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16 Dec 2022, 07:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
43% (02:07) correct
57%
(02:04)
wrong
based on 287
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Not Attempted Yet
12 Days of Christmas GMAT Competition with Lots of Fun
If √a > b^2 > c^3, which of the following may be true?
I. a > b > c
II. c > b > a
III. a > c > b
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
If √a > b^2 > c^3, which of the following may be true?
I. a > b > c
II. c > b > a
III. a > c > b
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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16 Dec 2022, 08:20
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a > b^2 > c^3
Think about the graph to solve it easily.
In may be true, we just need to find ONE example where each of the following hold:
I. a > b > c
II. c > b > a
III. a > c > b
If a > b^2 > c^3, only values between 0 to 1 will hold. See graph.
You will see that I, II, and III - all can hold.
I. Clearly true for the region (0,1).
II. c=0.6, b=0.5, a=0.4 holds. Take difference between a,b,c smaller and you will see this hold even without a precise graph. The attached graph is only for understanding purposes.
III. If II holds (where c>b), and a is greater, then III definitely holds.
Answer: E
Think about the graph to solve it easily.
In may be true, we just need to find ONE example where each of the following hold:
I. a > b > c
II. c > b > a
III. a > c > b
If a > b^2 > c^3, only values between 0 to 1 will hold. See graph.
You will see that I, II, and III - all can hold.
I. Clearly true for the region (0,1).
II. c=0.6, b=0.5, a=0.4 holds. Take difference between a,b,c smaller and you will see this hold even without a precise graph. The attached graph is only for understanding purposes.
III. If II holds (where c>b), and a is greater, then III definitely holds.
Answer: E
Attachments
Screenshot 2022-12-16 at 8.46.17 PM.png [ 323.37 KiB | Viewed 3854 times ]
16 Dec 2022, 10:59
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E is the answer. It is possible to create a scenario that all of the above statements are true given the original statement.
If √a > b^2 > c^3, which of the following may be true?
I. a > b > c
II. c > b > a
III. a > c > b
For questions like this, always consider "Special Numbers." These numbers are numbers that behave differently in different operations in math. Special numbers can include: {negatives, 0, fractions less than 1, 1, 2, and extremes.}
Too many possible scenarios exist with the original statement to either eliminate possibilities that won't work or to include only certain groups of numbers. For this reason, let's jump in and consider the options I, II, and III.
I. Is it possible that √a > b^2 > c^3 AND a>b>c?
This can be possible if a is a positive number (adequately) greater than b (they can even be fractions less than 1) and c is negative
Example: a=100
b=2 and
c=-1
II. Is it possible that √a > b^2 > c^3 AND c>b>a?
This can be possible if a , b and c are appropriately chosen fractions less than 1
Example: a=1/100
b=1/4 and
c=1/3
III. Is it possible that √a > b^2 > c^3 AND a>c>b?
This can be possible if a and c are appropriately chosen positive numbers and b is a negative number
Example:
a=100
b=-1 and
c=1/2
The answer is that I, II and III are ALL possible scenarios based on the properties of positive numbers, fractions less than one and negative numbers.
E is the correct answer!
If √a > b^2 > c^3, which of the following may be true?
I. a > b > c
II. c > b > a
III. a > c > b
For questions like this, always consider "Special Numbers." These numbers are numbers that behave differently in different operations in math. Special numbers can include: {negatives, 0, fractions less than 1, 1, 2, and extremes.}
Too many possible scenarios exist with the original statement to either eliminate possibilities that won't work or to include only certain groups of numbers. For this reason, let's jump in and consider the options I, II, and III.
I. Is it possible that √a > b^2 > c^3 AND a>b>c?
This can be possible if a is a positive number (adequately) greater than b (they can even be fractions less than 1) and c is negative
Example: a=100
b=2 and
c=-1
II. Is it possible that √a > b^2 > c^3 AND c>b>a?
This can be possible if a , b and c are appropriately chosen fractions less than 1
Example: a=1/100
b=1/4 and
c=1/3
III. Is it possible that √a > b^2 > c^3 AND a>c>b?
This can be possible if a and c are appropriately chosen positive numbers and b is a negative number
Example:
a=100
b=-1 and
c=1/2
The answer is that I, II and III are ALL possible scenarios based on the properties of positive numbers, fractions less than one and negative numbers.
E is the correct answer!
