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DS - Range

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by karthikpandian19 » Thu Jun 28, 2012 11:28 pm
If N is a set of four numbers a, b, c, and d . Is the range of the numbers in set N greater than 8?

a - d > 8
c is the smallest number in N.
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by Birottam Dutta » Thu Jun 28, 2012 11:44 pm
Range of a set is the difference between the highest and lowest number.

Here, from 1, a-d>8. So this is sufficient to conclude that the range is greater than 8.

The second statement is inconsequential.

So, 1 should be the correct option.
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by niketdoshi123 » Thu Jun 28, 2012 11:46 pm
karthikpandian19 wrote:If N is a set of four numbers a, b, c, and d . Is the range of the numbers in set N greater than 8?

a - d > 8
c is the smallest number in N.
a) sufficient
Consider following extreme combinations
1)a > b > c > d => Range = a-d > 8

2)(b or c) > (c or b) > a > d => Range = (b or c) - d > 8 (must be) (as (b or c) is greater than a)

b) insufficient
It doesn't tell us the value of any number.
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by karthikpandian19 » Thu Jun 28, 2012 11:54 pm
@birottam,

Can you explain your interpretation for statement 1?
Birottam Dutta wrote:Range of a set is the difference between the highest and lowest number.

Here, from 1, a-d>8. So this is sufficient to conclude that the range is greater than 8.

The second statement is inconsequential.

So, 1 should be the correct option.
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by Anurag@Gurome » Fri Jun 29, 2012 12:14 am
karthikpandian19 wrote:If N is a set of four numbers a, b, c, and d . Is the range of the numbers in set N greater than 8?

a - d > 8
c is the smallest number in N.
Statement 1: If we consider a as the greatest element and d is least element of N, then range of N = (a - d) > 8

But, if they are not so, then there will be some numbers (either maximum or minimum) which will have more distance from either a or d. Hence, the range will be always greater than (a - d).

For example, say b > a > d > c.
Hence, range = (b - c) > (a - d) > 8

Or, say c > a > b > d.
Hence, range = (c - d) > (a - d) > 8

Sufficient

Statement 2: We have no idea about the greatest element of N.
Hence, we cannot comment about range.

Not sufficient

The correct answer is A.
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by karthikpandian19 » Fri Jun 29, 2012 12:15 am
OA is A
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by Birottam Dutta » Fri Jun 29, 2012 5:27 am
@karthik:

Let us assume some values for a, b, c and d.

Let these values be a=13, b=1, c=5 and d=3.

Now, a-d = 10 which is greater than 8. Hence the condition is satisfied.

So, since this condition holds, the range of the set must be greater than 8, whatever the values of the other numbers.

For a-b=12, this is the actual range of the set.

So, if a-d>8, then the range of the set must be greater than 8, whatever the values of the other numbers.

I hope I am clear now!
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by optimist » Sat Jun 30, 2012 7:45 am
@Birottam

Does this imply that - the range of a set of numbers is always > difference between any 2 numbers of the same set ?
Birottam Dutta wrote:@karthik:

Let us assume some values for a, b, c and d.

Let these values be a=13, b=1, c=5 and d=3.

Now, a-d = 10 which is greater than 8. Hence the condition is satisfied.

So, since this condition holds, the range of the set must be greater than 8, whatever the values of the other numbers.

For a-b=12, this is the actual range of the set.

So, if a-d>8, then the range of the set must be greater than 8, whatever the values of the other numbers.

I hope I am clear now!
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