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26 Mar 2020, 06:38
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C
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:
68% (01:51) correct
32%
(01:37)
wrong
based on 87
sessions
History
Date
Time
Result
Not Attempted Yet
If \(n\) = \(\frac{25!}{20!}\), then which of the following is NOT an integer?
(A) \(\frac{n}{48}\\
\)
(B) \(\frac{n}{66}\)
(C) \(\frac{n}{96}\)
(D) \(\frac{n}{100}\)
(E) \(\frac{n}{385}\)
(A) \(\frac{n}{48}\\
\)
(B) \(\frac{n}{66}\)
(C) \(\frac{n}{96}\)
(D) \(\frac{n}{100}\)
(E) \(\frac{n}{385}\)
26 Mar 2020, 07:20
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sjuniv32
If \(n\) = \(\frac{25!}{20!}\), then which of the following is NOT an integer?
(A) \(\frac{n}{48}\\
\)
(B) \(\frac{n}{66}\)
(C) \(\frac{n}{96}\)
(D) \(\frac{n}{100}\)
(E) \(\frac{n}{385}\)
(A) \(\frac{n}{48}\\
\)
(B) \(\frac{n}{66}\)
(C) \(\frac{n}{96}\)
(D) \(\frac{n}{100}\)
(E) \(\frac{n}{385}\)
\(n\) = \(\frac{25!}{20!}=21*22*23*24*25=3*7*2*11*23*2^3*3*5^2=2^4*3*7*11*23\)
let us check the choices..
(A) \(\frac{n}{48}...[m]48=2^4*3\), so a factor of n.
[/m]
(B) \(\frac{n}{66}\)..\(66=2*3*11\), so a factor of n.
(C) \(\frac{n}{96}\)..\(96=2^5*3\), so not a factor of n. as n has 2^4
our answer C
26 Mar 2020, 07:21
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Solution
Given
In this question, we are given that
- • The value of n = 25!/20! = (20! X 21 x 22 x 23 x 24 x 25)/20! = 21 x 22 x 23 x 24 x 25
To find
We need to determine
- • From the given options, which number is not an integer
Approach and Working out
Checking each option individually:
- • n/48 = (21 x 22 x 23 x 24 x 25)/48 = (2 x 24 x 21 x 11 x 23 x 25)/48 = 21 x 11 x 23 x 25 = integer
• n/66 = (21 x 22 x 23 x 24 x 25)/66 = (3 x 22 x 7 x 23 x 24 x 25)/66 = 7 x 23 x 24 x 25 = integer
• n/96 = (21 x 22 x 23 x 24 x 25)/96 = (2 x 24 x 21 x 11 x 23 x 25)/96 = (21 x 11 x 23 x 25)/2 = not an integer
• n/100 = (21 x 22 x 23 x 24 x 25)/100 = (4 x 25 x 21 x 22 x 23 x 6)/100 = 21 x 22 x 23 x 6 = integer
• n/385 = (21 x 22 x 23 x 24 x 25)/385 = (5 x 7 x 11 x 3 x 2 x 23 x 24 x 5)/385 = 3 x 2 x 23 x 24 x 5 = integer
Thus, option C is the correct answer.
Correct Answer: Option C
