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PrashantPonde
Joined: 27 Jun 2012
Last visit: 29 Jan 2025
Posts: 311
Given Kudos: 185
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
17 Feb 2013, 12:16
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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:
75%
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Question Stats:
54% (02:17) correct
46%
(01:56)
wrong
based on 658
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Is x negative?
(1) At least one of x and x^2 is greater than x^3.
(2) At least one of x^2 and x^3 is greater than x.
(1) At least one of x and x^2 is greater than x^3.
(2) At least one of x^2 and x^3 is greater than x.
12 Jul 2016, 08:25
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Just draw out the number line and write out the order of the three functions in each region:
\(x^3<x<x^2 \) \(x<x^3<x^2\) \(x^3<x^2<x\) \(x<x^2<x^3\)
<------------------|------------------|------------------|------------------>
-1 0 1
(1) At least one of x and x^2 is greater than x^3.
This can be true in regions 1,2, and 3, x can be positive or negative. INSUFFICIENT
(2) At least one of x^2 and x^3 is greater than x.
This can be true in regions 1,2, and 4, x can be positive or negative. INSUFFICIENT
Taking the two together, this is true in regions 1 and 2, which means x is negative. SUFFICIENT.
Answer: C.
\(x^3<x<x^2 \) \(x<x^3<x^2\) \(x^3<x^2<x\) \(x<x^2<x^3\)
<------------------|------------------|------------------|------------------>
-1 0 1
(1) At least one of x and x^2 is greater than x^3.
This can be true in regions 1,2, and 3, x can be positive or negative. INSUFFICIENT
(2) At least one of x^2 and x^3 is greater than x.
This can be true in regions 1,2, and 4, x can be positive or negative. INSUFFICIENT
Taking the two together, this is true in regions 1 and 2, which means x is negative. SUFFICIENT.
Answer: C.
17 Feb 2013, 14:50
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If x > 1, then it is always true that x < x^2 < x^3.
If 0 < x < 1, then it is always true that x^3 < x^2 < x.
From the above, you can see that neither statement is sufficient alone, since in each case, x can be positive. Notice from the above that if x is positive, x^2 is never the largest of the three expressions x, x^2 and x^3. Since Statement 1 guarantees that x^3 is not the largest of the three expressions, and Statement 2 guarantees that x is not the largest of the three expressions, then using both statements, the only possibility is that x^2 is the largest of the three expressions. Since that can't happen when x is positive, x must be negative, and the answer is C.
If 0 < x < 1, then it is always true that x^3 < x^2 < x.
From the above, you can see that neither statement is sufficient alone, since in each case, x can be positive. Notice from the above that if x is positive, x^2 is never the largest of the three expressions x, x^2 and x^3. Since Statement 1 guarantees that x^3 is not the largest of the three expressions, and Statement 2 guarantees that x is not the largest of the three expressions, then using both statements, the only possibility is that x^2 is the largest of the three expressions. Since that can't happen when x is positive, x must be negative, and the answer is C.
