT problem or a problem with sensibly-designed options, then there will be just one option which is a multiple of 7. If in the exam, you think that more than one of the options are correct then you've certainly made a mistake somewhere.

For 'twists' such as the one you're talking about, there are the 'Data Sufficiency' problems.
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by ihatemaths » Thu May 24, 2012 5:48 am
lol:)