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# What is the value of x? (1) x/y = 3 (2) x – y = 9

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Math Expert
Joined: 02 Sep 2009
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What is the value of x? (1) x/y = 3 (2) x – y = 9  [#permalink]

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24 Oct 2017, 23:53
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Difficulty:

25% (medium)

Question Stats:

92% (00:41) correct 8% (00:40) wrong based on 42 sessions

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What is the value of x?

(1) x/y = 3
(2) x – y = 9

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Joined: 08 Apr 2017
Posts: 80
Re: What is the value of x? (1) x/y = 3 (2) x – y = 9  [#permalink]

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25 Oct 2017, 10:14
Statement A: X = 3Y ......... Insufficient
Statement B: X and Y can have multiple to satisfy X - Y = 9 .......... Insufficient
On combining,
Y = X - 9
Therefore, X = 3 (X - 9)
X = 3X - 27
2X = 27
X = 27/2
Therefore C
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Re: What is the value of x? (1) x/y = 3 (2) x – y = 9  [#permalink]

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25 Oct 2017, 19:37
We need to find single value of x

(1) x=3y [Insuff] As x can have multiple values
(2) x-y=9 [Insuff] As x can have multiple values

Put (1) in (2)

3y-y= 9
2y=9
y=$$\frac{9}{2}$$

So x= 3y; x= 3*$$\frac{9}{2}$$= $$\frac{27}{2}$$

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Re: What is the value of x? (1) x/y = 3 (2) x – y = 9  [#permalink]

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28 Oct 2017, 13:21
Bunuel wrote:
What is the value of x?

(1) x/y = 3
(2) x – y = 9

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Since we have 2 variables and 0 equation, C could be the answer most likely.

Condition 1) & 2)
y = x - 9 from the condition 2)
x/y = x/(x-9) = 3
x = 3(x-9)
x = 3x - 27
2x = 27
x = 27/2

Condition 1) only is not sufficient due to the variable y.

Condition 1) only is not sufficient due to the variable y, either.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: What is the value of x? (1) x/y = 3 (2) x – y = 9 &nbs [#permalink] 28 Oct 2017, 13:21
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