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02 Sep 2021, 03:34
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
59% (01:21) correct
41%
(01:20)
wrong
based on 345
sessions
History
Date
Time
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Not Attempted Yet
If x = m − 1, which of the following is true when \(m = \frac{1}{2}\) ?
(A) \(x^0 > x^2 > x^3 > x^1\)
(B) \(x^0 > x^2 > x^1 > x^3\)
(C) \(x^0 > x^1 > x^2 > x^3\)
(D) \(x^2 > x^0 > x^3 > x^1\)
(E) \(x^3 > x^2 > x^1 > x^0\)
(A) \(x^0 > x^2 > x^3 > x^1\)
(B) \(x^0 > x^2 > x^1 > x^3\)
(C) \(x^0 > x^1 > x^2 > x^3\)
(D) \(x^2 > x^0 > x^3 > x^1\)
(E) \(x^3 > x^2 > x^1 > x^0\)
02 Sep 2021, 04:15
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Bunuel
Solution:
We are given \(x = m − 1\) when \(m = \frac{1}{2}\).
This means the value of \(x=\frac{1}{2}-1=-\frac{1}{2}\)
Now there are \(2\) ways to go about this problem from here:
Method 1: When we actually find the value of \(x^0, x^1, x^2\) and \(x^3\) and then decide the order.
\(x^0=(-\frac{1}{2})^0=1\)
\(x^1=-\frac{1}{2}=-0.5\)
\(x^2=(-\frac{1}{2})^2=0.25\)
\(x^3=(-\frac{1}{2})^3=-0.175\)
Now we can very easily write the order \(x^0 > x^2 > x^3 > x^1\) and say that the right answer is Option A.
However, there is a better approach:
Method 2:
We infer that \(x=-\frac{1}{2}\) belong to the third region (\(>-1\) and \(<0\)) of the number line and we know in the 3rd region of the number line \(x^3 > x^1\) and \(x^0 > x^2\)
Now we can very easily write the order \(x^0 > x^2 > x^3 > x^1\) and say that the right answer is Option A.
pratiksha1998
Joined: 11 Aug 2021
Last visit: 22 Mar 2026
Posts: 98
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Given Kudos: 16
Location: India
Concentration: General Management, Strategy
Schools: Goizueta '25
GMAT 1: 600 Q47 V27
04 Sep 2021, 04:47
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For m =1/2, x = -1/2
Substituting the value in first option,
1>1/4>-1/8>-1/2
IMO Option A
Substituting the value in first option,
1>1/4>-1/8>-1/2
IMO Option A
