Brent@GMATPrepNow wrote:If x is a negative integer, what is the value of x?
(1) x² + 40x + 398 < 0
(2) (x + 17)(x + 20) < 0
Answer:
C
Source:
www.gmatprepnow.com
Difficulty level: 650-700
Given: x is a negative integer
Target question: What is the value of x?
Statement 1: x² + 40x + 398 < 0
If we recognize that x² + 40x + 398 is very close to the PERFECT SQUARE x² + 40x + 400, we can quickly deal with statement 1
Take: x² + 40x + 398 < 0
Add 2 to both sides to get: x² + 40x + 400 < 2
Factor: (x + 20)(x + 20) < 2
In other words: (x + 20)² < 2
Since we're told x is an INTEGER, we can see that there are 3 values of x that satisfy the inequality (x + 20)² < 2
So,
x can equal -21, -20 or -19
Statement 2: (x + 17)(x + 20) < 0
Notice that, when -20 < x < -17, we see that (x+17)(x+20) = (NEGATIVE)(POSITIVE) = NEGATIVE
In other words, when x is BETWEEN -20 and -17, (x+17)(x+20) < 0
So,
x can equal -18 or -19
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
x can equal -21, -20 or -19
Statement 2 tells us that
x can equal -18 or -19
Since both statements are TRUE, it
must be the case that
x = -19
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
