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02 Nov 2021, 05:00
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E
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Difficulty:
95%
(hard)
Question Stats:
48% (02:15) correct
52%
(02:20)
wrong
based on 481
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If x is positive, which of the following may be true?
I. \(x < x^2 < 1 + x\)
II. \(x < 1 - x < 2x\)
III. \(1 - x < x < \frac{1}{x}\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
I. \(x < x^2 < 1 + x\)
II. \(x < 1 - x < 2x\)
III. \(1 - x < x < \frac{1}{x}\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
02 Apr 2023, 00:45
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Bookmarks
NikTek
Number plugging:
How to Do Math on the GMAT Without Actually Doing Math
The Power of Estimation for GMAT Quant
How to Plug in Numbers on GMAT Math Questions
Number Sense for the GMAT
Can You Use a Calculator on the GMAT?
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT
For more check Ultimate GMAT Quantitative Megathread
Hope it helps.
02 Nov 2021, 06:19
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If x is positive, which of the following may be true?
May/could be true should at most occasion give you options that fit in almost all the times.
I. \(x < x^2 < 1 + x\)
\(x^2>x\) is true for all x>1.
\(x+1>x^2......x^2-x<1.....x(x-1)<1\), so x is almost equal and less than 1.6 as 1.6*0.6 = 0.96~1
So, a value such as 1.1 will fit ...\(1.1<1.1^2<2.1\)
II. \(x < 1 - x < 2x\)
\(1-x>x....x<\frac{1}{2}\)
Take x as 2/5, then \(\frac{2}{5}<1-\frac{2}{5}<2*\frac{2}{5}\)
III. \(1 - x < x < \frac{1}{x}\)
\(x>1-x....x>1/2\)
\(\frac{1}{x}>x........x^2<1....x<1\)
Take x as 2/3, so \(\frac{1}{x}=\frac{1}{\frac{2}{3}}=\frac{3}{2}\)....
\(1-\frac{2}{3}<\frac{2}{3}<\frac{1}{\frac{2}{3}}\)
All possible
E
May/could be true should at most occasion give you options that fit in almost all the times.
I. \(x < x^2 < 1 + x\)
\(x^2>x\) is true for all x>1.
\(x+1>x^2......x^2-x<1.....x(x-1)<1\), so x is almost equal and less than 1.6 as 1.6*0.6 = 0.96~1
So, a value such as 1.1 will fit ...\(1.1<1.1^2<2.1\)
II. \(x < 1 - x < 2x\)
\(1-x>x....x<\frac{1}{2}\)
Take x as 2/5, then \(\frac{2}{5}<1-\frac{2}{5}<2*\frac{2}{5}\)
III. \(1 - x < x < \frac{1}{x}\)
\(x>1-x....x>1/2\)
\(\frac{1}{x}>x........x^2<1....x<1\)
Take x as 2/3, so \(\frac{1}{x}=\frac{1}{\frac{2}{3}}=\frac{3}{2}\)....
\(1-\frac{2}{3}<\frac{2}{3}<\frac{1}{\frac{2}{3}}\)
All possible
E
