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

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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
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60% (01:48) correct 40% (02:09) wrong based on 111 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, 08:25
(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, 08:40
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.
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What is the value of (8a + a - b)/(a - b) ? (1) (5a + 4b)/(a - b) = 2  [#permalink]

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Updated on: 21 Aug 2019, 04:12
So (2) looks simple ,not sufficient as we have extra “a” in the numerator
(1) Gives a linear equation which we can derive a relationship between a and b ,so sufficient

Posted from my mobile device

Originally posted by Staphyk on 21 Aug 2019, 03:51.
Last edited by Staphyk on 21 Aug 2019, 04:12, edited 1 time in total.
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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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21 Aug 2019, 03:56
Staphyk wrote:
So (2) looks simple ,not sufficient as we have extra “a” in the numerator
(1) Gives is one linear equation
(1+2) Gives two systems of equations hence value can be found

Posted from my mobile device

If we solve the option A we will get a = -2b.
substituting this value in the main equation will yield a value of 19/3.
Hence the we are able to get a definite value from option A which will be the answer.
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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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21 Aug 2019, 04:01
Lolx was not even solving
sandeep211986 wrote:
Staphyk wrote:
So (2) looks simple ,not sufficient as we have extra “a” in the numerator
(1) Gives is one linear equation
(1+2) Gives two systems of equations hence value can be found

Posted from my mobile device

If we solve the option A we will get a = -2b.
substituting this value in the main equation will yield a value of 19/3.
Hence the we are able to get a definite value from option A which will be the answer.
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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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21 Aug 2019, 04:43
Bunuel wrote:
What is the value of $$\frac{(8a + a - b)}{(a - b)}$$ ?

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

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

Source: GmatFree

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

(1) $$\frac{(5a + 4b)}{(a - b)} = 2$$
5a + 4b = 2a - 2b
3a + 6b = 0
a = -2b
$$\frac{(8a + a - b)}{(a - b)} = (-16b -2b -b) / (-2b-b) = (-19b)/(-3b) = 19/3$$
SUFFICIENT

(2) $$a - b = 9$$
We need ratio of a/b to solve
NOT SUFFICIENT

IMO 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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19 Sep 2019, 03:15
Bunuel wrote:
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] 19 Sep 2019, 03:15
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