Is the integer x a 3-digit integer?

AbeNeedsAnswers wrote:Is the integer x a 3-digit integer?

(1) x is the square of an integer.
(2) 90 < x < 150

Target question: Is the integer x a 3-digit integer?

Statement 1: x is the square of an integer.
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 10² = 100. In this case, the answer to the target question is YES, x IS a 3-digit integer
Case b: x = 9² = 81. In this case, the answer to the target question is NO, x is NOT a 3-digit integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 90 < x < 150
TEST some cases.
Case a: x = 100. In this case, the answer to the target question is YES, x IS a 3-digit integer
Case b: x = 91. In this case, the answer to the target question is NO, x is NOT a 3-digit integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are THREE values of x that satisfy BOTH statements: x = 100, x = 121 and x = 144
In all three cases, the answer to the target question is the same: YES, x IS a 3-digit integer
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Hi All,

We're told that X is an integer. We're asked if X is a 3-digit integer. This question can be solved by TESTing VALUES.

(1) X is the SQUARE of an INTEGER.

Fact 1 tells us that X is a 'perfect square.' For example, X could be 1, 4, 9.....100, 121, 144....10,000, etc.
IF....
X = 1, then the answer to the question is NO.
X = 100, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

(2) 90 < X < 150

Fact 2 gives us a range of possible values for X.
IF....
X = 91, then the answer to the question is NO.
X = 100, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know...
X is the SQUARE of an INTEGER.
90 < X < 150

There are only a few perfect squares in this given range: 100, 121 and 144. Regardless of which value X actually is, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich