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# What is the range of the 6 numbers x, y, 8, 10, 14, and 16?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the range of the 6 numbers x, y, 8, 10, 14, and 16?  [#permalink]

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14 Dec 2017, 02:06
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Difficulty:

35% (medium)

Question Stats:

69% (01:25) correct 31% (01:44) wrong based on 53 sessions

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[GMAT math practice question]

What is the range of the $$6$$ numbers $$x, y, 8, 10, 14$$, and $$16$$?

1) Their average (arithmetic mean) is $$12$$
2) $$8<x<y<16$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 17 Oct 2016 Posts: 317 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16? [#permalink] ### Show Tags 14 Dec 2017, 02:20 B From st1 we can infer that x and y can be of any value but x+y=24. If x is 2 and y is 22 then the range is 16-2=14. If x is 12 and y is 12 then the range is 16-8=8. Hence insufficient. From st2 we can conclude that the least number is 8 and the highest number is 16. Hence range is 16-8=8. Sufficient Posted from my mobile device _________________ Help with kudos if u found the post useful. Thanks Math Expert Joined: 02 Sep 2009 Posts: 56244 Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16? [#permalink] ### Show Tags 14 Dec 2017, 03:49 MathRevolution wrote: [GMAT math practice question] What is the range of the $$6$$ numbers $$x, y, 8, 10, 14$$, and $$16$$? 1) Their average (arithmetic mean) is $$12$$ 2) $$8<x<y<16$$ Similar question: https://gmatclub.com/forum/there-are-6- ... 30921.html _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7588 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16? [#permalink] ### Show Tags 18 Dec 2017, 00:19 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer, and so we should consider conditions 1) & 2) together first. Conditions 1) & 2): Condition 1) states that $$\frac{( x + y )}{2} = 12$$ or $$x +y = 24$$. Condition 2) tells us that $$8 < x < y < 16$$. So, x can be no smaller than $$8$$, and y can be no larger than $$16$$. Therefore, the range of $$x,y,8,10,14,16 is 8 = 16 – 8$$. Since this is an inequality question (one of the key question areas), we should also consider choices A and B by CMT 4(A). Condition 1) If $$x = 7$$ and $$y = 17$$, the range is $$17 – 7 = 10$$. If $$x = 9$$ and $$y = 15$$, the range is $$16 – 8 = 8$$. As we do not have a unique answer, condition 1) is not sufficient. Condition 2) Since $$8 < x < y < 16$$, the maximum value in the list is $$16$$, and the minimum value in the list is $$8$$. Therefore, the range is $$8 = 16 – 8$$. The answer is A. Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16?   [#permalink] 18 Dec 2017, 00:19
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