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# If ab ≠ 0, what is the value of (a+b)/(a-b)?

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Math Expert
Joined: 02 Sep 2009
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If ab ≠ 0, what is the value of (a+b)/(a-b)?  [#permalink]

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18 Jul 2018, 23:17
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Difficulty:

85% (hard)

Question Stats:

37% (02:30) correct 63% (01:37) wrong based on 46 sessions

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If ab ≠ 0, what is the value of $$\frac{a+b}{a-b}$$ ?

(1) $$3a^2 = 2b^2$$

(2) b = 10

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Re: If ab ≠ 0, what is the value of (a+b)/(a-b)?  [#permalink]

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18 Jul 2018, 23:43
Statement 1: This provides only the ratio a/b. Hence insufficient
Statement 2: b=10. Provides no info about a. Insufficient

Statement 1&2: We can solve statement 1 and get values of a and b. Sufficient

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If ab ≠ 0, what is the value of (a+b)/(a-b)?  [#permalink]

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Updated on: 18 Jul 2018, 23:54
1
To find the value of $$\frac{a+b}{a-b}$$

Statement 1

$$3a^2 = 2b^2$$

=> $$\frac{a^2}{b^2}$$ = $$\frac{2}{3}$$

=> $$\frac{a}{b}$$ = $$\pm \sqrt{\frac{2}{3}}$$

Statement 1 is not sufficient

Statement 2

b = 10

Does not give any information about value of a

Statement 2 is insufficient

Combining statements 1 and 2

=> $$3a^2 = 200$$

=> a = $$\pm \sqrt{\frac{200}{3}}$$

We don't get the unique value for "a"

Statements 1 and 2 together are not sufficient

Hence option E
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Originally posted by workout on 18 Jul 2018, 23:52.
Last edited by workout on 18 Jul 2018, 23:54, edited 1 time in total.
Math Expert
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Posts: 6815
Re: If ab ≠ 0, what is the value of (a+b)/(a-b)?  [#permalink]

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18 Jul 2018, 23:53
If ab ≠ 0, what is the value of $$\frac{a+b}{a-b}$$ ?

(1) $$3a^2 = 2b^2$$
since terms contain squares, we can have both positive value and negative value..
$$3a^2=2b^2.........a=\sqrt{\frac{2}{3}}*b$$ or $$a=-\sqrt{\frac{2}{3}}*b$$
Although variables will get cancelled, TWO answers are possible
insuff

(2) b = 10
insuff

Individually both are clearly insufficient, so let us see combined
as we can see that the variables get cancelled in statement 1, so statement II does not help by giving value of b
insuff

E

Akash720, always be careful when you have SQUARES
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If ab ≠ 0, what is the value of (a+b)/(a-b)? &nbs [#permalink] 18 Jul 2018, 23:53
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# If ab ≠ 0, what is the value of (a+b)/(a-b)?

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