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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, 09:30
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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: ExamPALKudos 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, 11:37
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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: ExamPALKudos 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 4Hence, 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, 22:42
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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: ExamPALKudos 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, 03:37
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: ExamPALKudos 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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07 Feb 2018, 13:05
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 option b has a numerator that is a factor of 4 (4*1)/(4*3)=4/12=1/3



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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, 19:25
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: ExamPALKudos 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, 09:56
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. Answer: B
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