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05 Apr 2022, 04:00
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B
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Difficulty:
95%
(hard)
Question Stats:
24% (02:38) correct
76%
(02:26)
wrong
based on 336
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If \(f(x) = |3x - 20| + |11 - x | + |2x - 17|\), for how many integers n is \(f(n) = f(n + 1\)) ?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Are You Up For the Challenge: 700 Level Questions
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Are You Up For the Challenge: 700 Level Questions
19 Jun 2022, 05:32
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If f(x)=|3x−20|+|11−x|+|2x−17|f(x)=|3x−20|+|11−x|+|2x−17|, for how many integers n is f(n)=f(n+1f(n)=f(n+1) ?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Here is a way to solve this problem..
Hope it assists..
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Here is a way to solve this problem..
Hope it assists..
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29 May 2022, 01:37
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f(n) = |3n - 20| + |11 - n | + |2n - 17|
f(n+1) = |3n + 3 - 20| + |11 - n -1 | + |2n + 2 - 17| = |3n - 17| + |10 - n | + |2n - 15|
Now since both are expressions in modulus, we know by property of modulus that it means absolute value implying that anything inside a modulus can be positive or negative so we can say that:
f(n) {on simplification using all modulus as themselves} = 4n - 26 or f(n) {all modulus negative} = -4n + 26
f(n+1) = 4n - 22 or f(n+1) = -4n + 22
Question asks us for how many integers is f(n) = f(n+1):
Now here we can have 4 different situations:
1. Both positive: 4n - 26 = 4n - 22; both variables get cancelled so not possible
2. Both negative: Same as above both variables will get cancelled so not possible
3. f(n) positive and f(n+1) negative: 4n - 26 = -4n + 22; we can solve for n
4. f(n) negative and f(n+1) positive: Similar expression and same value for n
So, there is just 1 integer that satisfied f(n) = f(n+1) hence answer B
f(n+1) = |3n + 3 - 20| + |11 - n -1 | + |2n + 2 - 17| = |3n - 17| + |10 - n | + |2n - 15|
Now since both are expressions in modulus, we know by property of modulus that it means absolute value implying that anything inside a modulus can be positive or negative so we can say that:
f(n) {on simplification using all modulus as themselves} = 4n - 26 or f(n) {all modulus negative} = -4n + 26
f(n+1) = 4n - 22 or f(n+1) = -4n + 22
Question asks us for how many integers is f(n) = f(n+1):
Now here we can have 4 different situations:
1. Both positive: 4n - 26 = 4n - 22; both variables get cancelled so not possible
2. Both negative: Same as above both variables will get cancelled so not possible
3. f(n) positive and f(n+1) negative: 4n - 26 = -4n + 22; we can solve for n
4. f(n) negative and f(n+1) positive: Similar expression and same value for n
So, there is just 1 integer that satisfied f(n) = f(n+1) hence answer B
