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If x is the number on the number line between 4 and 16 that

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Director
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If x is the number on the number line between 4 and 16 that [#permalink] New post 30 Mar 2018, 01:44
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Question Stats:

40% (00:22) correct 60% (00:34) wrong based on 5 sessions
If x is the number on the number line between 4 and 16 that is twice as far from 4 as it is from 16, then x is?

A)6
B)8
C)8.5
D)10.33
E)12
[Reveal] Spoiler: OA
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Re: If x is the number on the number line between 4 and 16 that [#permalink] New post 31 Mar 2018, 17:22
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If this number is twice as far from 4 as from 16, it must be 2/3 of the way from 4 to 16. (One way to imagine this is that if you broke the distance between 4 and 16 into 3 parts, then the number will have two parts to the left and one part to the right.) Since the distance between them is 12, and 2/3 of 12 is 8, then we can add 8 to 4 to get 12, giving us E.

BONUS QUESTION: What's the other number that is twice as far from 4 as from 16? Answer in the next reply.
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Re: If x is the number on the number line between 4 and 16 that [#permalink] New post 31 Mar 2018, 17:31
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So we can solve my bonus question using algebra. If the distance from 4 is double the distance from 16, x can be either smaller than both, between both, or bigger than both. We already solved the between option. The smaller than both option doesn't make sense because if it's smaller than both, it must be closer to 4, so how can it be twice as far from 4 as from 16? But that would work if x is bigger than both. So we can set up an equation as follows:

x - 4 = 2(x - 16)
Expand:
x - 4 = 2x - 32
Collect terms:
28 = x

This makes sense since 28 is 24 greater than 4, and 12 greater than 16.
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Re: If x is the number on the number line between 4 and 16 that [#permalink] New post 31 Mar 2018, 20:37
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if we suppose the number line is x-axis of the 2-d co-ordinate system, then the points are (4,0) and (16,0).
then a point (x,0) divides the line in the ratio 2:1; the point is 2 times the distance from 4 as it is from 16.

using section formula,
x=(4*1+16*2)/(2+1) =12
Re: If x is the number on the number line between 4 and 16 that   [#permalink] 31 Mar 2018, 20:37
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