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555-605 (Medium)|   Algebra|      
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Bunuel
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What is the value of (n+13)!+(n+14)!/((n+11)!+(n+12)!) ? 25 Jan 2022, 07:30
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What is the value of \(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!}\) ?


A. \((n+12)(n+15)\)

B. \((n+11)(n+12)\)

C. \((n+10)(n+13)\)

D. \((n+10)(n+15)\)

E. \((n+9)(n+12)\)
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A
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What is the value of (n+13)!+(n+14)!/((n+11)!+(n+12)!) ? 25 Jan 2022, 08:10
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Asked: What is the value of \(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!}\) ?

\(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!} = \frac{(n+13)! (1+ n+14)}{(n+11)!(1 + n+12)} = \frac{(n+13)(n+12)(n+15)}{(n+13)} = (n+12)(n+15)\)

IMO A
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What is the value of (n+13)!+(n+14)!/((n+11)!+(n+12)!) ? 02 Apr 2022, 00:04
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Asked: What is the value of \(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!}\) ?

\(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!} = \frac{(n+13)! (1+ n+14)}{(n+11)!(1 + n+12)} = \frac{(n+13)(n+12)(n+15)}{(n+13)} = (n+12)(n+15)\)

IMO A
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Can anyone explain this?
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What is the value of (n+13)!+(n+14)!/((n+11)!+(n+12)!) ? 02 Apr 2022, 02:12
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prashantjanghel
Kinshook
Asked: What is the value of \(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!}\) ?

\(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!} = \frac{(n+13)! (1+ n+14)}{(n+11)!(1 + n+12)} = \frac{(n+13)(n+12)(n+15)}{(n+13)} = (n+12)(n+15)\)

IMO A

Can anyone explain this?
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prashantjanghel if you find it a little confusing might I suggest a slightly different approach. We know that \(n\) is a constant, and we have not been given any limitations on \(n\). In this case we can assign any value to \(n\). The easiest would be to let \(n = 0\). Plugging that in gives us:

\(\frac{(0+13)!+(0+14)!}{(0+11)!+(n+12)!}\)

\(\frac{13!+14!}{11!+12!}\)

\(\frac{13!(1+14)}{11!(1+12)}\)

\(\frac{13!(15)}{11!(13)}\) which can be rewriten as \(\frac{11!*12*13(15)}{11!(13)}\)

\(12(15)\)

As we made \(n=0\) there is no need to do any calculations with the answer choices, answer choice A is identical to the answer. Therefore, the answer is A.
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What is the value of (n+13)!+(n+14)!/((n+11)!+(n+12)!) ? 11 Jan 2023, 10:28
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What is the value of (n+13)!+(n+14)!(n+11)!+(n+12)!(n+13)!+(n+14)!(n+11)!+(n+12)! ?


A. (n+12)(n+15)(n+12)(n+15)

B. (n+11)(n+12)(n+11)(n+12)

C. (n+10)(n+13)(n+10)(n+13)

D. (n+10)(n+15)(n+10)(n+15)

E. (n+9)(n+12)

In the expression \((N + 13)! + (N + 14)!/(N + 11)! + (N + 12)! \)We use the concept of factoring out the lowest common term
In the numerator the lowest common term is (N + 13)! = N + 13!(1 + N + 14)
In the denominator the lowest common term is (N + 11)! = N + 11!(1 + N + 12)
Simplifying: \(N + 13!(N + 15)/N + 11!(1 + N + 12)\) =
\(N + 13 * N + 12 * N + 11!(N + 15)/N + 11! * N + 13\)
When terms get cancelled out (N + 15)(N+12) remains
A
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What is the value of (n+13)!+(n+14)!/((n+11)!+(n+12)!) ? 30 Oct 2024, 03:19
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