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# The points A, B, C and D lie on the number line in that order. If AB=B

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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The points A, B, C and D lie on the number line in that order. If AB=B  [#permalink]

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19 Feb 2018, 00:27
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Difficulty:

45% (medium)

Question Stats:

74% (03:26) correct 26% (02:36) wrong based on 47 sessions

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[GMAT math practice question]

The points $$A, B, C$$ and $$D$$ lie on the number line in that order. If $$AB=\frac{BC}{3},$$ $$AC=(\frac{4}{7})CD$$, $$A=-1$$, and $$D=10$$, what is the value of $$B$$?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3327 Location: India GPA: 3.12 The points A, B, C and D lie on the number line in that order. If AB=B [#permalink] ### Show Tags 19 Feb 2018, 01:35 MathRevolution wrote: [GMAT math practice question] The points $$A, B, C$$ and $$D$$ lie on the number line in that order. If $$AB=\frac{BC}{3},$$ $$AC=(\frac{4}{7})CD$$, $$A=-1$$, and $$D=10$$, what is the value of $$B$$? $$A. -2$$ $$B. -1$$ $$C. 0$$ $$D. 1$$ $$E. 2$$ Attachment: iMAGE.png [ 3.96 KiB | Viewed 527 times ] From the question stem, AD = 11 From the diagram, we can write that $$\frac{Y}{4} + \frac{Y}{7} = 11$$ -> $$\frac{7Y + 4Y}{28} = 11$$ -> Y = 28 Now, AC = $$\frac{Y}{7}$$ = 4 and AB + BC = AC = 4 $$x + 3x = 4$$ -> $$x = 1$$ Therefore, AB = 1 and A = -1, B will be 0(Option C) _________________ You've got what it takes, but it will take everything you've got Manager Joined: 22 Jun 2016 Posts: 245 Re: The points A, B, C and D lie on the number line in that order. If AB=B [#permalink] ### Show Tags 19 Feb 2018, 01:39 Given A=-1 and D=10 and ABCD are collinear in the same order, then D>C>B>A. Option A is out as A>B. Option B is out as A and B will lie on the same point and AB=0. So, BC will also be 0 and AC and CD will also become 0. Option C. B=0. So, AB=1. So, BC=3. Hence, C = 3. AC will then be 4 and CD = 10. This satisfies the equation AC = (4/7) CD. Hence, this would be the answer. Answer C. _________________ P.S. Don't forget to give Kudos Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6663 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The points A, B, C and D lie on the number line in that order. If AB=B [#permalink] ### Show Tags 21 Feb 2018, 00:05 => Attachment: 2.21.png [ 1015 Bytes | Viewed 447 times ] Let $$BC = 3d$$. Then $$AB = \frac{BC}{3} = d$$ and $$AC = 4d$$. Also, $$AC = 4d = (\frac{4}{7})CD$$ and $$CD = 7d$$. Therefore, $$AD = AC + CD = 4d + 7d = 11d = 10 – (-1) = 11$$. So, $$d = 1$$, and $$B = -1 + d = -1 + 1 = 0.$$ 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$99 for 3 month Online Course"
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Re: The points A, B, C and D lie on the number line in that order. If AB=B &nbs [#permalink] 21 Feb 2018, 00:05
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