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We understand that the units digit of \(f(n)=1155^2-1\) 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)
Originally posted by chondro48 on 28 Nov 2019, 07:45.
Last edited by chondro48 on 13 Jan 2020, 07:01, edited 2 times in total.
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 00:18
1
1
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'
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 04:11
1
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)=3n-2 3n-2=1,334,024 3n=1,334,022 n=444,674 Since f(n) is defined for integers and the function f(n)=3n-2 yields an integer when equated to 1154*1156, then f(n) is true for 3n-2, when n=444,674
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 05:22
2
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)
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres
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28 Nov 2019, 06:51
2
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
\(f(n)=1154*1156=1155^2-1^2=1155^2-1\)
A. \(3n−2=1155^2-1…3n=1155^2+1…1155=factor(3)…1≠factor(3)\) B. \(5n−2=1155^2-1…5n=1155^2+1…1155=f(5)…1≠f(5)\) C. \(5n+3=1155^2-1…1155=f(5)…-1-3=-4…-4≠f(5)\) D. \(7n−2=1155^2-1…1155=f(7)…-1+2=1…1≠f(7)\) E. \(11n+10=1155^2-1…1155=f(11)…-1-10=-11…-11=f(11)…f(n)=11n+10=valid\)
If f(n) = 1154*1156 for some integer, n, which of the following expres
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14 Jan 2020, 12:28
1154/3, Remainder= 2 1156/3, Remainder= 1 So, 1154*1156/3, Remainder= 2*1= 2 Therefore 3n+2 or 3n-1 can be the functions and not 3n-2 as we need to remove this Remainder to make it divisible by 3.
Similarly, 1154/5, Remainder= 4 1156/5, Remainder= 1 So, 1154*1156/5, Remainder= 4*1= 4 Therefore 5n+4 or 5n-1 can be the functions and not 5n-2 or 5n+3 as we need to remove this Remainder to make it divisible by 5.
Similarly, 1154/7, Remainder= 6 1156/7, Remainder= 1 So, 1154*1156/7, Remainder= 6*1= 6 Therefore 7n+6 or 7n-1 can be the functions and not 7n-2 as we need to remove this Remainder to make it divisible by 7.
Now, 1154/11, Remainder= 10 1156/11, Remainder= 1 So, 1154*1156/11, Remainder= 10*1= 10 Therefore 11n+10 or 11n-1 can be the function as we need to remove this Remainder to make it divisible by 11.
We understand that the units digit of \(f(n)=1155^2-1\) 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
We understand that the units digit of \(f(n)=1155^2-1\) 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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38% (02:17) correct 
