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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
25 Jun 2012, 02:04

1

This post received KUDOS

Expert's post

SOLUTION

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If x=1 and y=4 then the range=6-1=5<9 but if x=100 then the range>9. Not sufficient.

(2) y > x > 3. If x=4 and y=5 then the range=6-3=3<9 but if x=100 then the range>9. Not sufficient.

(1)+(2) From x > 3 we have that the least value of x is 4, and from y > 3x=12 we have that the least value of y is 13, hence the least value of the range is 13-3=10>9. Sufficient.

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
25 Jun 2012, 07:41

Hi,

Range = Largest value - smallest value.

6, 3, y, 4, 5, and x, where x & y are integers

Using (1), y>3x, if x=1, then y = 4, 5,..100.... in each case range can be 5, 6,....So, range is greater than 5. Insufficient.

Using (2), y>x>3. Minimum value of x = 4, y=5,6,7... We can't say whether range is greater than 9.

Combining both statements; x_{min} = 4 & since, y > 3x, y_{min}=13, thus, 3, 4, 4, 5, 6, & 13 has range (13-3)=10, which is greater than 9 and on increasing x, range will also increase.

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
29 Jun 2012, 03:36

Expert's post

SOLUTION

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If x=1 and y=4 then the range=6-1=5<9 but if x=100 then the range>9. Not sufficient.

(2) y > x > 3. If x=4 and y=5 then the range=6-3=3<9 but if x=100 then the range>9. Not sufficient.

(1)+(2) From x > 3 we have that the least value of x is 4, and from y > 3x=12 we have that the least value of y is 13, hence the least value of the range is 13-3=10>9. Sufficient.

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
02 May 2014, 12:38

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