Is the range of the integers 6, 3, y, 4, 5, and x greater th

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=6<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.

Answer: C.
_________________

Hey Bunuel,

In the question, we are talking about integers so why are we not considering negative values. Wouldn't the statements be insufficient in that case. Can you please explain why negative integers are out of scope

Second statement says that y > x > 3, so both x and y are positive.

Hoe it's clear.
_________________

Hi Bunuel,

From x > 3 the minimal value of x is 4, and the min value of y is 13 as per y> 3x=12, So the range should br 13-4=9
Can you please explain why the value of the range is 10 .

Thanks

It should be 13-4 = 9 only.

It MUST be a typo from Bunuel side.
_________________

Hi abhimahna ,

If their is typo , then even after combining condition a and b , we are not getting the answer i.e C.

Abhijit

Sorry, I missed it. It's not a typo. Thanks for bringing this point.

He has written the least value of Range. We know that y is atleast 13 and the lowest integer in the list is 3.

So, range would be atleast 13-3 = 10 >9

Hence, C.
_________________

Dear friends,
If we read the question carefully it means that the range of the 6,3,y,4,5 and (of) x greater than 9. If we combine the 2 statements and take x=4 then y >12, say 13 then the range of the series is 13-3=10 and range of series and x = 10-4= 6 which is less than 9. if we take x=7, then y>21 say 22, then range of series is 22-3=19 and range of 19 and 7 is 12. so E should be the ans.

Am i not right?

The question asks whether the range of {3, 4, 5, 6, x, y} is greater than 9.

It is not clear why are you subtracting x from the range of {3, 4, 5, 6, x, y}. We are not asked to find the difference between the range of {3, 4, 5, 6, x, y} and x.
_________________

Dear Bunuel,
Thanks for your reply. I got it.

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

(1) y > 3x
(2) y > x > 3

take statement1: y>3x if x=3 then y>3*3=9 means y can take value as 10,11,12,13 ..... then range comes as 10-3=7 , or may be 10
Hence this statement alone is not sufficient
take statement2: y > x > 3 , say x=4 and y=5 then range is 6-3=3 ; say x=4 and y=15 then range is 15-3=12
Hence this statement alone is not sufficient

Take both statement together:

from statement 2, it is clear that x can take value 4 or greater
Say x=4
then from statement 1,y>3x means y>12 so Y can take value 13 or greater
say Y=13
then range = highest value - lowest value in the set = 13- 3=10
sufficient

Hence Ans : C
_________________

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-the-range- ... 34897.html
_________________