GMAT Question Patterns: Absolute ValueWe have gone through the GMAT Prep Tests and
OG 13 and analyzed all of the questions to spot the most common patterns. This discussion is dedicated to the types of absolute value problems that could appear on the test.
The idea behind this project is to find as many common question patterns as possible for 3 reasons:
- Get a higher score - make sure you know how to answer every pattern and you don't miss one of these in your practice
- Save Time - you don't need to solve hundreds of questions; you just need to solve a few questions from each pattern and if you answered them correctly, you can move on
- Peace of Mind - know that you have covered all known question patterns
Background - Most GMAT absolute value problems are encountered in data sufficiency section.
- Both number plugging method and algebra are suitable to solve absolute value questions.
- Usually you get 2-3 questions on absolute values on the test (based on GMAT Prep CATs)
Typical questions:NOTE:
- The questions below are from OG13 and GMAT Prep. There are 6 questions on absolute value in OG13.
- The question patterns are listed from most common to least common.
Pattern #1: Absolute Value and Inequalities.OG13 Practice Questions, question 159If x is an integer, is x|x|<2^x ?(1) x < 0
(2) x = -10
Discussed
HEREIs |x-y|>|x|-|y| ?(1) y < x
(2) xy < 0
Discussed
HEREIs x> 1?(1) (x+1) (|x| - 1) > 0
(2) |x| < 5
Discussed
HEREIs |x| > |y|?(1) x^2 > y^2
(2) x > y
Discussed
HEREIf x≠0, is |x| < 1 ?(1) x^2 < 1
(2) |x| < 1/x
Discussed
HERE Pattern #2: Absolute Value and Algebra.OG13 Practice Questions, question 1What is the value of |x| ?(1) x = - |x|
(2) x^2 = 4
Discussed
HEREIf \(x\neq{0}\), then \(\frac{\sqrt{x^2}}{x}=\)A. -1
B. 0
C. 1
D. x
E. \(\frac{|x|}{x}\)
Discussed
HEREIf x<0, then \(\sqrt{-x|x|}\) is:A. -x
B. -1
C. 1
D. x
E. \(\sqrt{x}\)
Discussed
HEREIs \(\sqrt{(x-3)^2}=3-x\)?(1) \(x\neq{3}\)
(2) \(-x|x| >0\)
Discussed
HERE Pattern #3: Must ot Could be true questions with Absolute Value.OG13 Practice Questions, question 14If \(|y-\frac{1}{2}| < \frac{11}{2}\), which of the following could be a value of y?(A) -11
(B) -11/2
(C) 11/2
(D) 11
(E) 22
Discussed
HEREIf |x| > 3, which of the following must be true?
I. x > 3
II. X^2 > 9
III. |x-1|>2A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Discussed
HERE Pattern #4: Absolute Value and Distance.OG13 Practice Questions, question 24Of the five coordinates associated with points A, B, C, D, and E on the number line above, which has the greatest absolute value?(A) A
(B) B
(C) C
(D) D
(E) E
Discussed
HEREOG13 Practice Questions, question 143Which of the following inequalities is an algebraic expression for the shaded part of the number line above?(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4
Discussed
HEREIf s and t are two different numbers on the number line, is s + t = 0 ? (1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t
Discussed
HERE Pattern #5: Min/Max and Absolute Value.OG13 Practice Questions, question 51If y is an integer, then the least possible value of |23 - 5y| is(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Discussed
HERE Theory on absolute value is
HERE.
All OG13 questions with solutions are
HERE.
PS absolute value questions are
HERE.
DS absolute value questions are
HERE.
700+ absolute value questions
HERE.