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# Points A, B, C, and D lie on the number line as shown in th

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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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[GMAT math practice question]

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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. $$\frac{11}{14}$$
[Reveal] Spoiler: OA

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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 12 Dec 2017, 01:42. Last edited by MathRevolution on 14 Dec 2017, 02:10, edited 1 time in total. Director Joined: 13 Mar 2017 Posts: 590 Location: India Concentration: General Management, Entrepreneurship GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Points A, B, C, and D lie on the number line as shown in th [#permalink] ### Show Tags 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 _________________ CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store. MBA Social Network : WebMaggu Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish". Intern Joined: 29 May 2012 Posts: 39 Re: Points A, B, C, and D lie on the number line as shown in th [#permalink] ### Show Tags 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 C I worked out C too. But why E? Intern Joined: 15 Oct 2017 Posts: 16 GMAT 1: 630 Q39 V38 Re: Points A, B, C, and D lie on the number line as shown in th [#permalink] ### Show Tags 12 Dec 2017, 07:01 I got 9/14 as well. Anyone got the OE? Senior Manager Joined: 31 Jul 2017 Posts: 332 Location: Malaysia WE: Consulting (Energy and Utilities) Re: Points A, B, C, and D lie on the number line as shown in th [#permalink] ### Show Tags 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 _________________ If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! SC Moderator Joined: 22 May 2016 Posts: 1538 Re: Points A, B, C, and D lie on the number line as shown in th [#permalink] ### Show Tags 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. _________________ At the still point, there the dance is. -- T.S. Eliot Formerly genxer123 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5245 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: Points A, B, C, and D lie on the number line as shown in th [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: Points A, B, C, and D lie on the number line as shown in th   [#permalink] 14 Dec 2017, 02:13
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