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# In the figure above, AB is a line segment. What is the value of

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Math Expert
Joined: 02 Sep 2009
Posts: 49206
In the figure above, AB is a line segment. What is the value of  [#permalink]

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05 Jul 2018, 05:13
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Difficulty:

15% (low)

Question Stats:

94% (01:00) correct 6% (01:18) wrong based on 36 sessions

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In the figure above, AB is a line segment. What is the value of $$\frac{x - y}{x + y}$$ ?

(A) $$\frac{5}{24}$$

(B) $$\frac{1}{4}$$

(C) $$\frac{7}{16}$$

(D) $$\frac{11}{24}$$

(E) $$\frac{7}{13}$$

Attachment:

xy.jpg [ 12.4 KiB | Viewed 471 times ]

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Re: In the figure above, AB is a line segment. What is the value of  [#permalink]

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05 Jul 2018, 05:20
Bunuel wrote:

In the figure above, AB is a line segment. What is the value of $$\frac{x - y}{x + y}$$ ?

(A) $$\frac{5}{24}$$

(B) $$\frac{1}{4}$$

(C) $$\frac{7}{16}$$

(D) $$\frac{11}{24}$$

(E) $$\frac{7}{13}$$

Attachment:
xy.jpg

since AB is a line segment, it makes a 180 angle on both side at the point of meet of all the rays ..

so $$x+x+x=180......3x=180...x=60$$

and $$5*y=180....y=\frac{180}{5}=36$$

since we know x = 60 and y = 36 we can substitute and find the answer
$$\frac{x - y}{x + y}=\frac{60-36}{60+36}=\frac{24}{96}=\frac{1}{4}$$

B
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Re: In the figure above, AB is a line segment. What is the value of  [#permalink]

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05 Jul 2018, 05:31
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Bunuel wrote:

In the figure above, AB is a line segment. What is the value of $$\frac{x - y}{x + y}$$ ?

(A) $$\frac{5}{24}$$

(B) $$\frac{1}{4}$$

(C) $$\frac{7}{16}$$

(D) $$\frac{11}{24}$$

(E) $$\frac{7}{13}$$

Attachment:
xy.jpg

from the figure, we have, 3x=5y

Now, $$\frac{x - y}{x + y}$$= $$\frac{3x - 3y}{3x + 3y}$$
=$$\frac{5y - 3y}{5y + 3y}$$ (substituting for 3x)
=$$\frac{2y}{8y}$$
=$$\frac{1}{4}$$

Ans.(B)
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Re: In the figure above, AB is a line segment. What is the value of  [#permalink]

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09 Jul 2018, 20:00
Bunuel wrote:

In the figure above, AB is a line segment. What is the value of $$\frac{x - y}{x + y}$$ ?

(A) $$\frac{5}{24}$$

(B) $$\frac{1}{4}$$

(C) $$\frac{7}{16}$$

(D) $$\frac{11}{24}$$

(E) $$\frac{7}{13}$$

Attachment:
xy.jpg

We can create the equations:

3x = 180

and

5y = 180

So x = 60 and y = 36.

Thus, (x - y)/(x + y) = (60 - 36)/(60 + 36) = 24/96 = 1/4.

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Re: In the figure above, AB is a line segment. What is the value of  [#permalink]

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10 Jul 2018, 03:18
Bunuel wrote:

In the figure above, AB is a line segment. What is the value of $$\frac{x - y}{x + y}$$ ?

(A) $$\frac{5}{24}$$

(B) $$\frac{1}{4}$$

(C) $$\frac{7}{16}$$

(D) $$\frac{11}{24}$$

(E) $$\frac{7}{13}$$
Attachment:
xy.jpg

3x=5y=180
x=60
y=36
x-y/x+y=24/96=1/4

OR,

3x=5y
x=5y/3
x-y=5y/3-y=2y/3
x+y=5y/3+y=8y/3
x-y/x+y=1/4
Re: In the figure above, AB is a line segment. What is the value of &nbs [#permalink] 10 Jul 2018, 03:18
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