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24 Nov 2019, 12:14
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:27) correct
50%
(02:37)
wrong
based on 179
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x\) is a negative integer, what is the value of \(x\)?
(1) \(x^2 + 40x + 398 < 0\)
(2) \((x+17)(x+20) < 0\)
(1) \(x^2 + 40x + 398 < 0\)
(2) \((x+17)(x+20) < 0\)
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24 Nov 2019, 19:59
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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
(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
25 Nov 2019, 10:51
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GMATPrepNow
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
