If x is the number on the number line between 5 and 15 that is twice a

Question

If x is the number on the number line between 5 and 15 that is twice as far from 5 as from 15, then x is

A.  5 \frac{2}{3}

B.  10

C.  11 \frac{2}{3}

D.  12 \frac{1}{2}

E.  13 \frac{1}{3}

PKN · Answer

Given , x is the number on the number line between 5 and 15 that is twice as far from 5 as from 15. Translating from word to algebra.

a) 2x=5 
b) x=15
c) 2x+x=15-5=10(distance between 5 and 15)
 or, 3x=10 or x=10/3 
We have to find the value of x that satisfies of all the above criteria.

Now 'x' can be  15-x=15-\frac{10}{3} =  11 \frac{2}{3}

Ans. (C)

Sreyoshi007 · Answer

Going through elimination of options,

First checking B since its the easiest to eliminate, 10 is equidistant from 5 and 15. And since options are arranged in ascending order, it can't be A either. 
Eliminate A and B.

Check for C,  11 \frac{2}{3}  is 35/3 which is approximately 11.6. Distance between 5 and 11.6 is 6.66 and distance from 11.6 to 15 is 3.33.
As we can see  6.66 is double of 3.33 , and hence answer should be  (C). 
Do let me know if there is any other approach, thanks.

SantoshSukumaran · Answer

X - 5 = 2(15 - x) 
X - 5 = 30 - 2x 
3x = 35
X = 35/3
X = 11 2/3

Posted from my mobile device

BrentGMATPrepNow · Answer

Since x is BETWEEN 5 and 15, we know that:
 15 - x  = the distance from x to 15
 x - 5  = the distance from x to 5

GIVEN: x is  twice  as far from 5 as x is from 15 
In other words, the distance from x to 5 is TWICE the distance from x to 15. 
So, we can write:  x - 5  = 2( 15 - x )
Expand: x - 5 = 30 - 2x
Rearrange values to get: 3x = 35
Solve: x = 35/3 = 11 2/3

Answer: C

Cheers,
Brent

Fdambro294 · Answer

Set up a Ratio: If the Distance from 5 is TWICE the Distance from 15

Distance from 5 : Distance from 15 : TOTAL = 2g : 1g : 3g

Actual Value of the TOTAL Distance between 5 and 15 = 15 - 5 = 10

3g = 10

g = 3 + 1/3***

2g = 2 (3 + 1/3) = 6 + 2/3

X is therefore + (6 and 2/3) AWAY from 5 ----

5 + (6 and 2/3) = 11 and 2/3

-C-

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If x is the number on the number line between 5 and 15 that is twice a

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