If x and y are integers, what is the value of y ?

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.

If x and y are integers, what is the value of y ?

(1) xy = 27
(2) x = y^2

There are 2 variables (x,y) and 2 equations are given from the 2 conditions, so there is high chance (C) will be our answer.
If we look at the conditions together, we get x=9, y=3, so the conditions are sufficient and the answer becomes (C).

For cases where we need 2 more equation, 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, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. 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 using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

SOLUTION

If x and y are integers, what is the value of y ?

(1) xy = 27. Not sufficient.
(2) x = y^2. . Not sufficient.

(1)+(2) Substitute: y^2*y = 27 --> y^3 = 27 --> y = 3. Sufficient.

Answer: C.

If x and y are integers, what is the value of y ?
(1) xy = 27
(2) x = y^2

St1: we have multiple values of y possible from 1 to 27 to -27...many options
St2:not sufficient
Combining we get that y^3=27 and since y is an integer so y=3

And C

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Statement (1):
y can have many possible values, including negative ones: 1,3,9,27...; Insufficient.

Statement (2):
x = y^2; Clearly insufficient, since many values are possible.

Both together,
(y^2)*y = 27;
y^3 = 27;
y = 3;

Hence, (C) is the answer.

Statement 1) We don't value of x, so not sufficient.
Statement 2) x = y^2. We don't know the value of x.

Combining the two statement, xy=27 => y^3 = 27, so y = 3 Sufficient.
Hence Option C)

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