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If k is a multiple of 24 but not a multiple of 16, which of the follow
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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) \(\frac{k}{81}\)
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Re: If k is a multiple of 24 but not a multiple of 16, which of the follow
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13 Aug 2018, 08:07
Bunuel wrote: 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) \(\frac{k}{81}\) 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.
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If k is a multiple of 24 but not a multiple of 16, which of the follow
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13 Aug 2018, 20:43
Bunuel wrote: 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) \(\frac{k}{81}\) 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)
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Re: If k is a multiple of 24 but not a multiple of 16, which of the follow
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18 Aug 2018, 19:29
Bunuel wrote: 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) \(\frac{k}{81}\) If k is a multiple of 24, then k could be: 24, 48, 72, 96, 120, 144, … However, since k is not a multiple of 16, then k can’t be: 48, 96, 144, … So we see that k could only be: 24, 72, 120, … That is, k is an odd multiple of 24. We see that k/8 is an integer since 24 is divisible by 8. Furthermore, k/9 and k/81 could each be an integer if k is 9 x 24 and 81 x 24, respectively. Lastly, k/36 could be an integer if k is 9 x 24 (notice that 9 x 24 = 9 x 4 x 6 = 36 x 6). Therefore, k/32 can’t be integer (notice that 32 = 16 x 2, so if k is not a multiple of 16, then k can’t be a multiple of 32). Answer: C
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Re: If k is a multiple of 24 but not a multiple of 16, which of the follow
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19 Aug 2018, 06:46
Solution Given:• k is a multiple of 24 but not a multiple of 16 To find:• The option which cannot be an integer.
Approach and Working: • K is multiple of 24 then K can be written as \(2^{(3+a)}*3^{(1+b)}* some other prime factors\). o However, k is not a multiple of 16. o So, a must be 0. • Thus, K= \(2^3+*3^{(1+b)}* some other prime factors\). Now, among the given options, only \(\frac{K}{32}\) will not be an integer. Hence, the correct answer is option C. Answer: C
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Re: If k is a multiple of 24 but not a multiple of 16, which of the follow
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19 Aug 2018, 07:19
Bunuel wrote: 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) \(\frac{k}{81}\) We are given: k is a multiple of 24, k can be any of the following: 24, 48, 72, 96, 120, 144... We are also told: k is not a multiple of 16. Thus, we can eliminate: 48, 96, 144... We are left with values: 24, 72, 120... On substituting in the values above in the given options, 24/32 , 72/32, 120/32 are not integers. Thus, the answer is C.




Re: If k is a multiple of 24 but not a multiple of 16, which of the follow
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19 Aug 2018, 07:19






