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PS Question

by chaitanya.mehrotra » Fri Jul 01, 2011 1:43 pm
a and b are integers such that a/b=3.45. If R is the remainder of a/b which of the following could NOT be equal to R?

a) 3
b) 9
c) 36
d) 81
e) 144
Can somebody tell how to approach this question .

[spoiler]correct answer is (A)[/spoiler]
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by goalevan » Fri Jul 01, 2011 6:36 pm
A problem of this type appears very difficult to test numbers, so I would always start by rephrasing the question.

In many remainder problems, the formula dividend/divisor = quotient + remainder/divisor can be used to discover basic relationships between the inputs of the problem.

In this case, we have a/b = 3 + R/b. But the question stem also states that a/b = 3.45 = 3 + 45/100, so R/b = 45/100.

In problems testing integer properties of a variable, I like to isolate the other variable in the problem and identify possible values that create an integer.

Isolating the other variable, b, we see:

b = 100R/45,
b = 25R/9

We are told that b is an integer, and 25 is not divisible by 9, so R must be divisible by 9. In other words, 9 must be factor of R, or R is a multiple of 9.

It can be seen clearly that 3 is the only answer choice that is not a multiple of 9.

A
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by sunilrawat » Fri Jul 01, 2011 9:52 pm
since R is the remainder,
b*0.45=R
or,
b=20R/9
for b to be an integer, R should be completely divisible by 9.
Only option A is not
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by sunilrawat » Fri Jul 01, 2011 9:54 pm
goalevan wrote:A problem of this type appears very difficult to test numbers, so I would always start by rephrasing the question.

In many remainder problems, the formula dividend/divisor = quotient + remainder/divisor can be used to discover basic relationships between the inputs of the problem.

In this case, we have a/b = 3 + R/b. But the question stem also states that a/b = 3.45 = 3 + 45/100, so R/b = 45/100.

In problems testing integer properties of a variable, I like to isolate the other variable in the problem and identify possible values that create an integer.

Isolating the other variable, b, we see:

b = 100R/45,
b = 25R/9

We are told that b is an integer, and 25 is not divisible by 9, so R must be divisible by 9. In other words, 9 must be factor of R, or R is a multiple of 9.

It can be seen clearly that 3 is the only answer choice that is not a multiple of 9.

A


b=20R/9
I highlighted it because these kind of mistakes sometimes lead to the wrong answer (i am still a victim :().
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by chaitanya.mehrotra » Sat Jul 02, 2011 1:25 am
Thanks Folks
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by goalevan » Sat Jul 02, 2011 1:38 pm
Thanks for the correction sunilrawat.
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