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Points A, B, C, and D lie on the number line as shown in th [#permalink]
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Updated on: 14 Dec 2017, 02:10
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69% (02:52) correct 31% (02:03) wrong based on 49 sessions
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[GMAT math practice question] Attachment:
12.12.png [ 1.16 KiB  Viewed 523 times ]
Points \(A, B, C\), and \(D\) lie on the number line as shown in the figure above. If \(AC=BD\) and \(AB=\frac{BC}{5}\), what is the value of \(C\)? A. \(\frac{7}{14}\) B. \(\frac{8}{14}\) C. \(\frac{9}{14}\) D. \(\frac{10}{14}\) E. \(\frac{11}{14}\)
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Re: Points A, B, C, and D lie on the number line as shown in th [#permalink]
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12 Dec 2017, 03:52
MathRevolution wrote: [GMAT math practice question] Attachment: 12.12.png Points \(A, B, C\), and \(D\) lie on the number line as shown in the figure above. If \(AC=BD\) and \(AB=\frac{BC}{5}\), what is the value of \(C\)? A. \(\frac{7}{14}\) B. \(\frac{8}{14}\) C. \(\frac{9}{14}\) D. \(\frac{10}{14}\) E. \(\frac{11}{14}\) Let BC = x, so, AB = x/5 Also, AC = BD AB + BC = BC + CD AB = CD = x/5 AD = AB + BC + CD = x/ 5 + x+ x/5 = 7x/5 Also, AD = 2/3  1/2 = 1/6 7x /5 = 1/6 x = 5/42 C = A + AB + BC = 1/2 + x/5 +x = 1/2 + 6x/5 = 1/2 + (6/5)*(5/42) = 1/2 + 1/7 = 9/14 Answer C
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Re: Points A, B, C, and D lie on the number line as shown in th [#permalink]
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12 Dec 2017, 06:38
shashankism wrote: MathRevolution wrote: [GMAT math practice question] Attachment: 12.12.png Points \(A, B, C\), and \(D\) lie on the number line as shown in the figure above. If \(AC=BD\) and \(AB=\frac{BC}{5}\), what is the value of \(C\)? A. \(\frac{7}{14}\) B. \(\frac{8}{14}\) C. \(\frac{9}{14}\) D. \(\frac{10}{14}\) E. \(\frac{11}{14}\) Let BC = x, so, AB = x/5 Also, AC = BD AB + BC = BC + CD AB = CD = x/5 AD = AB + BC + CD = x/ 5 + x+ x/5 = 7x/5 Also, AD = 2/3  1/2 = 1/6 7x /5 = 1/6 x = 5/42 C = A + AB + BC = 1/2 + x/5 +x = 1/2 + 6x/5 = 1/2 + (6/5)*(5/42) = 1/2 + 1/7 = 9/14 Answer CI worked out C too. But why E?



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Re: Points A, B, C, and D lie on the number line as shown in th [#permalink]
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12 Dec 2017, 07:01
I got 9/14 as well. Anyone got the OE?



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Re: Points A, B, C, and D lie on the number line as shown in th [#permalink]
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12 Dec 2017, 08:14
MathRevolution wrote: [GMAT math practice question] Attachment: 12.12.png Points \(A, B, C\), and \(D\) lie on the number line as shown in the figure above. If \(AC=BD\) and \(AB=\frac{BC}{5}\), what is the value of \(C\)? A. \(\frac{7}{14}\) B. \(\frac{8}{14}\) C. \(\frac{9}{14}\) D. \(\frac{10}{14}\) E. \(\frac{11}{14}\) Hi MathRevolution, Is the OA correct?? Getting C = 9/14
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Re: Points A, B, C, and D lie on the number line as shown in th [#permalink]
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12 Dec 2017, 21:31
MathRevolution wrote: [GMAT math practice question] Attachment: The attachment 12.12.png is no longer available Points \(A, B, C\), and \(D\) lie on the number line as shown in the figure above. If \(AC=BD\) and \(AB=\frac{BC}{5}\), what is the value of \(C\)? A. \(\frac{7}{14}\) B. \(\frac{8}{14}\) C. \(\frac{9}{14}\) D. \(\frac{10}{14}\) E. \(\frac{11}{14}\) Attachment:
line.png [ 11.07 KiB  Viewed 379 times ]
If\(AB = \frac{BC}{5}\), then \(BC\) is 5 times bigger than\(AB\) Let \(BC = 5x\) Thus \(AB = x\) And \(AC = 6x\) \(AC = BD = 6x\) They share middle part \(BC = 5x\) \(CD\)? \(= x\) Both segments above the line are equal They share \(5x\). One has another segment of length x (AB). The other segment must have a segment with length x, too. That's CD. \(CD = AB = x\) Length of whole segment \(AD = (x + 5x + x) = 7x\) Length of whole segment also \(AD = (\frac{2}{3}  \frac{1}{2}) = \frac{1}{6}\) \(7x = \frac{1}{6}\) \(x = \frac{1}{42}\) Point \(C = D  \frac{1}{42}\) \(C = (\frac{2}{3}  \frac{1}{42}) = (\frac{28}{42}  \frac{1}{42}) = (\frac{27}{42}) = \frac{9}{14}\) Answer C Bunuel , would you please check the OA? Thanks in advance.
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Re: Points A, B, C, and D lie on the number line as shown in th [#permalink]
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14 Dec 2017, 02:13
=> Suppose \(d\) is the distance between \(A\) and \(B\). Then \(CD = d\) and \(BC = 5d\). Thus, \(AD = d + 5d + d = 7d\). Since \(A = \frac{1}{2}\) and \(D = \frac{2}{3}\), \(7d = \frac{2}{3} – \frac{1}{2} = \frac{4}{6} – \frac{3}{6} = \frac{1}{6},\) and \(d = \frac{1}{42}.\) So, \(D – C = \frac{1}{42}\), and \(C = \frac{2}{3} – \frac{1}{42} = \frac{28}{42} – \frac{1}{42} = \frac{27}{42} = \frac{9}{14}.\) Therefore, the answer is C. Answer: C
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Re: Points A, B, C, and D lie on the number line as shown in th
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