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# If set s={7,y,12,8,,x,9} is x+y less than 18? 1.range of set

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Manager
Joined: 11 Feb 2011
Posts: 129

Kudos [?]: 249 [1], given: 21

If set s={7,y,12,8,,x,9} is x+y less than 18? 1.range of set [#permalink]

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24 Mar 2011, 00:50
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Question Stats:

56% (01:13) correct 44% (00:49) wrong based on 78 sessions

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If set s={7,y,12,8,,x,9} is x+y less than 18?

1.range of set s is less than 9
2.average of x and y is less than average of set s.
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Kudos [?]: 249 [1], given: 21

SVP
Joined: 16 Nov 2010
Posts: 1597

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
Re: explain the concept ! [#permalink]

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24 Mar 2011, 02:19
If range is less than 9, then the difference between the largest and teh smallest members of the set should be ,9

The difference of all the given numbers < 9

So even if we were to assume that the difference between x and y is less than 18

then let us try to find values of x and y

So x = 7 + 10 = 17

y can be the same as well = 7 + 10 = 17

So x + y can be > 18,

Again, x+y can be any other numbers as 1 and 2, and the range is still < 9.

so (1) is not sufficient.

From (2)

(x+y)/2 < (7 + y + 12 + 8 + x + 9)/6

=> 6(x+y) < 2(x+y + 36)

=> 4(x+y) < 2*36

=> (x+y) < 18

So Answer - B
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Kudos [?]: 592 [0], given: 36

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 615

Kudos [?]: 1134 [1], given: 39

Re: explain the concept ! [#permalink]

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25 Mar 2011, 06:22
1
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AnkitK wrote:
If set s={7,y,12,8,,x,9} is x+y less than 18?

1.range of set s is less than 9
2.average of x and y is less than average of set s.

(1) x= 5, y= 11 range (12-5) is less than 9 and x+y <18
but x= 5, y= 13 here range is less than 8 but x+y=18 so INSUFFICIENT.

(2) (X+Y)/2<(7+y+12+8+x+9)/6
X+Y<18 SUFF.
ANS B
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Kudos [?]: 1134 [1], given: 39

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Re: If set s={7,y,12,8,,x,9} is x+y less than 18? 1.range of set [#permalink]

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14 Apr 2016, 02:20
In order to prove that option B is the right answer we are multiplying the inequality by the LCM (6) without knowing if x+y is positive or negative.

Is there any reason for x+y to be assumed to be positive?

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

Re: If set s={7,y,12,8,,x,9} is x+y less than 18? 1.range of set   [#permalink] 14 Apr 2016, 02:20
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# If set s={7,y,12,8,,x,9} is x+y less than 18? 1.range of set

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