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24 Nov 2025, 23:33
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:24) correct
17%
(01:15)
wrong
based on 183
sessions
History
Date
Time
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Not Attempted Yet
If x^4 > x^5 > x^3, which of the following could be the value of x?
A. -3
B. -2
C. -2/3
D. 2/3
E. 3
A. -3
B. -2
C. -2/3
D. 2/3
E. 3
25 Nov 2025, 06:53
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Bunuel
Given that : x^4 > x^5 > x^3
Divide the terms by x^4 , we get
1 > x > (1/x)
We have two different equations: x<1 and x > (1/x)
Let’s take the second case:
x > (1/x)
x - (1/x) > 0
(x^2 - 1 )/x >0
Multiply by x^2 on both sides, we get
(x^2 - 1 ) * x >0
This can be further simplified as : x * (x+1)*(x-1) > 0
ploting it on the number line using wavy method, we get
Critical points are : -1, 0, 1
-infinity to -1 : less than zero
Between -1 and 0: greater than zero
Between 0 and 1: Less than zero
Greater than 1: Greater than Zero.
We are looking for regions which are greater than Zero.
First Case: x < 1
The overlapping regions between First case and Second case is
Between -1 and 0.
So, our answer choice must lie between -1 and 0. The only option which satisfies this criteria is OPTION C (-2/3)
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25 Nov 2025, 09:38
Kudos
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Fairly straightforward. We have x^4 as the largest, hence the first conclusion I drew straightaway was x should be negative. Next, look at x^5 > x^3. This tells me that it should be a negative fraction, since negative integers mean x^5 would be less than x^3 (e.g. (-2)^5 = -32 and (-2)^3 = -8). The only negative fraction we have is -2/3 so I go with that.
Double checking, x = -2/3, then x^4 = 16/81, x^5 = -32/243, x^3 = -8/27
Indeed, here x^4 > x^5 > x^6
If the latter is tougher to derive mentally (like it is for me), I typically think about (-1/2)^1 = -1/2 = -0.5 and (-1/2)^3 = -1/8 = -0.125. The latter is closer to 0 on the number line, hence must be greater -> higher power of a negative fraction > lower power
(There are probably simpler ways of doing this, but this approach made the most intuitive sense to me right away without using any real manipulations or complex theory)
Double checking, x = -2/3, then x^4 = 16/81, x^5 = -32/243, x^3 = -8/27
Indeed, here x^4 > x^5 > x^6
If the latter is tougher to derive mentally (like it is for me), I typically think about (-1/2)^1 = -1/2 = -0.5 and (-1/2)^3 = -1/8 = -0.125. The latter is closer to 0 on the number line, hence must be greater -> higher power of a negative fraction > lower power
(There are probably simpler ways of doing this, but this approach made the most intuitive sense to me right away without using any real manipulations or complex theory)
