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13 Aug 2018, 04:54
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If k is a multiple of 24 but not a multiple of 16, which of the following cannot be an integer?
(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
13 Aug 2018, 08:07
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Bunuel
If k is a multiple of 24 but not a multiple of 16, which of the following cannot be an integer?
(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
k is a multiple of 24 but not a multiple of 16.
k=2x2x2x3xp
k is not equal to 2x2x2x2xq
A) Integer when k=24
B) Integer when k=72
C) Not an integer since each multiple of 32 will definitely be a multiple of 16
D) Integer when k=72
E) Integer when \(k=2X2X2X3^4\)
Answer C.
13 Aug 2018, 20:43
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Bunuel
If k is a multiple of 24 but not a multiple of 16, which of the following cannot be an integer?
(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
We have \(k=2^3*3^1*\)(any odd integer)Let's check the options:-
A. k/8 is an integer when k=24*any odd integer
B. k/9 is an integer when k=24*3*any odd integer
C. \(\frac{k}{32}\) can never be an integer . (\(32=2^5\), we can't make the odd integer=\(2^2\) since k is not a multiple of 16)
D. \(36=2^2*3^2=2^3*3^1*\frac{3}{2}\) , so k/36 is an integer.
E. 81=3^4=2^3*3^1*\frac{3^3}{2^3}[/m], so k/36 is an integer.
Ans. (C)
