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In a decimal, a bar over a digit indicates that the digit repeats inde

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In a decimal, a bar over a digit indicates that the digit repeats inde  [#permalink]

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New post 13 Jun 2017, 22:30
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In a decimal, a bar over a digit indicates that the digit repeats indefinitely. If a and b are integers, \(a/3 - b/4 = 0.41\overline{6}\) and \(a + b = 17\), what is the value of \(a\)?

(A) 5
(B) 7
(C) 8
(D) 9
(E) 10

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Re: In a decimal, a bar over a digit indicates that the digit repeats inde  [#permalink]

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New post Updated on: 13 Jun 2017, 22:54
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hazelnut wrote:
In a decimal, a bar over a digit indicates that the digit repeats indefinitely. If a and b are integers, a/3 - b/4 = 0.416 and a + b = 17, what is the value of a?

(A) 5
(B) 7
(C) 8
(D) 9
(E) 10


Note : Rule to convert mixed recurring decimal to fraction : In the numerator write the entire given number formed by the (recurring and non - recurring parts) and subtract from it the part of the decimal that is not recurring. In the denominator, write as many nines as the number of digits recurring and then place next to it as many zeros as there are digits without recurring in the given decimal.

Converting the mixed recurring decimal to fraction we get;

0.416 = \(\frac{(416 - 41)}{900} = \frac{375}{900} = \frac{5}{12}\)

\(\frac{a}{3} - \frac{b}{4} = \frac{5}{12}\)

\(\frac{4a - 3b}{12} = \frac{5}{12}\)

4a - 3b = 5 ---------- (i)

Given, a + b = 17 ==> a = 17 - b -------- (ii)

Substituting (ii) in (i) we get;

68 - 4b - 3b = 5

68 - 7b = 5

7b = 68 - 5 = 63

b = \(\frac{63}{7}\) = 9

Substituting value of b in (ii) we get;

a = 17 - 9 = 8.

Answer (C)

Originally posted by sashiim20 on 13 Jun 2017, 22:46.
Last edited by sashiim20 on 13 Jun 2017, 22:54, edited 1 time in total.
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In a decimal, a bar over a digit indicates that the digit repeats inde  [#permalink]

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New post 13 Jun 2017, 22:59
If a/3 - b/4 = 0.416666 and a+b = 17, we are required to find the value of a?

\(\frac{a}{3} - \frac{b}{4} = \frac{{4a - 3b}}{{12}}\)
Assume 4a-3b = x

If \(\frac{x}{12} = 4.16666\), x should be a little more than 48.
I used trial and error to arrive at the number 50.
Since we need value .416666, x is \(\frac{50}{10}\) = 5,

Now we have 2 equations
4a - 3b = 5
a + b = 17 => 3a + 3b = 51

Adding these 2 equations a 7a = 56, and the value of a is 8(Option C)
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Re: In a decimal, a bar over a digit indicates that the digit repeats inde  [#permalink]

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New post 13 Jun 2017, 23:35
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hazelnut wrote:
In a decimal, a bar over a digit indicates that the digit repeats indefinitely. If a and b are integers, \(a/3 - b/4 = 0.41\overline{6}\) and \(a + b = 17\), what is the value of \(a\)?

(A) 5
(B) 7
(C) 8
(D) 9
(E) 10


\(P=0.41\overline{6}=0.416666...\)
\(10P=4.1\overline{6}=4.166666...\)
\(9P=3.75 \implies P = \frac{3.75}{9}=\frac{15}{36}=\frac{5}{12}\)

\(\frac{a}{3} - \frac{b}{4}= \frac{4a-3b}{12} = \frac{5}{12} \implies 4a-3b=5\)
\(a+b=17 \implies 4a - 3(17-a)=12 \implies a=8\)
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Re: In a decimal, a bar over a digit indicates that the digit repeats inde  [#permalink]

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New post 14 Jun 2017, 01:30
a+b=17
go with options
if a=10 b=7 ; then 10/3+7/4>1
if a=9 b=8 ; then 9/3+8/4>1
if a=8 b=9 ; then 8/3+9/4= 2.66-2.25 =0.4
Option C is correct
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Re: In a decimal, a bar over a digit indicates that the digit repeats inde  [#permalink]

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New post 23 Sep 2018, 19:50
My solution=

Since 0.416666 can be approximated to 3/7 which is 0.43 approximately which is only a little above 0.41666

now we can solve for the equation as follows

a/3-b/4=3/7 ……………. (1)
a+b=17...……………………(2)

solving the above via substitution, we get a=8.02 which is only a little above 8


But since we also took a fraction approximate a little above 0.41666, therefore our answer will be closer to 8


Hence C
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Re: In a decimal, a bar over a digit indicates that the digit repeats inde &nbs [#permalink] 23 Sep 2018, 19:50
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