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# If AC=BD and AB=BC/3 in the number line, then what is the value of C?

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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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If AC=BD and AB=BC/3 in the number line, then what is the value of C?  [#permalink]

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11 Oct 2017, 06:46
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Difficulty:

45% (medium)

Question Stats:

61% (02:16) correct 39% (02:18) wrong based on 57 sessions

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--|---------|-----------------------|---------|-----------
A(1) B C D(2)

If AC=BD and AB=BC/3 in the number line, then what is the value of C?

A. 11/10
B. 19/10
C. 29/15
D. 6/10
E. 9/5

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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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 29 May 2012 Posts: 39 If AC=BD and AB=BC/3 in the number line, then what is the value of C? [#permalink] ### Show Tags 11 Oct 2017, 07:17 2 MathRevolution wrote: --|---------|-----------------------|---------|----------- A(1) B C D(2) If AC=BD and AB=BC/3 in the number line, then what is the value of C? A. 11/10 B. 19/10 C. 29/15 D. 6/10 E. 9/5 Just to clarify...is the question suggesting that A=1, and D=2 on the number line? It doesn't seem to be clear to me. If it is... Because AC=BD, then AB=CD Assuming AB=x, and AB=BC/3, then BC=3x Therefore, AD=AB+BC+CD=x+3x+x=5x=1 (i.e., AD=2-1=1) => x=1/5 Because the number line starts with A which is 1, C is in the position of 1+AB+BC=1+1/5+(1/5)*3=9/5. Answer is E. Senior SC Moderator Joined: 22 May 2016 Posts: 1978 If AC=BD and AB=BC/3 in the number line, then what is the value of C? [#permalink] ### Show Tags 11 Oct 2017, 09:22 MathRevolution wrote: --|---------|-----------------------|---------|----------- A(1) B C D(2) If AC=BD and AB=BC/3 in the number line, then what is the value of C? A. 11/10 B. 19/10 C. 29/15 D. 6/10 E. 9/5 Attachment: nmbrline.png [ 6.69 KiB | Viewed 619 times ] Assign numbers, starting with the most limiting factor: AB = BC/3, BC = 3AB The smaller number (AB) is usually easier. I chose 3, not 1, on purpose. I wanted segments to be in multiples of 3. Let AB = 3. BC is three times that long. BC = 9 AC = BD means that AB = CD. AC = BD because: AD - AC = CD AD - BD = AB The two lengths being subtracted from the whole length AD are equal. Their differences, AB and CD, therefore are equal AB = 3, so CD = 3 (and BD = 9) -- parts of ___ Now add, to see how many equal lengths the segment could be divided into: 3 + 9 + 3 = 15 If the line were divided into fifteenths, on the number line, letters would correspond to cardinal numbers in this way: $$A = 1\frac{0}{15}, B = 1\frac{3}{15}, C = 1\frac{12}{15}, D = 1\frac{15}{15}$$ Point C is at ($$1 + \frac{12}{15}$$) = $$1\frac{12}{15}$$ = $$\frac{27}{15} = \frac{9}{5}$$ Answer: E _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6227 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If AC=BD and AB=BC/3 in the number line, then what is the value of C? [#permalink] ### Show Tags 15 Oct 2017, 06:13 Assume AC = d. Then, we have BC = 3d. Since we have AC = BD and BC is common in AC and BD, CD = AB = d. 5d = 1 or d = 1/5. C = 2 – 1/5 = 9/5. _________________ 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: If AC=BD and AB=BC/3 in the number line, then what is the value of C? &nbs [#permalink] 15 Oct 2017, 06:13
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