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11 Oct 2017, 06:46
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (02:31) correct
31%
(02:43)
wrong
based on 257
sessions
History
Date
Time
Result
Not Attempted Yet
--|---------|-----------------------|---------|-----------
- 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
11 Oct 2017, 07:17
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MathRevolution
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.
11 Oct 2017, 09:22
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MathRevolution
Attachment:
nmbrline.png [ 6.69 KiB | Viewed 5572 times ]
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
