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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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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, 05:46
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64% (02:13) correct 36% (01:45) wrong based on 45 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
[Reveal] Spoiler: OA

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Kudos [?]: 3302 [0], given: 0

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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, 06:17
1
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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

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.

Kudos [?]: 5 [1], given: 11

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Joined: 22 May 2016
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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, 08:22
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 454 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:
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 ($$1 + \frac{12}{15}$$) = $$1\frac{12}{15}$$ = $$\frac{27}{15} = \frac{9}{5}$$

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Kudos [?]: 454 [0], given: 670

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4669

Kudos [?]: 3302 [0], given: 0

GPA: 3.82
Re: If AC=BD and AB=BC/3 in the number line, then what is the value of C? [#permalink]

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15 Oct 2017, 05:13
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.
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Re: If AC=BD and AB=BC/3 in the number line, then what is the value of C?   [#permalink] 15 Oct 2017, 05:13
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