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Joined: 20 Feb 2017
Posts: 2506
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Which of the following integers is NOT a divisor of x if x = (21)(3^7)
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03 Apr 2021, 21:22
03 Apr 2021, 21:22
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54% (02:34) correct
45% (03:49) wrong based on 24 sessions
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Which of the following integers is NOT a divisor of x if \(x = (21)(3^7) – (112)\)?
A 7
B 11
C 15
D 17
E 35
A 7
B 11
C 15
D 17
E 35
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Re: Which of the following integers is NOT a divisor of x if x = (21)(3^7)
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04 Apr 2021, 01:05
04 Apr 2021, 01:05
GeminiHeat wrote:
Which of the following integers is NOT a divisor of x if \(x = (21)(3^7) – (112)\)?
A 7
B 11
C 15
D 17
E 35
A 7
B 11
C 15
D 17
E 35
\(x = (21)(3^7) – (112)\)
\(x = (3)(7)(3^7) - (7)(2^4)\)
\(x = (7)(3^8) - (7)(2^4)\)
\(x = 7[3^7 - 2^4] = 7[6545] = (7)(5)(11)(7)(17)\)
So, Factors of \(x\) could be \(7, 11, 17,\) and \(35\)
Hence, option C
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Re: Which of the following integers is NOT a divisor of x if x = (21)(3^7)
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05 Apr 2021, 06:05
05 Apr 2021, 06:05
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GeminiHeat wrote:
Which of the following integers is NOT a divisor of x if \(x = (21)(3^7) – (112)\)?
A 7
B 11
C 15
D 17
E 35
A 7
B 11
C 15
D 17
E 35
Let's factor this thing like crazy.
(21)(3^7) – (112) = (3)(7)(3^7) – (7)(2)(2)(2)(2)
= (7)(3^8) – (7)(2^4)
= 7(3^8 - 2^4) NOTE: The part in the brackets is a difference of squares, since 3^8 = (3^4)^2 and 2^4 = (2^2)^2
= 7(3^4 + 2^2)(3^4 - 2^2) we factored the difference of squares
= 7(3^4 + 2^2)(3^2 - 2)(3^2 + 2) we factored another difference of squares
= 7(81 + 4)(9 - 2)(9 + 2) evaluated
= 7(85)(7)(11) evaluated
= (7)(5)(17)(7)(11)
We can see that the above product is divisible by 7, 11, 17, and 35
BUT it is not divisible by 15
Answer: C
Cheers,
Brent
