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

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New post 19 Feb 2018, 00:27
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A
B
C
D
E

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

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New post 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
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)
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Re: The points A, B, C and D lie on the number line in that order. If AB=B  [#permalink]

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New post 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.

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

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New post 21 Feb 2018, 00:05
=>

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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
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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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