Set N is populated with all numbers m, where |m|

Question

Set N is populated with all numbers m, where |m| < 5. Which of the following is the closest to the value of the range of Set N?

A. 3
B. 4
C. 5
D. 8
E. 10

tapabrata · Answer

Given |m|<5 which means -5-5 => - m_2 <5 So we have m_1 <5 - m_2 <5 Adding both equations, we get m_1 - m_2 <10 That is the range of the set is less that 10. The closest number to the range is therefore 10 There is another graphical way to look at this Consider the number line below --------------- -5 ---------------- 0 ------------------ 5 ----------- All the number in set N lie between 5 and -5 and the distance between 5 and -5 is 10. Since the smallest number is a little greater that -5 ( -4.99 for e.g.) it will lie to the right of -5 on the number line and since the largest number is a little less than 5 (4.99 for example) will lie to the left of 5. So distance between the two numbers will be less than 10 (Range will be 4.99 - (-4.99) = 9.98 in our example). As you can see, 10 is closest to the range. Answer E

broall · Answer

$N = \{x \in R | -5 <x<5\}$

The range of set $N$ is the difference between the maximum element $a$ and the minimum element $b$ in that set.

We could have $a \approx 5$ and $b \approx -5$ so $a-b \approx 10$

The answer is E

IanStewart · Answer

Test takers do not need to know anything about how to compute statistics for infinite sets (to even define what statistics mean over infinite sets, you need to use limits and other ideas from calculus, and calculus is not tested on the GMAT), so this question is out of GMAT scope.

VarshithaRS · Answer

Won't the answer be 8 (option D)?
In this question it is asked |m|<5 not |m|<=5
I also found this question similar to the above one, where the answer is 8
Bunuel can you please help me resolve this ?
https://gmatclub.com/forum/set-x-is-con ... 32745.html
Thank you

Bunuel · Answer

The value of m is not necessarily an integer, hence |m| < 5 does not imply |m| ≤ 4.

Next, if it were |m| ≤ 5, the range would be 10. However, since |m| is slightly less than 5, the range approaches but does not reach 10. Having said that, you won't need to know this for the GMAT, and you can safely disregard this question altogether.

bumpbot · Answer

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Set N is populated with all numbers m, where |m| < 5. Which of the

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