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

Question

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

ScottTargetTestPrep · Accepted Answer

Solution:

Question Stem Analysis:

We need to determine the value of y given that x and y are integers.

Statement One Alone:

Since we don’t know anything about the value x, there could be multiple values for y. For example, y could be 1, 3, 9 or 27. Statement one alone is not sufficient.

Statement Two Alone:

Even though we know x is the square of y, but y still could be any integer value. Statement two alone is not sufficient.

Statements One and Two Together:

Since x = y^2, we can substitute y^2 for x in the equation in statement one, obtaining:

y^2 * y = 27

y^3 = 27

y = 3

Both statements together are sufficient.

Answer: C

BrentGMATPrepNow · Answer

Given : x and y are integers

Target question :    What is the value of y ?

Statement 1 : xy = 27  
There are several values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 1 and y = 27. In this case, the answer to the target question is  y = 27 
 Case b : x = 3 and y = 9. In this case, the answer to the target question is  y = 9 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : x = y² 
There are several values of x and y that satisfy statement 2. Here are two: 
 Case a : x = 1 and y = 1. In this case, the answer to the target question is  y = 1 
 Case b : x = 4 and y = 2. In this case, the answer to the target question is  y = 2 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that xy = 27. 
If we divide both sides of the equation by y, we get: x = 27/y
Statement 2 tells us that x = y²

Since both equations (x = 27/y and x = y²) are set equal to x, we can set them equal to each other to get: 27/y = y²
Now multiply both sides of the equation by y to get: 27 = y³
At this point, we can see that the equation has only one solution:  y = 3

Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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.

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.

Bunuel · Answer

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.

WoundedTiger · Answer

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

Posted from my mobile device

nutshell · Answer

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.

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

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