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Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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25 Jun 2012, 03:03
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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25 Jun 2012, 03:04
SOLUTIONIs 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=61=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=63=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 133=10>9. Sufficient. Answer: C.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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25 Jun 2012, 08:41
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 (133)=10, which is greater than 9 and on increasing x, range will also increase.
Thus, answer is (C),
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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29 Jun 2012, 04:36
SOLUTIONIs 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=61=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=63=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 133=10>9. Sufficient. Answer: C.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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27 Mar 2016, 19:25
Here is a visual that should help.
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Screen Shot 20160327 at 7.23.57 PM.png [ 93.38 KiB  Viewed 7347 times ]
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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03 Nov 2016, 06:49
Bunuel wrote: Is the range of the integers 6, 3, y, 4, 5, and x greater than 9? (1) y > 3x (2) y > x > 3 Diagnostic Test Question: 32 Page: 25 Difficulty: 650 pretty easy for a 700 level question... 1. x can be 1, and y can be 4  so the answer is NO x can be 4, and y can be 13  so the answer is YES. 1 alone is insufficient. A and D are out. 2. y>x>3. x can be 4, y =5  answer is no x can be 4, y can be 20  answer is YES. 2 alone is not sufficient. B is out. 1+2. x>3 y>3x minimum value for x is 4. minimum value for y is 13 yes, the range is greater than 9. sufficient. answer is C.



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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]
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29 May 2018, 16:31
Bunuel wrote: Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?
(1) y > 3x (2) y > x > 3 Statement One Alone: y > 3x Statement one is not sufficient to answer the question. For example, if x = 0, y could be 1 and the range is 6  0 = 6, which is less than 9. However, if x = 10, y could be 31 and the range is 31  3 = 28, which is greater than 9. Statement Two Alone: y > x > 3 Statement two is not sufficient to answer the question. For example, if x = 4, y could be 5 and the range is 6  0 = 6, which is less than 9. However, if x = 14, y could be 15 and the range is 15  3 = 12, which is greater than 9. Statements One and Two Together: From the two statements, we know that x > 3 and y > 3x. So the smallest integer x can be is 4 and the smallest integer y can be is 3(4) + 1 = 13. Thus the smallest range of the integers is 13  3 = 10, which is greater 9. Since 10 is the smallest range, any other range of the integers will be greater than 10 and hence greater than 9. Answer: C
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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