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Is the range of the integers 6, 3, y, 4, 5, and x greater
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25 Jun 2012, 03:03
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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
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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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
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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
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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
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27 Mar 2016, 19:25
Here is a visual that should help.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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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
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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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12 Sep 2018, 10:35
In the solution of these questions it is not asked to take minimum value and x and y can take any numbers so why we have solved this by taking minimum values



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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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16 Oct 2018, 00:05
arpitalewe wrote: In the solution of these questions it is not asked to take minimum value and x and y can take any numbers so why we have solved this by taking minimum values Hi arpitalewe, Welcome to the GMAT Club! So the logic behind trying to take the minimum permissible values for x and y is: we want to see if the minimum permissible value of y is such that range of the given set is greater than 9. If for minimum value this condition holds then for all other values it will hold as well.Hope this solves your doubt. Let me know if you need further clarification or if the above solutions make sense with the above logic. Regards, Gladi
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Is the range of the integers 6, 3, y, 4, 5, and x greater
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16 Oct 2018, 00:28
Statement 1) y > 3x if x = 1 then y must be at least 4 but we cannot tell any further. 61 = 5 > 9 no. If x = 5 y must be at least 16. 16  3 = 13 > 9 yes Insufficient. Statement 2) y > x > 3 we can try the x = 4 and y = 5 we get an answer 63 = 3 > 9 no. Try x = 4 y = 16, 163 = 13 > 9 yes. Insufficient. Now combine (1 and 2) If x = 4 then y at least 13 (given that we took the minimum possible value for x) 13  3 = 10 > 9 Try x = 10 then y at least 31 31  3 = 28 > 9 Sufficient. Answer choice C arpitalewe check the above solution it might help. Also as Gladiator59 explained that the logic is to test if the minimum value satisfies the condition (range > 9) then the maximum will satisfy it too since y > 3x Posted from my mobile device



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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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18 Jul 2019, 19:17
Hi everyone,
This thread is very helpful and a good example of something that is currently holding me back a bit. I understand the process to get to the answer, I can get to the answer by myself but in around 3.15 minutes and not under 2 minutes. There are many problems like this one where I get to the solution but it takes me a lot of time to gather my thoughts. Any thoughts on how I can improve my thinking process?
Kind regards,
Majinn



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Is the range of the integers 6, 3, y, 4, 5, and x greater
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29 Nov 2019, 20:27
Bunuel wrote: 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=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. Hi Bunuel  Between C and E , I chose E unfortunately Just wondering why does this not work ? S1 : y > 3x S2 : y > x > 3. Adding S1 + S2 2y > 4x > 3 dividing by 2 y > 2x > (3/2) Hence i said per above ....okay x = 2 and y = 6 satisfies above inequality .. if x = 2 and y can be =6  the range is below 9 if x = 2 and y can be = 600  the range is above 9 Hence i chose E



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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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30 Nov 2019, 00:44
jabhatta@umail.iu.edu wrote: Bunuel wrote: 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=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. Hi Bunuel  Between C and E , I chose E unfortunately Just wondering why does this not work ? S1 : y > 3x S2 : y > x > 3. Adding S1 + S2 2y > 4x > 3 dividing by 2 y > 2x > (3/2) Hence i said per above ....okay x = 2 and y = 6 satisfies above inequality .. if x = 2 and y can be =6  the range is below 9 if x = 2 and y can be = 600  the range is above 9 Hence i chose E Adding inequalities in this case gives you broader ranges. How can x be 2, if we are given that x > 3?
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Is the range of the integers 6, 3, y, 4, 5, and x greater
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30 Nov 2019, 11:27
Hi Bunuel Just wondering where my understanding about the math fundamentals is wrong here ...I have seen answer solutions where inequalities that are facing the same way are added Why doesnt it work in this case ? So if x and y are both positive equation 1) x > 3y equation 2) x > y 1 + 2 2x > 4 y or x > 2y x > 2y does not make sense when equation 1 is saying x > 3y Why doesnt this tactic of adding equations in this case work out



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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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02 Dec 2019, 08:38
Bunuel wrote: 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=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. Hello Bunuel, In no explaination i see anyone considering x or y to be negative. In quesion it is mentioned they are integers, so will be right to consider negative values? Am i missing somethinghere? Also i assumed all the integers would be distinct, but unless stated , we can consider that integers are repeating, something i missed. Thank you in advance for answering



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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
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02 Dec 2019, 08:49
Rishbha wrote: Bunuel wrote: 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=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. Hello Bunuel, In no explaination i see anyone considering x or y to be negative. In quesion it is mentioned they are integers, so will be right to consider negative values? Am i missing somethinghere? Also i assumed all the integers would be distinct, but unless stated , we can consider that integers are repeating, something i missed. Thank you in advance for answering (2) says that y > x > 3, so neither of them can be negative.
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