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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
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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, 01:06
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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) $$8<x<y<16$$
[Reveal] Spoiler: OA

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Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16? [#permalink]

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14 Dec 2017, 01:20
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

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Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16? [#permalink]

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14 Dec 2017, 02:49
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
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Kudos [?]: 139308 [0], given: 12783

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4676

Kudos [?]: 3309 [0], given: 0

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Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16? [#permalink]

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17 Dec 2017, 23:19
=>

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 $$8 = 16 – 8$$.

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.

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Re: What is the range of the 6 numbers x, y, 8, 10, 14, and 16?   [#permalink] 17 Dec 2017, 23:19
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