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

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New post 11 Oct 2017, 05:46
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Question Stats:

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

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New post 11 Oct 2017, 06:17
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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

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.

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

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New post 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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