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12 Mar 2025, 10:42
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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(N/A)
Question Stats:
0% (00:00) correct
100% (01:01) wrong based on 3 sessions
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If x and y are integers such that \(x^3 = y^2,\) which of the following could not be the value of y?
Indicate all such values.
A. –1
B. 1
C. 8
D. 12
E. 16
F. 27
Indicate all such values.
A. –1
B. 1
C. 8
D. 12
E. 16
F. 27
13 Mar 2025, 11:51
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OE
Test each choice until you find all the correct answers.
(A) Could y = –1? Is there an integer x such that \(x^3 = (–1)^2 = 1?\) Yes, x = 1.
(B) Similarly, if y = 1, x = 1.
(C) Could y = 8? Is there an integer x such that \(x^3 = (8)^2 = 64\)? Yes, x = 4.
(D) Could y = 12? Is there an integer such that \(x^3 = 12^2 = 144\)? No, \(5^3 = 125\), which is too small; and \(6^3 = 216\), which is too big.
(E) Could y = 16? Is there an integer x such that \(x^3 = 16^2 = 256\)? No, \(6^3 = 216\), which is too small, and \(7^3 = 343\), which is too big.
(F) Could y = 27? Is there an integer x such that \(x^3 = 27^2 = 729\)? Yes, \(9^3 = 729.\)
The answer is D and E.
Test each choice until you find all the correct answers.
(A) Could y = –1? Is there an integer x such that \(x^3 = (–1)^2 = 1?\) Yes, x = 1.
(B) Similarly, if y = 1, x = 1.
(C) Could y = 8? Is there an integer x such that \(x^3 = (8)^2 = 64\)? Yes, x = 4.
(D) Could y = 12? Is there an integer such that \(x^3 = 12^2 = 144\)? No, \(5^3 = 125\), which is too small; and \(6^3 = 216\), which is too big.
(E) Could y = 16? Is there an integer x such that \(x^3 = 16^2 = 256\)? No, \(6^3 = 216\), which is too small, and \(7^3 = 343\), which is too big.
(F) Could y = 27? Is there an integer x such that \(x^3 = 27^2 = 729\)? Yes, \(9^3 = 729.\)
The answer is D and E.
