If x^2

Question

If x^2 < 25, which of the following expressions must be true?

I. |x-3| < 10
II. |2x – 3| < 8
III. |2x^2| < 42

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

ManifestDreamMBA · Answer

x^2 < 25 OR -5 < x < 5 I x-3<10 => x<13 x-3>-10 => x >-7 -7 < x< 13 True Eliminate B,C III 2x^2<42 x^2<21 True Eliminate A,D Answer E

crimson_king · Answer

Answer is A) I only

For the third statement if you take x as 4.9 it will give you a value greater than 42 when you plug it in

Krunaal · Answer

x^2 < 25 => -5 < x < 5

I. |x - 3| < 10 => -7 < x < 13

Since x is between -5 and 5, it will always be between -7 and 13. Therefore, statement I must be true.

II. |2x - 3| < 8 => -2.5 < x < 5.5

Since x is between -5 and 5, x can be -3 and statement II will not hold true. Statement II may or may not be true.

III. |2x^2| < 42 => 0 < x^2 < 21 => approx. -4.6 < x < approx. 4.6

Since x is between -5 and 5, x can be 4.8 and statement III will not hold true. Statement III may or may not be true.

Thus, from above only statement I must be true. Answer A.

Kinshook · Answer

If x^2 < 25, which of the following expressions must be true?

|x| < 5
-5 < x < 5

I. |x-3| < 10; -10<x-3<10; -7<x<13; MUST BE TRUE since {-5,5} is covered in {-7,13}
II. |2x – 3| < 8; -8<2x-3<8; -5<2x<11; -2.5<x<5.5; if x = - 3; Not true; COULD BE TRUE
III. |2x^2| < 42; -42<2x^2<42; -21<x^2<21; 0<=x^2<21; -4.6<x<4.6; If x = 4.7; Not true; COULD BE TRUE

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

IMO A

If x^2<25, which of the following expressions must be true?

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 Problem Solving (PS) Questions