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If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 00:05
Question Stats:
35% (01:49) correct 65% (02:31) wrong based on 40 sessions
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Competition Mode Question If \(f(n) = 1154*1156\) for some integer, n, which of the following expressions could be equal to \(f(n)\)? A. \(3n  2\) B. \(5n  2\) C. \(5n + 3\) D. \(7n  2\) E. \(11n + 10\) Are You Up For the Challenge: 700 Level Questions
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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 00:58
the last two digits = 24 options a,b,c,d wont be possible IMO E ; 11n+10
If f(n)=1154∗1156f(n)=1154∗1156 for some integer, n, which of the following expressions could be equal to f(n)f(n)?
A. 3n−2
B. 5n−2
C. 5n+3
D. 7n−2
E. 11n+10



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 01:18
1154 = 1155  1 = 11k  1, for some positive value k & 1156 = 1155 + 1 = 11k + 1
So, 1154*1156 = (11k  1)(11k + 1) = (11k)^2  1 = 11(11k^2)  1 = 11(n + 1)  1 = 11n + 11  1 = 11n + 10 > f(n) = 1154*1156 can be expressed of the form 11n + 10 for some value of 'n'
IMO Option E



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 02:01
f(n)=1154∗1156 = 1155^2 1
From options its visible that 1155 is divisible by 11.... so E: 1155^2 110 = 1155^2 11= which is divisible by 11
OA:E



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 05:11
If f(n)=1154∗1156 for some integer, n, which of the following expressions could be equal to f(n)?
For could be true questions, we only need to prove that the function is true for just one case.
1154*1156 = 1,324,024
Testing with f(n)=3n2 3n2=1,334,024 3n=1,334,022 n=444,674 Since f(n) is defined for integers and the function f(n)=3n2 yields an integer when equated to 1154*1156, then f(n) is true for 3n2, when n=444,674
The answer is option A.



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 06:22
1154x1156= 1334024
Of the five answer choices, We notice that the last term is 2 in three of the options. But after adding 2, the resulting number 1334026 is not divisible by 5 or 3 or 7. Therefore eliminate A,B and D.
We add 10 to the number and notice that the result,1334014 is divisble by 11. (divisibility test : difference between sum of odd digits and even digits should be divisble by 11)
Therefore E is the answer



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 07:51
Quote: If f(n)=1154∗1156 for some integer, n, which of the following expressions could be equal to f(n)?
A. 3n−2 B. 5n−2 C. 5n+3 D. 7n−2 E. 11n+10 \(f(n)=1154*1156=1155^21^2=1155^21\) A. \(3n−2=1155^21…3n=1155^2+1…1155=factor(3)…1≠factor(3)\) B. \(5n−2=1155^21…5n=1155^2+1…1155=f(5)…1≠f(5)\) C. \(5n+3=1155^21…1155=f(5)…13=4…4≠f(5)\) D. \(7n−2=1155^21…1155=f(7)…1+2=1…1≠f(7)\) E. \(11n+10=1155^21…1155=f(11)…110=11…11=f(11)…f(n)=11n+10=valid\) Ans (E)



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 08:45
\(f(n)=1154∗1156=(11551)*(1155+1)=1155^21=(3^2*5^2*7^2*11^2)1\)
We understand that the units digit of \(f(n)=1155^21\) must be 4. (B) f(n)=5n−2 > units digit of the result is either 3 or 8 (C) f(n)=5n+3 > units digit of the result is either 3 or 8 Thus, we confidently eliminate choices (B) and (C), since both choices NEVER yield results with units digit of 4
A. f(n)=3n−2 \(f(n)=3n−2=(3^2*5^2*7^2*11^2)1\) \(3n=(3^2*5^2*7^2*11^2)+1\) \(n=(3*5^2*7^2*11^2)+1/3\) > \(n\) is NOT an integer, so we confidently eliminate choice (A), since \(n\) has to be some integer
D. f(n)=7n−2 \(f(n)=7n−2=(3^2*5^2*7^2*11^2)1\) \(7n=(3^2*5^2*7^2*11^2)+1\) \(n=(3^2*5^2*7*11^2)+1/7\) > \(n\) is NOT an integer, so we confidently eliminate choice (D), since \(n\) has to be some integer
E. 11n+10 \(f(n)=11n+10=(3^2*5^2*7^2*11^2)1\) \(11n=(3^2*5^2*7^2*11^2)11\) \(n=(3^2*5^2*7^2*11)1\) > \(n\) is an integer, so we are confident that choice (E) is the CORRECT ANSWER
Final answer is (E)



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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 13:02
IMO, Ans A.
Both 1154 and 1156 when divided by 3 leaves a remainder of 2.
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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 17:09
\(f(n) = 1154*1156= (1155 —1)(1155 +1)= 1155^{2}—1\)
\(1155^{2} —1= 11*11*105*105—1\)
E) \(11n + 10= 11n + 11—1= 11(n+1)—1\)
The answer is E
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Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 17:09






