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# What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2  [#permalink]

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15 Jul 2018, 06:40
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:52) correct 48% (02:00) wrong based on 44 sessions

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What is the value of $$\frac{(8a + a - b)}{(a - b)}$$ ?

(1) $$\frac{(5a + 4b)}{(a - b)} = 2$$

(2) $$a - b = 9$$

Source: GmatFree

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Re: What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2  [#permalink]

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15 Jul 2018, 06:55
1
Bunuel wrote:

(1) $$\frac{(5a + 4b)}{(a - b) = 2}$$

Source: GmatFree

Bunuel : This seems to be a typo
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Math Expert
Joined: 02 Sep 2009
Posts: 51280
Re: What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2  [#permalink]

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15 Jul 2018, 06:58
sudarshan22 wrote:
Bunuel wrote:

(1) $$\frac{(5a + 4b)}{(a - b) = 2}$$

Source: GmatFree

Bunuel : This seems to be a typo

Edited the formatting error. Thank you.
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Re: What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2  [#permalink]

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15 Jul 2018, 07:25
(8a+a−b) / (a−b)
(9a-b) /(a-b) Dividing both numerator and denominator by b, we get:
(9a/b - 1) / (a/b-1) ----> (A)

(1) (5a+4b) / (a−b)=2 (solving, we get)
3a-2b = 0
3a = 2b
a/b = 2/3
Now, putting the value of a/b in equation A the final value can be obtained, Sufficient.

(2) a−b = 9
putting b = a+9 in equation A we get 8a + 9 (not solvable), Insufficient

Hence, A.
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Re: What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2  [#permalink]

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15 Jul 2018, 07:40
OA: A
$$\frac{(8a+a−b)}{(a−b)}$$ can be simplified as $$\frac{8a}{a-b}+1$$
$$\frac{8a}{a-b}+1$$ = $$\frac{8}{(1- \frac{b}{a})}+1$$
So we have to find value of $$\frac{b}{a}$$

1) $$\frac{(5a+4b)}{(a−b)}=2$$
if we take $$a=0$$ ,$$L.H.S\neq{R.H.S}$$, so it means $$a\neq{0}$$
Dividing numerator and denominator of $$L.H.S$$ by $$a$$ , we get
$$\frac{(5+4*\frac{b}{a})}{(1−\frac{b}{a})}=2$$
Solving above equation , we can find value of $$\frac{b}{a}$$
So Statement 1 alone is sufficient.

2) $$a−b = 9$$
Putting $$a-b$$ in $$\frac{8a}{a-b}+1$$ , we get $$\frac{8a}{9}+1$$
We still need value of $$a$$.
So Statement 2 alone is not sufficient.
Re: What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2 &nbs [#permalink] 15 Jul 2018, 07:40
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