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Points A, B, C, and D are on the number line above

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Points A, B, C, and D are on the number line above [#permalink] New post 12 May 2016, 04:55
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45% (02:04) correct 54% (02:37) wrong based on 22 sessions
Image

Points A, B, C, and D are on the number line above, and AB = CD = \(\frac{1}{3}BC\) What is the
coordinate of C ?

A. \(\frac{13}{30}\)
B. \(\frac{9}{20}\)
C. \(\frac{11}{24}\)
D. \(\frac{7}{15}\)
E. \(\frac{29}{60}\)

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Question: 11
Page: 63


[Reveal] Spoiler: img
Attachment:
test.jpg
test.jpg [ 11.38 KiB | Viewed 17150 times ]
[Reveal] Spoiler: OA

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Re: Points A, B, C, and D are on the number line above [#permalink] New post 12 May 2016, 05:05
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Explanation

From the figure you can see that since the coordinate of A is: \(\frac{1}{3}\), it follows that the coordinate of C
is \(\frac{1}{3}+ AB + BC\). Since we are given that \(AB = \frac{1}{3}BC\) , the coordinate of C can be rewritten in terms of AB as follows:

\(\frac{1}{3}+ AB + BC= \frac{1}{3} + AB + 3 AB = \frac{1}{3} + 4AB\)

To find the coordinate of C, you need to know AB. From the figure, you know that AD = AB + BC + CD = AB + 3(AB) + AB = 5 (AB). On the other hand, since the coordinate of A is \(\frac{1}{3}\), and the coordinate of D is\(\frac{1}{2}\), it follows that \(AD = \frac{1}{2}- \frac{1}{3}\) = \(\frac{1}{6}\). Therefore you can conclude that:

\(\frac{1}{6}= 5 AB\) and \(AB= \frac{1}{30}\).

Thus the coordinate of C is \(\frac{1}{3}+ 4AB = \frac{1}{3} + 4* \frac{1}{30}\) or \(\frac{7}{15}\). The correct answer is Choice D.
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Re: Points A, B, C, and D are on the number line above [#permalink] New post 15 Jul 2016, 05:34
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sandy wrote:
Image

Points A, B, C, and D are on the number line above, and AB = CD = \(\frac{1}{3}BC\) What is the
coordinate of C ?

A. \(\frac{13}{30}\)
B. \(\frac{9}{20}\)
C. \(\frac{11}{24}\)
D. \(\frac{7}{15}\)
E. \(\frac{29}{60}\)



Distance from A to D = 1/2 - 1/3
= 3/6 - 2/6
= 1/6

Let x = the distance from A to B
This means that 3x = the distance from B to C
And x = the distance from C to D
So, the TOTAL DISTANCE from A to D = x + 3x + x = 5x

So, we can conclude that 5x = 1/6
Divide both sides by 5 to get: x = 1/30

We want the coordinate of C.
C is 1/30 LESS THAN 1/2 (the coordinate of D)
1/2 - 1/30 = 15/30 - 1/30
= 14/30
= 7/15

Answer:
[Reveal] Spoiler:
D

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Re: Points A, B, C, and D are on the number line above [#permalink] New post 10 Feb 2017, 18:50
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How did you calculate that the distance from B to C was 3x?
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Re: Points A, B, C, and D are on the number line above [#permalink] New post 10 Feb 2017, 19:23
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EleV12 wrote:
How did you calculate that the distance from B to C was 3x?


AB = CD = (1/3)BC

We can look at this in two equivalent ways:
1) AB is 1/3 the length of BC
or
2) BC is 3 times the length of AB

So, (if we use #2 above) if AB = x, then BC = 3x

Cheers,
Brent
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Re: Points A, B, C, and D are on the number line above [#permalink] New post 26 May 2017, 07:49
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each interval wll be ( 1/2 - 1/3 ) / 5 = 1/30
c is one interval behind d (1/2)

therfore c => 1/2 - 1/30 = 7/15
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Re: Points A, B, C, and D are on the number line above [#permalink] New post 31 May 2017, 14:08
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This is how I thought about it.

1. Instead of thinking of the point of A as 1/2 and the point of D as 1/3 think of them as points 0.5 and 0.33.

2. Since AB= 1/3 of BC that means that you can fit AB 3 times in BC, another way to think about it is AB=1/3 of BC, multiply both sides by 3 and get 3AB=BC. Also CD=AB.

3. You know that the distance between 0.5 and 0.33 is (0.5-0.33)= 0.17( this is the same as 1/2-1/3 =1/6 )

4. Up to this point you know 3 things.

a. The difference between points A and D is 0.17 (1/6)
b. There are 5 equal parts from A to D ( which are AB+3 AB that you can fit in BC and CD that is equal to AB )
c. The C coordinate is on the 4th equal portion on the line. If you can figure out what is the value of each of the 5 portions then you just have to add this value 4 times ( one for each portion, to find the value for C).

5. To find the value for each of the 5 AB (portions) you just divide 0.17(total distance) by 5 (5 equal portions) and get 0.034 (which is the same as 1/6 divided 5= 1/30).

6. You now know that C is 1/30+1/30+1/30+1/30 from A and A is 1/3 so if you add all up will get 1/3+4(1/30) which is 7/15. (The previous is the same as 0.33+4(0.034) which is 0.466
Re: Points A, B, C, and D are on the number line above   [#permalink] 31 May 2017, 14:08
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