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09 Aug 2025, 01:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
12% (00:20) correct
87% (00:31) wrong based on 8 sessions
History
Date
Time
Result
Not Attempted Yet
16 Aug 2025, 04:39
Kudos
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Official Explanation
First, try to find a number which multiplied by itself four times equals 81. Observe that 81 = 9 × 9, and that 9 = 3 × 3, so that \(81 = 3 × 3 × 3 × 3 = 3^4,\) so x = 3 satisfies the first equation. Next, solve for y by dividing both sides of the second equation by 8 to obtain \(y^3 = 8,\) and \(y = 2 \)(since 2× 2 × 2 = 8). It may seem that if x = 3 and y = 2, then (A) is greater, but recall that a negative number raised to an even power is positive. Here, \((-3)^4\) also equals 81, so x could equal 3 or -3. Since 3 > 2, but -3 < 2, (D) is correct.
Answer: D
First, try to find a number which multiplied by itself four times equals 81. Observe that 81 = 9 × 9, and that 9 = 3 × 3, so that \(81 = 3 × 3 × 3 × 3 = 3^4,\) so x = 3 satisfies the first equation. Next, solve for y by dividing both sides of the second equation by 8 to obtain \(y^3 = 8,\) and \(y = 2 \)(since 2× 2 × 2 = 8). It may seem that if x = 3 and y = 2, then (A) is greater, but recall that a negative number raised to an even power is positive. Here, \((-3)^4\) also equals 81, so x could equal 3 or -3. Since 3 > 2, but -3 < 2, (D) is correct.
Answer: D
