GMAT Data Sufficiency Practice Question 26
Inequalities | Number Properties | Difficult Data Sufficiency Question
The given question is a challenging GMAT data sufficiency question in Inequalities. Concepts covered: Inequalities, absolute values and number properties
GMAT Data Sufficiency | Directions | Click Here ▼
This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Note
In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.
Question 26: Is x|x| = x2?
Statement 1: x(1 – x2) < 0
Statement 2: x(1 – x) < 0
Get to 705+ in the GMAT
Online GMAT Course
@ INR 8000 + GST
Video Explanation
GMAT Live Online Classes
Starts Thu, Dec 19, 2024
Explanatory Answer | GMAT Inequalities
Step 1: Decode the Question Stem and Get Clarity
Q1. When is the data sufficient?
If we are able to get a conclusive YES or NO, the data is sufficient.
Q2. What should you watch out for ?
If x > 0, x |x| = x2
If x = 0, x |x| = x2
If x < 0, x |x| is negative and x2 is positive. So, x |x| < x2 ?
So, the question is essentially asking whether x is non negative i.e., Is x ≥ 0 ?
Step 2: Evaluate Statement 1 ALONE
Statement 1: x(1 – x2) < 0
i.e., x - x3 < 0 or x < x3
For what values of x will x < x3 ?
Interval 1: (1 < x < ∞)
x < x3. Here, x is greater than zero. Answer to the question - YES
Interval 2: (-1 < x < 0)
x < x3. Here, x is lesser than zero. Answer to the question - NO
We are not able to get a conclusive answer using Statement 1.
Hence, statement 1 is not sufficient.
Eliminate answer option A and D.
Step 3: Evaluate Statement 2 ALONE
Statement 2: x(1 - x) < 0
i.e., x – x2 < 0 or x < x2
For what values of x will x < x2 ?
Interval 1: (1 < x < ∞)
x < x2. Here, x is greater than zero. Answer to the question - YES
Interval 2: (-1 < x < 0)
x < x2. Here, x is lesser than zero. Answer to the question - NO
We are not able to get a conclusive answer using Statement 2.
Hence, statement 2 is not sufficient.
Eliminate answer option B.
Step 4: Evaluate Statements TOGETHER
Statements: From Statement 1: x < x3
From Statement 2: x < x2
Both conditions hold good in the following intervals,
Interval 1: (1 < x < ∞)
x < x3 and x < x2. Here, x is greater than zero. Answer to the question - YES
Interval 2: (-∞ < x < 0)
x < x3 and x < x2. Here, x is lesser than zero. Answer to the question - NO
Despite combining the statements, we are not able to get a conclusive answer.
Eliminate answer option C.
Choice E is the correct answer.
GMAT Hard Math Videos On YouTube
GMAT Sample Questions | Topicwise GMAT Questions
Copyrights © 2016 - 24 All Rights Reserved by Wizako.com - An Ascent Education Initiative.
Privacy Policy | Terms & Conditions
GMAT® is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.
GRE® is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.
SAT® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.
How to reach Wizako?
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: [email protected]
Leave A Message