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# Is the range of a six-number set greater than 3?

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Math Expert
Joined: 02 Sep 2009
Posts: 52431
Is the range of a six-number set greater than 3?  [#permalink]

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07 Mar 2016, 08:05
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Difficulty:

45% (medium)

Question Stats:

68% (02:02) correct 32% (02:22) wrong based on 162 sessions

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Is the range of a six-number set greater than 3?

(1) The sum of the five largest numbers is greater than 16.
(2) The average of the five smallest numbers is less than 2.6.

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Joined: 02 Aug 2009
Posts: 7213
Re: Is the range of a six-number set greater than 3?  [#permalink]

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08 Mar 2016, 05:53
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Bunuel wrote:
Is the range of a six-number set greater than 3?

(1) The sum of the five largest numbers is greater than 16.
(2) The average of the five smallest numbers is less than 2.6.

Hi,
A good Q..

we require to know the smallest and largest number in the set to find Range..

lets see the statements:-
(1) The sum of the five largest numbers is greater than 16.
we do not know the spread if number from this..
Insuff

(2) The average of the five smallest numbers is less than 2.6
Since average is 2.6, the sum of five integers is < 5*2.6..
or Sum< 13..
we do not know the spread if number from this..
Insuff

Combined
we know sum of Largest + middle 4>16..
sum of smallest +middle 4<13
so largest -smallest >3
Suff

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Re: Is the range of a six-number set greater than 3?  [#permalink]

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08 Mar 2016, 16:30
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the range of a six-number set greater than 3?

(1) The sum of the five largest numbers is greater than 16.
(2) The average of the five smallest numbers is less than 2.6.

In the original condition, from range=Max-min, there are 3 variables and 1 equation, which should match with the number of equations. So you need 2 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), they become n1+n2+n3+n4+M>16 and m+n1+n2+n3+n4<2.6*5=13. When multiplying -1 to the equation, it becomes -m-n1-n2-n3-n4>-13, which is yes and sufficient.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Is the range of a six-number set greater than 3?  [#permalink]

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03 Nov 2016, 14:06
1
let the numbers are a, b, c,d,e, f , let's say the biggest number is a and the smallest is f so the range is f-a

1) if sum of the largest 5 integer ( b+c+d+e+f) is greater than 16, so sum of 6 integer will also be higher

a+b+c+d+e+f >16 ........................ inequality 1

2) average of the smallest 05 numbers - (a+ b+c+d+e ) /5 < 2.6

or (a+ b+c+d+e ) < 13

or -(a+ b+c+d+e ) > -13 .................inequality 2

f-a > 3

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Re: Is the range of a six-number set greater than 3?  [#permalink]

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13 Apr 2018, 05:03
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Re: Is the range of a six-number set greater than 3? &nbs [#permalink] 13 Apr 2018, 05:03
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