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

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S is the set of all numbers that can be written as a sum [#permalink]

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New post 14 Aug 2008, 14:00
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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





Please explain your answer.
Thanks

Kudos [?]: 978 [0], given: 1

Director
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Joined: 10 Sep 2007
Posts: 936

Kudos [?]: 327 [0], given: 0

Re: PS: Range [#permalink]

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New post 14 Aug 2008, 14:07
|x|/x = 1 if x is +ve or -1 if x is -ve.
On same basis, we can get sum = -1 -2 -3 -4 -5 = -15
And sum = 1+2+3+4+5=15
Range = 15-(-15) = 30

IMO E.

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Re: PS: Range [#permalink]

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New post 14 Aug 2008, 14:14
tarek99 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





Please explain your answer.
Thanks

to get the range try to find the max and min value possible for the sum

|a|/a can be -1 or 1
|2b|/b can be -2 or 2
|3c|/c can be -3 or 3
|4d|/d can be -4 or -4
|5abcd|/abcd -5 or 5 ( here -5 is possible only when one or three of them are negative)


max value = 1+2+3+4+5 = 15 (all are postive)

minimu possible when |5abcd|/abcd -ve and samllest value (|a|/a ) +ve

1+ (-2)+(-3)+(-4)+(-5) = -13

range = 15- (-13) = 28

C
What is OA
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Kudos [?]: 1034 [0], given: 5

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Joined: 21 Jul 2006
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Kudos [?]: 978 [0], given: 1

Re: PS: Range [#permalink]

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New post 14 Aug 2008, 14:19
OA is C. Thanks guys

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Re: PS: Range   [#permalink] 14 Aug 2008, 14:19
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S is the set of all numbers that can be written as a sum

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