If x is a negative integer, is x

Question

If x is a negative integer, is x < −3?

(1) x^2 + 6x < 7

(2) x^2 + |x| ≤ 2

DavidTutorexamPAL · Answer

1) x^2 + 6x -7 <0 ==> (x+7)(x-1) < 0 ==> -7

rahul16singh28 · Answer

Statement I: Take X = 0, - 4 ------------ Not Sufficient
Statement II: Here, X can be only 0,-1,1... Sufficient.

MarcoAD · Answer

Dear David, Please confirm my understanding. In statement 2 you can say that x=-1 because of the following reasoning. IxI<= 2 - x^2 we have 2 cases: 1) x>0 --> x<=2-x^2 2) x<0 --> x >= x^2-2 However we know that x is negative hence we pick only case 2. x >= x^2-2 x^2-x-2<=0 (x-2)(x+1)<=0 so x>=-1 & x<=2 We know that x is a negative integer so within this range only x=-1 is acceptable. Am I correct?

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 1 variable ( x ) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) x^2 + 6x < 7 ⇔ x^2 + 6x - 7 < 0 ⇔ (x+7)(x-1) < 0 ⇔ -7 < x < 1 ⇔ -6 ≤ x ≤ -1 since x is a negative integer. The possible values of x are -6, -5, -4, -3, -2 and -1 . Since condition 1) does not yield a unique solution, it is not sufficient. Condition 2) x^2 + |x| ≤ 2 ⇔ x^2 + |x| - 2 ≤ 0 ⇔ |x|^2 + |x| - 2 ≤ 0 since |x|^2 = x^2 ⇔ (|x| - 1 )( |x| + 2 ) ≤ 0 ⇔ -2 ≤ |x| ≤ 1 ⇔ 0 ≤ |x| ≤ 1 since 0 ≤ |x| ⇔ |x| ≤ 1 ⇔ -1 ≤ x ≤ 1 Then x = -1 is the unique solution since x is a negative integer. Since condition 2) yields a unique solution, it is sufficient. Therefore, B is the answer.

Harshjha001 · Answer

Can someone please explain me how statement 2 is sufficient ?
i did not understand any of the above solutions.

Bunuel · Answer

Notice that we are given than x is a negative  integer  (-1, -2, -3, -4, ...). Next, notice that if x is -2 or less (-3, -4, -5) than x^2 + |x| is more than 2. So, for negative integers, x^2 + |x| ≤ 2 hold true only if x = -1. Thus the answer to the question whether x < -3 is NO.

Thekingmaker · Answer

B satisfies +1 and -1 since negative hence -1 suff.
A satisfies all negative nos

hwnce IMO B

If x is a negative integer, is x < −3? (1) x^2 + 6x < 7 (2) x^2 + |

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions