Is |x - 3| 0 (2) x

Question

Is |x - 3| < 7 ?

(1) x > 0
(2) x < 10

DS21224

Kinshook · Answer

Asked: Is |x - 3| < 7 ? |x-3|<7 -4 0 If x<10; YES But if x>=10; NO NOT SUFFICIENT (2) x < 10 If x>-4; YES But if x<=-4; NO NOT SUFFICIENT (1) + (2) (1) x > 0 (2) x < 10 0

yashikaaggarwal · Answer

Is |x - 3| < 7 ?

(1) x > 0
Case 1: put x= 1
|1-3|<7
2<7 (sufficient)

Case 2: put x = 12
|12-3|>7
9>7 (insufficient)

Statement 1: (insufficient alone)

(2) x < 10

Case 1: put x= 1
|1-3|<7
2<7 (sufficient)

Case 2: put x = -12
|-12-3|>7
15>7 (insufficient)
Statement 2 is insufficient alone.

Statement 1 and 2:
0<x<10
Case 1: put x= 9
|9-3|<7
6<7 (sufficient)

Case 2: put x= 1
|1-3|<7
2<7 (sufficient)

(Sufficient)

Answer is C

Posted from my mobile device

Anuragjn · Answer

Statement 1 and 2: 0

yashikaaggarwal · Answer

Yes got my mistake
 Thank you.

bM22 · Answer

Is |x - 3| < 7 We get 2 cases. Case 1: if x - 3 > 0 => x- 3 < 7 => x < 10. Case 2: if x - 3 < 0 => - x + 3 < 7 => - x < 4 => x > -4. Thus we get : -4 < x < 10. Now, Statement 1: x > 0. It satisfies x< 10. but what if x > = 10. The the inequality wont hold true. So Insufficient. Statement 2: x < 10 It satisfies both : x < 10 x > -4. But what if x < -4 also, So this statement is also Insufficient . Statement 1 + Statement 2: 0 < x < 10. It satisfies both the sides of Inequality. Thus Sufficient. Answer C.

NitishJain · Answer

Given: |x - 3| < 7 Lets analyze the qtn statement: x is 7 points away from 3 on the number line => -4 0 i.e x can be 3,5,10 or even 20 but we know x<10 NOT SUFFICIENT II: x < 10 i.e. x can be 5,3,0 ,-4 or even -10 but we know -40 from II: x<10 ==> 0

VietKieu · Answer

|x - 3| < 7 can be re-written as below: ~ -70: x>10 does not make the inequality correct >> INSUFFICIENT (2): x<10: if x<-4 >> does not make the inequality correct >> INSUFFICIENT (1) + (2): 0

CEdward · Answer

Is |x - 3| < 7 ?

Rephrased: -4 < x < 10?

(1) x > 0
Clearly insufficient. 
e.g. x = 11 or 100 then the answer is NO.
e.g. x = 5 then YES

(2) x < 10
Clearly insufficient.
x = 5 then YES
x = -100 then NO

C: Sufficient b/c 0 < x < 10 overlaps with the defined region.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is |x - 3| < 7 ? (1) x > 0 (2) x < 10

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