If x is a negative integer, what is the value of x?

Question

If  x  is a negative integer, what is the value of  x ?

(1)  x^2 + 40x + 398 < 0

(2)  (x+17)(x+20) < 0

chetan2u · Answer

If  x  is a negative integer, what is the value of  x ?

(1)  x^2 + 40x + 398 < 0......x(x+40)+398<0 
x(x+40)<-398
This will happen when x is between 0 and -40..
x =-20......x(x+40)=-20*20=-400
x=-19.......-19*21=-399
Insuff

(2)  (x+17)(x+20) < 0 
This means x lies between-17 and -20, so x can be -18 or -19.
Insuff

Combined 
x =-19
Suff

C

BrentGMATPrepNow · Answer

Given : x is a negative integer

Target question :    What is the value of x?

Statement 1 :  x^2 + 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

firsttimenoob · Answer

GMATPrepNow  How did you get from: (x+17)(x+20)<0(x+17)(x+20)<0 to -20 < x < -17? My first instinct was to get x<-17 and x<-20?

BrentGMATPrepNow · Answer

First notice that (x+17)(x+20) = 0, when x = -17 and when x = -20 Let's examine 3 possible ranges for the value of x. case i x < -20 If x < -20, then (x+17) is NEGATIVE, and (x+20) is NEGATIVE So, (x+17)(x+20) = (NEGATIVE)(NEGATIVE) = POSITIVE So, when x < -20, x is NOT a solution to the inequality (x+17)(x+20) < 0 case ii -20 < x < -17 If -20 < x < -17 then (x+17) is NEGATIVE, and (x+20) is POSITIVE So, (x+17)(x+20) = (NEGATIVE)(POSITIVE) = NEGATIVE So, when -20 < x < -17, x IS a solution to the inequality (x+17)(x+20) < 0 case iii x > -17 If x > -17, then (x+17) is POSITIVE, and (x+20) is POSITIVE So, if (x+17)(x+20) = (POSITIVE)(POSITIVE) = POSITIVE So, when x > -17, x is NOT a solution to the inequality (x+17)(x+20) < 0 Does that help? Cheers, Brent

naveeng15 · Answer

Statement 1: 
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: 
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

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If x is a negative integer, what is the value of x?

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If x is a negative integer, what is the value of x?

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