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1) from 1- x> -9/2 not suff
2) from 2 - x< -3 not suff

from 1 and 2 combined

-4.5<x<-3
=>x= -4 Sufficient (C)
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You know X is an I, you are looking for value of X. So that can range from negative, 0, positive integers.

Statement 1:
-2(X+5)<-1
-2X-10<-1
-2X<9
X>-4.5 (flip the inequality if divide or multiply by a negative).

Well statement 1 means that it could be -4, -3, 0, 1, 2 etc... so A and D are not correct.

Statement 2:
-3X>9
X<-3 (again flip the inequality if divide or multiply by a negative).

Well this means that X can be -4, -5, -6, etc... so B is not correct.

Combining the two statements you get the following inequality
-4.5<X<-3 and since X needs to be an integer you know that X=-4 so C is correct.
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banksy

Project DS Butler: Day 52: Data Sufficiency (DS103)


For DS butler Questions Click Here

If x is an integer, what is the value of x?

(1) –2(x + 5) < -1
(2) –3x > 9

Target question: What is the value of x?

Statement 1: –2(x + 5) < -1
Expand the left side: –2x - 10 < -1
Add 10 to both sides: –2x < 9
Divide both sides by -2 to get: x > -4.5 [note: Since I divided both sides of the inequality by a negative value, I had to reverse the direction of the inequality symbol]
Since x is an INTEGER, x could equal -4, -3, -2, -1 . . . .
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: –3x > 9
Divide both sides of the equation by -3 to get: x < -3
Since x is an INTEGER, x could equal -4, -5, -6, -7 . . . .
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 x > -4.5
Statement 2 tells us that x < -3
Combine the two inequalities to get: -4.5 < x < -3
Since x is an INTEGER, x MUST equal -4
The combined statements are SUFFICIENT

Answer: C
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