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04 Jul 2025, 08:00
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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:
47% (02:01) correct
53%
(01:53)
wrong
based on 447
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a < b < c\), and \(c^4 < b^4 < a^4\), which of the following could be true?
I. \(abc > 0\)
II. \(a^3b^5c^7 < 0\)
III. \(a^2b^4c^6 = 0\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. \(abc > 0\)
II. \(a^3b^5c^7 < 0\)
III. \(a^2b^4c^6 = 0\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
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04 Jul 2025, 08:30
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Bunuel
GMAT Club Official Explanation:
Taking the fourth root of \(c^4 < b^4 < a^4\) gives \(|c| < |b| < |a|\).
Given that \(a < b\) and \(|b| < |a|\), we can deduce that a must be negative. That's because for a to be further from zero than b (\(|b| < |a|\)) and still be less than b (\(a < b\)), a must be negative.
Given that \(b < c\) and \(|c| < |b|\), we can deduce that b must also be negative. That's because for b to be further from zero than c (\(|c| < |b|\)) and still be less than c (\(b < c\)), b must be negative.
So both a and b must be negative numbers. However, c can be negative, 0, or positive. For example, if a = -3 and b = -2, then c can be -1, 0, or 1.
Since c can be any of those, and each option contains c, then each option could be true, making option E correct.
Still, if interested, let's analyze the options, keeping in mind that we are asked to determine which of the following COULD be true:
I. \(abc > 0\)
ab will be positive, and since c could be positive, \(abc\) could be positive.
II. \(a^3b^5c^7 < 0\)
a^3b^5 will be positive, and if c is negative, then \(a^3b^5c^7\) could be negative.
III. \(a^2b^4c^6 = 0\)
Since c can be 0, \(a^2b^4c^6\) can also be 0.
Answer: E.
General Discussion
04 Jul 2025, 08:08
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Information given:
- a<b<c
- c^4<b^4<a^4
Question:
- Which of the following statements could be true?
Solutions:
- Note that since raising to the fourth power 'flips' the order, the sign pattern is all negative
- 1: Impossible. Product of three negatives is negative, abc < 0
- 2: Possible. Odd powers preserve signs, so the product is negative x negative x negative, less than 0
- 3: Impossible. Squares and even powers are always positive. Variables can't be zero, and therefore the product can't be zero.
Answer: B, II only
- a<b<c
- c^4<b^4<a^4
Question:
- Which of the following statements could be true?
Solutions:
- Note that since raising to the fourth power 'flips' the order, the sign pattern is all negative
- 1: Impossible. Product of three negatives is negative, abc < 0
- 2: Possible. Odd powers preserve signs, so the product is negative x negative x negative, less than 0
- 3: Impossible. Squares and even powers are always positive. Variables can't be zero, and therefore the product can't be zero.
Answer: B, II only
Bunuel
