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# If a and b are positive integers so that the remainder, when dividing

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Manager
Joined: 01 Jan 2016
Posts: 57
GPA: 3.75
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If a and b are positive integers so that the remainder, when dividing  [#permalink]

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06 Feb 2018, 10:30
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85% (hard)

Question Stats:

44% (01:22) correct 56% (01:47) wrong based on 99 sessions

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If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

Source: ExamPAL

Kudos for detailed explanation!

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If a and b are positive integers so that the remainder, when dividing  [#permalink]

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06 Feb 2018, 12:37
1
Teerex wrote:
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

Source: ExamPAL

Kudos for detailed explanation!

This is the method that I used to solve this problem
We need the fraction a/b such that we get remainder as 4.

Evaluate the various answer options available
a) 3x/4x
When x=1, remainder of 3
When x=2, remainder of 6
When x=3, remainder of 9
When x=4, remainder of 12
b) x/3x
When x=1, remainder of 1
When x=2, remainder of 2
When x=3, remainder of 3
When x=4, remainder of 4

Hence, Option B(1/3) could be the value of the expression (a/b)
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Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

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06 Feb 2018, 23:42
1
pushpitkc wrote:
Teerex wrote:
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

Source: ExamPAL

Kudos for detailed explanation!

This is ExamPAL's solution:
Since all the answers are smaller than 1, a must be smaller than b. So a must be the remainder itself.
so, 4/b=fraction such that b is an integer.
Checking this:
Option A: 4/b=3/4 => b=16/3 (incorrect as b is not an integer)
Option B: 4/b=1/3 =>b=12 (Correct as b is an integer)

So, B is the correct answer!

I thought the solution is really cool coz I didn't think like that at all! Hope you like it :D
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Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

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07 Feb 2018, 04:37
Teerex wrote:
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

Source: ExamPAL

Kudos for detailed explanation!

As per the question -

$$a - 4 = bq$$, which means as a & b are positive integers, a value will always be greater than or equal to 4.
Lets take $$a = 5, bq = 1 (a>b)$$
$$a = 6, bq = 2 (a > b).$$
But as per the options a < b. So, the only value possible for $$a = 4, bq = 0$$ (here, $$q = 0$$ as b is positive integer)
As $$a = 4$$, to make $$a < b, b = 4k$$ (Where $$k = 2,3,4,5,6,7,8.....$$ etc).
Only Option is $$\frac{4}{12} = \frac{1}{3}$$
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If a and b are positive integers so that the remainder, when dividing  [#permalink]

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Updated on: 11 Mar 2018, 18:21
Teerex wrote:
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

let q=quotient
a=bq+4
assume b>a
then q=0 and a=4
only 4/b=1/3 makes b an integer
4/12=1/3
B

Originally posted by gracie on 07 Feb 2018, 14:05.
Last edited by gracie on 11 Mar 2018, 18:21, edited 1 time in total.
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If a and b are positive integers so that the remainder, when dividing  [#permalink]

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07 Feb 2018, 20:25
1
Teerex wrote:
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

Source: ExamPAL

Kudos for detailed explanation!

Hi....

All the choices are in simplest form with denominator>numerator..
So the REMAINDER will be MULTIPLE of numerator..
All other except A and B have a numerator>4, so none of the C, D and E can have a Remainder of 4..
A has 3 in numerator so the Remainder will be 3,6,9...
4 is not a MULTIPLE of 3, so A out
Ans B.
and a and b are 4 and 12..

Note:- choices should have been in increasing/decreasing order.
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Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

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09 Feb 2018, 10:56
Teerex wrote:
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?

a)3/4

b) 1/3

c) 5/8

d) 5/7

e) 7/8

Scanning the answer choices, we observe that all the choices are proper fractions. This means that b is greater than a, which in turn implies that the remainder from the division of a by b is in fact a. Therefore, a = 4.

We note that for any answer choice besides 1/3, it is not possible to obtain an equivalent fraction where the numerator is 4. Since 1/3 = 4/12, the remainder when dividing 4 by 12 is 4.

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Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

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12 Mar 2018, 08:50
Mathematically, a=kb+4 where k=0,1,2,.....

so, a/b = k+4/b .. hence a/b has to be greater than 1 for all values of k except 0. For k=0, a=4.
Hence the numerator must be a multiple of 4. Hence, B.

Hope this makes sense.

Tx.
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