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In a decimal, a bar over a digit indicates that the digit repeats inde
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03 Apr 2021, 21:16
03 Apr 2021, 21:16
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In a decimal, a bar over a digit indicates that the digit repeats indefinitely. If a and b are integers, \((\frac{a}{3} - \frac{b}{4} =\) \(0.41\overline{6})\) and \(a + b = 17,\) what is the value of \(a\)?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
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In a decimal, a bar over a digit indicates that the digit repeats inde
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04 Apr 2021, 07:56
04 Apr 2021, 07:56
1
GeminiHeat wrote:
In a decimal, a bar over a digit indicates that the digit repeats indefinitely. If a and b are integers, \((\frac{a}{3} - \frac{b}{4} =\) \(0.41\overline{6})\) and \(a + b = 17,\) what is the value of \(a\)?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
\((\frac{a}{3} - \frac{b}{4} =\) \(0.41\overline{6})\)
\(4a - 3b = 12(0.416666...) ≈ 5\) ..... (i)
Given, \(a + b = 17\) ..... (ii)
Solve the Linear equations (Multiplying ii by \(3\) and adding to i);
\(4a - 3b ≈ 5\)
\(3a + 3b = 51\)
\(7a ≈ 56\)
\(a ≈ 8\)
Hence, option C
Re: In a decimal, a bar over a digit indicates that the digit repeats inde
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04 Apr 2021, 09:06
04 Apr 2021, 09:06
1
Converting the mixed recurring decimal to fraction we get;
0.416 = (416- 41)/900=375/900=5/12
a/3 - b/4 = 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 = 63/7 = 9
Substituting value of b in (ii) we get;
a = 17 - 9 = 8.
Answer (C)
0.416 = (416- 41)/900=375/900=5/12
a/3 - b/4 = 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 = 63/7 = 9
Substituting value of b in (ii) we get;
a = 17 - 9 = 8.
Answer (C)
