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• $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. Points A, B, C, and D lie on the number line as shown in th  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6504 GMAT 1: 760 Q51 V42 GPA: 3.82 Points A, B, C, and D lie on the number line as shown in th [#permalink] Show Tags Updated on: 14 Dec 2017, 01:10 00:00 Difficulty: 95% (hard) Question Stats: 67% (02:51) correct 33% (02:14) wrong based on 57 sessions HideShow timer Statistics [GMAT math practice question] Attachment: 12.12.png [ 1.16 KiB | Viewed 674 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. $$\frac{11}{14}$$ _________________ 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$99 for 3 month Online Course"
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Originally posted by MathRevolution on 12 Dec 2017, 00:42.
Last edited by MathRevolution on 14 Dec 2017, 01:10, edited 1 time in total.
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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, 02:52
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

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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, 05:38
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

I 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, 06:01
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, 07:14
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, 20:31
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 530 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 $$C = D - \frac{1}{42}$$

$$C = (\frac{2}{3} - \frac{1}{42}) = (\frac{28}{42} - \frac{1}{42}) = (\frac{27}{42}) = \frac{9}{14}$$

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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, 01:13
=>

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
$$C = \frac{2}{3} – \frac{1}{42} = \frac{28}{42} – \frac{1}{42} = \frac{27}{42} = \frac{9}{14}.$$

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Re: Points A, B, C, and D lie on the number line as shown in th &nbs [#permalink] 14 Dec 2017, 01:13
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