Is x 0? (1) |x + 3|

Question

Is x > 0?

(1) |x + 3| < 4 
(2) |x - 3| < 4

This is how I approached it:
1) Sufficient as range of x is -7<x<1 which shows X can't be greater than 0 (Definite no)
2) Sufficient as range of x is -1<x<7 which shows that X is greater than 0 (Definite yes)

Hence D

However OA is E, can somebody please explain whats wrong in my approach.

Bunuel · Accepted Answer

Is x > 0? Notice that we are not told that x is an integer. (1) |x + 3| < 4 --> -4 < x + 3 < 4 --> -7 x can be positive as well as negative number. Not sufficient. (2) |x - 3| < 4 --> -4 < x - 3 < 4 --> -1 x can be positive as well as negative number. Not sufficient. (1)+(2) Overlap of the ranges is -1

aniketb · Answer

Thanks for the tip Bunuel, this is going into the quant notes...I will check this thing from now on. :thumbup:

PerfectScores · Answer

Is x > 0?

(1) |x + 3| < 4 
(2) |x - 3| < 4

Statement I is insufficient:

x = -0.5 (NO)
x = 0.1 (YES)

Statement II is insufficient:

x = -0.5 (NO)
x = 0.1 (YES)

Combining is not necessary because x = -0.5 and x = 0.1 disprove statement I and II. Hence the answer is E.

aniketb · Answer

Thanks for the reply PerfectScores, it would be helpful if you could please elaborate on what basis have you chosen the values? (For example -0.1 or -1 would also have done the job, why -0.5 and 0.1 only?) It will help, as I tend to pick wrong values some times and hence chose Bunuel's method.

PerfectScores · Answer

It is about Z O N E D

We will try to use Zero, One, Negative, Extreme (Even/Odd) (Small/Large), Decimals.

Here -0.5 and 0.1 seemed to eliminate both the answer options.

rohanGmat · Answer

we could also use visualization here: 
|x + 3| < 4 is basically distance of point x from point (-3) is less than 0. So the extreme points are -3+4 = 1 and -3-4 = -7 (not inclusive)

Since 1 is not a valid point, lets pick something smaller, say 0.5 and -7 is not valid so something greater, say -0.5 
st1. 
|-0.5+3| = 2.5 <4 & |0.5+3|=3.5<4 -- not sufficient 
St2. 
|-0.5-3| = 3.5 <4 & |0.5-3| = 2.5 <4 -- not sufficient
Combining also you see both point taken suffice both conditions so Ans: E. (PS I calculated -0.5 as second point by eyeballing second eq & using above visualization approach).

aniketb · Answer

Hey PerfectScore Thanks alot, the ZONED technique is helpful... :yes

aniketb · Answer

Hey Rohan, thanks for the reply. This is slightly off the topic, but I can see your Verbal score has improved a lot in second attempt. I am scoring around 650 with similar breakup of your first attempt. It will be very much helpful if you let me know how you did it? (The plan, last minute strategy, Mocks etc) Thanks in advance...

GordonFreeman · Answer

I don't see any question options... am I missing something? This is the second math question with which I've had this issue.

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

chetan2u · Answer

lets see the statement straight as there is no info from the statements.. (1) |x + 3| < 4 we can form two eq.. x+3<4 so x<1.. x+3>-4, so x>-7.. so -7-4,, so x>-1.. so -1

TeamGMATIFY · Answer

Required : Is x > 0? Statement 1 : |x + 3| < 4 On solving, we get -4 < x + 3 < 4 -7 < x < 1 Since x is not restricted to integers, it can take any value. INSUFFICIENT Statement 2 : |x – 3| < 4 On Solving, -4 < x - 3 < 4 -1 < x < 7 Since x is not restricted to integers, it can take any value. INSUFFICIENT Statement 1 and Statement 2 Combined : The common values of -7 < x < 1 and -1 < x < 7 are: - 1 < x < 1 Still we cannot say if x > 0 or not. INSUFFICIENT Option E

tommannanchery · Answer

Is  x  > 0?

(1) | x  + 3| < 4

(2) | x  – 3| < 4

tommannanchery · Answer

Official Answer/Explanation (1) INSUFFICIENT: We can solve this absolute value inequality by considering both the positive and negative scenarios for the absolute value expression |x + 3|. If x > -3, making (x + 3) positive, we can rewrite |x + 3| as x + 3: x + 3 < 4 x < 1 If x < -3, making (x + 3) negative, we can rewrite |x + 3| as -(x + 3): -(x + 3) < 4 x + 3 > -4 x > -7 If we combine these two solutions we get -7 < x < 1, which means we can’t tell whether x is positive. (2) INSUFFICIENT: We can solve this absolute value inequality by considering both the positive and negative scenarios for the absolute value expression |x – 3|. If x > 3, making (x – 3) positive, we can rewrite |x – 3| as x – 3: x – 3 < 4 x < 7 If x < 3, making (x – 3) negative, we can rewrite |x – 3| as -(x – 3) OR 3 – x 3 – x < 4 x > -1 If we combine these two solutions we get -1 < x < 7, which means we can’t tell whether x is positive. (1) AND (2) INSUFFICIENT: If we combine the solutions from statements (1) and (2) we get an overlapping range of -1 < x < 1. We still can’t tell whether x is positive. The correct answer is E.

tommannanchery · Answer

The highlighted area shows that x = 0. Thus, x is not > 0.  Shouldn't the answer for this be C?

Bunuel · Answer

Merging topics. Please refer to the discussion above.

Bunuel · Answer

No. We are not told that x is an integer. It can be any number between -1 and 1, not necessarily 0.

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Is x > 0? (1) |x + 3| < 4 (2) |x - 3| < 4

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