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S is the set of all numbers that can be written as a sum

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kevincan
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S is the set of all numbers that can be written as a sum [#permalink] New post   24 Jun 2007, 16:01
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S is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d : |a|/a + |2b|/b + |3c|/c + |4d|/d + |5abcd|/abcd . What is the range of S ?

(A) 20 (B) 25 (C) 28 (D) 29 (E) 30



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Re: S is the set of all numbers that can be written as a sum [#permalink] New post   24 Jun 2007, 16:47
kevincan wrote:
S is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d : |a|/a + |2b|/b + |3c|/c + |4d|/d + |5abcd|/abcd . What is the range of S ?

(A) 20 (B) 25 (C) 28 (D) 29 (E) 30


E. 30.

the minimum is -15 and the max is 15. so the difference = 30.
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Re: S is the set of all numbers that can be written as a sum [#permalink] New post   24 Jun 2007, 18:33
Juaz wrote:
kevincan wrote:
S is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d : |a|/a + |2b|/b + |3c|/c + |4d|/d + |5abcd|/abcd . What is the range of S ?

(A) 20 (B) 25 (C) 28 (D) 29 (E) 30


Range is 28 i.e. -13 to 15


:oops: Booooo! I fell for it too. abcd would be positive when all the variables are negative.
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Re: S is the set of all numbers that can be written as a sum [#permalink] New post   24 Jun 2007, 19:50
could you guys explain your answers please?
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Re: S is the set of all numbers that can be written as a sum [#permalink] New post   24 Jun 2007, 21:01
Himalayan wrote:
kevincan wrote:
S is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d : |a|/a + |2b|/b + |3c|/c + |4d|/d + |5abcd|/abcd . What is the range of S ?

(A) 20 (B) 25 (C) 28 (D) 29 (E) 30


E. 30.

the minimum is -15 and the max is 15. so the difference = 30.



agree with 28.

if a, b, c and d are +ves: |a|/a + |2b|/b + |3c|/c + |4d|/d + |5abcd|/abcd = 15

if a is +ve and b, c and d are -ves: |a|/a + |2b|/b + |3c|/c + |4d|/d + |5abcd|/abcd = -13

Difference = 28.



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Thank you for understanding, and happy exploring!
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Re: S is the set of all numbers that can be written as a sum [#permalink]
24 Jun 2007, 21:01
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