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# What is the range of the 5 numbers x, y, 10, 15, and 20?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the range of the 5 numbers x, y, 10, 15, and 20?  [#permalink]

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11 May 2018, 00:26
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Difficulty:

15% (low)

Question Stats:

81% (01:00) correct 19% (00:53) wrong based on 56 sessions

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[GMAT math practice question]

What is the range of the 5 numbers x, y, 10, 15, and 20?

1) x and y lie between 10 and 20, inclusive.
2) The average (arithmetic mean) of the five numbers is 15

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 27 Feb 2018 Posts: 36 Location: India WE: Engineering (Real Estate) Re: What is the range of the 5 numbers x, y, 10, 15, and 20? [#permalink] ### Show Tags 11 May 2018, 01:23 MathRevolution wrote: [GMAT math practice question] What is the range of the 5 numbers x, y, 10, 15, and 20? 1) x and y lie between 10 and 20, inclusive. 2) The average (arithmetic mean) of the five numbers is 15 Can anyone explain why answer is A? If x and y lie between 10 and 20 inclusive i.e. 10<=x & y<=20. It can be anything 10,11,12. ok i get it now, dumb me. if the numbers lie between 10 and 20, then the lowest possible value 10 is already there so irrespective of x and y the answer will always be 10. Thanks Math Revolution Team Director Joined: 21 May 2013 Posts: 659 Re: What is the range of the 5 numbers x, y, 10, 15, and 20? [#permalink] ### Show Tags 11 May 2018, 02:36 praveenkuragodi wrote: MathRevolution wrote: [GMAT math practice question] What is the range of the 5 numbers x, y, 10, 15, and 20? 1) x and y lie between 10 and 20, inclusive. 2) The average (arithmetic mean) of the five numbers is 15 Can anyone explain why answer is A? If x and y lie between 10 and 20 inclusive i.e. 10<=x & y<=20. It can be anything 10,11,12. ok i get it now, dumb me. if the numbers lie between 10 and 20, then the lowest possible value 10 is already there so irrespective of x and y the answer will always be 10. Thanks Math Revolution Team Let me explain why the answer is A Statement 1:x and y lie between 10 and 20, inclusive. This means minimum and maximum value of x and y can be between 10 and 20 inclusive. Therefore range will have to be 10. Sufficient Statement 2: The average (arithmetic mean) of the five numbers is 15[/quote]. Total of 5 numbers is 75. Therefore x+y=30. Now, x and y can be 10, 20 or 9, 21. So range is not only 10 but can take other values Answer A Manager Joined: 28 Nov 2017 Posts: 145 Location: Uzbekistan Re: What is the range of the 5 numbers x, y, 10, 15, and 20? [#permalink] ### Show Tags 11 May 2018, 02:57 1 MathRevolution wrote: [GMAT math practice question] What is the range of the 5 numbers x, y, 10, 15, and 20? 1) x and y lie between 10 and 20, inclusive. 2) The average (arithmetic mean) of the five numbers is 15 (1) If $$x$$ and $$y$$ lie between $$10$$ and $$20$$, inclusive, then Maximum element $$= 20$$ Minimum element $$= 10$$, So, range is $$20-10=10$$. Hence, sufficient. (2) $$x+y+10+15+20=5*15$$ $$x+y=30$$ If $$x=1$$, $$y=29$$, then $$range=29-1=28$$ If $$x=2$$, $$y=28$$, then $$range=28-2=26$$. Hence, not sufficient. Answer: A _________________ Kindest Regards! Tulkin. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6826 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the range of the 5 numbers x, y, 10, 15, and 20? [#permalink] ### Show Tags 13 May 2018, 17:41 => 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. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2): Since we have 10 ≤ x ≤ 20 and 10 ≤ y ≤ 20 by condition 1), the maximum of the numbers is 20 and the minimum of the numbers is 10. The range is the difference between the maximum and the minimum, which is 20 – 10 = 10. Both conditions together are sufficient. Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4 (A) of the VA (Variable Approach) method tells us that we should also check answers A and B. Condition 1) Since 10 ≤ x ≤ 20 and 10 ≤ y ≤ 20 by condition 1), the maximum of the numbers is 20 and the minimum of the numbers is 10. The range is the difference between the maximum and the minimum, which is 20 – 10 = 10. Thus, condition 1) is sufficient. Condition 2) If x = 10 and y = 20, the range is 10. If x = 9 and y = 21, the range is 12. Since we don’t have a unique solution, condition 2) is not sufficient. Therefore, A is the answer. Answer: A Normally, in problems which require 2 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. _________________ 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$149 for 3 month Online Course"
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Re: What is the range of the 5 numbers x, y, 10, 15, and 20?  [#permalink]

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14 May 2018, 15:59
MathRevolution wrote:
[GMAT math practice question]

What is the range of the 5 numbers x, y, 10, 15, and 20?

1) x and y lie between 10 and 20, inclusive.
2) The average (arithmetic mean) of the five numbers is 15

We need to determine the range of x, y, 10, 15, and 20. Recall that range of a set = the greatest value in the set - the least value in the set.

Statement One Alone:

x and y lie between 10 and 20, inclusive.

Since the smallest value of x and y can be are 10, and the largest they can be are 20, and since we already see that the least number in the list is 10 and the greatest is 20, the range is 10. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The average (arithmetic mean) of the five numbers is 15

Although we know that the average of the numbers is 15, its possible to have a number less than 10 or greater than 20. Thus, we cannot determine the range.

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Re: What is the range of the 5 numbers x, y, 10, 15, and 20? &nbs [#permalink] 14 May 2018, 15:59
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