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# Is the sum of seven positive integers > 99? 1). 16 is the

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Director
Joined: 14 Jan 2007
Posts: 774
Is the sum of seven positive integers > 99? 1). 16 is the [#permalink]

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20 May 2007, 05:47
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Is the sum of seven positive integers > 99?
1). 16 is the max number
2). range is 10
SVP
Joined: 01 May 2006
Posts: 1796

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20 May 2007, 06:25
(E) for me

Let S be the set of integers

From 1
max(S) = 16

o If S={16,16,16,16,16,16,16}, then Sum(S) = 16*7 = 112 (>99)
o If S={1,1,1,1,1,1,16}, then Sum(S) = 6*1 + 16 = 22 (<99)

INSUFF.

From 2
range(S) = 10

o If S={1,1,1,1,1,1,11}, then Sum(S) = 6*1 + 11 = 17 (<99)
o If S={100,100,100,100,100,100,110}, then Sum(S) = 6*100 + 110 = 710 (>99)

INSUFF.

Both (1) & (2)

o If S={6,16,16,16,16,16,16}, then Sum(S) = 16*6 + 6 = 102 (>99)
o If S={6,6,6,6,6,6,16}, then Sum(S) = 6*6 + 16 = 52 (<99)

INSUFF.
Intern
Joined: 12 May 2007
Posts: 23

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20 May 2007, 10:09
it doesnt say that they have to be different numbers...
Manager
Joined: 12 Apr 2007
Posts: 168

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20 May 2007, 12:42
Agree with Fig on this on. E.

One question, though.

When the question says that 16 is the max number, does it mean that there HAS to be a 16 in the set, or just that 16 is the highest possible number that can be in the set. Not that it makes a difference here, I'm just curious.

Thanks!
Manager
Joined: 23 Mar 2007
Posts: 173

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20 May 2007, 13:08
Fig wrote:
(E) for me

Let S be the set of integers

From 1
max(S) = 16

o If S={16,16,16,16,16,16,16}, then Sum(S) = 16*7 = 112 (>99)
o If S={1,1,1,1,1,1,16}, then Sum(S) = 6*1 + 16 = 22 (<99)

INSUFF.

From 2
range(S) = 10

o If S={1,1,1,1,1,1,11}, then Sum(S) = 6*1 + 11 = 17 (<99>99)

INSUFF.

Both (1) & (2)

o If S={6,16,16,16,16,16,16}, then Sum(S) = 16*6 + 6 = 102 (>99)
o If S={6,6,6,6,6,6,16}, then Sum(S) = 6*6 + 16 = 52 (<99)

INSUFF.

Excellent explanation. I had chosen A , but after reading this explantion agree on E.
Director
Joined: 14 Jan 2007
Posts: 774

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20 May 2007, 17:13
Fig has given the perfect explanation.
OA is 'E'
20 May 2007, 17:13
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