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

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VP
Joined: 21 Jul 2006
Posts: 1495
S is the set of all numbers that can be written as a sum [#permalink]

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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

Thanks
Director
Joined: 10 Sep 2007
Posts: 923

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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.
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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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

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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VP
Joined: 21 Jul 2006
Posts: 1495

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14 Aug 2008, 14:19
OA is C. Thanks guys
Re: PS: Range   [#permalink] 14 Aug 2008, 14:19
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