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

Question

What is the value of x?

(1) x/y = 3
(2) x – y = 9

GMATSkilled · Answer

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

varun4s · Answer

We need to find single value of x

(1) x=3y   As x can have multiple values
(2) x-y=9   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}

Answer: C.

MathRevolution · Answer

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.

Thus C is the answer.

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.

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

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GMAT Data Sufficiency (DS) Questions

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

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