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07 May 2020, 00:51
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (02:03) correct
24%
(02:13)
wrong
based on 55
sessions
History
Date
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If \(u=2^{5}-2\), \(v=3^{5}-3\) and \(w=4^{5}-4\), what is the greatest common divisor of u,v and w?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
07 May 2020, 03:07
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Ravixxx
\(u=2^{5}-2 = 32-2 = 30\)
i.e. answer can NOT be options C, D and E which we can eliminate now
Also, Option A can be eliminated because 20 is not the factor of u so it can NOT be HCF of u, v and w
Hence, Answer: Option B
However, with confusing options we need to do the following calculations
\(v=3^{5}-3= 3*(3^4-1) = 3*(3^2+1)*(3^2-1) = 3*10*8 \)
\(w=4^{5}-4= 4*(4^4-1) = 4*(4^2+1)*(4^2-1) = 4*17*15 \)
so GCD of u, v and w = 30
07 May 2020, 05:23
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Ravixxx
we can individually simplify each term also.
u = \(2^5 - 2 = 2(2^4 - 1) = 2(2^2 + 1)(2^2 - 1) = 2*5*3 = 2^1 * 3^1 * 5^1\)
v = \(3^5 - 3 = 3(3^4 - 1) = 3(3^2 + 1)(3^2 - 1) = 3*10*8 = 2^4 * 3^1 * 5^1\)
w = \(4^5 - 4 = 4(4^4 - 1) = 4(4^2 + 1)(4^2 - 1) = 4*17*15 = 2^2 * 3^1 * 5^1 * 17^1\)
therefore, the GCD(u, v, w) = \(2^1 * 3^1 * 5^1 = 30\) (option B)
