Explanation

The range of 200 measurements = 17 cms

If 49.5 is the lowest measurement in the set

The highest measurement in the set of measurement = 49.5 + range = 49.5 + 17 = 66.5 cms

If 49.5 is the highest measurement in the set

The lowest measurement in the set of measurement = 49.5 - range = 49.5 - 17 = 32.5 cms.

In the second case we have two values that lie between 32.5 cms and 49.5 cms.

Thus option is C and D is correct.
_________________

As the range between the measurement is given as 17, it means the highest and lowest measurement has difference between 17.
As it a could be question, we can take all possible answer into consideration, if the difference between the number is less than 17.
so the answer is C and D. since 49.5- C < 49.5 - D < 17.

A at Quality Control Analyst Collected 200 Measurements of length. At The the Range of at The 200 Measurements IS 17 centimeters, and One of at The Measurements IS 49.5 centimeters. Which of at The following could BE Another One of at The 200 Measurements, in centimeters?

Indicate All SUCH Measurements.

A 31.0

B 32.0

C 33.0

D 34.0

What's the answer?

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Regards
_________________

thanks

This question infuriates me. Unless I'm mistaken, it is terribly worded. When I read "One of at The Measurements is 49.5 centimeters" I assumed they were talking about any one of the 200 measurements. Why would I presume they were giving me the upper or lower extent of the range?

The question is perfectly worded. This is a question made to test your reasoning about a range.

Of course, you can choose whatever number among the 200. You in the end will solve the question for sure but NOT in one minute, maybe in one hour.

However, the stem gave you the range for one reason. It is the difference between the upper value and the lowest value by definition.

So, if you wanna find the other number inside the range you have to reason in terms of minimum and maximum: the range.

Regards
_________________

My point is that there is no reason I would assume that the 49.5 cm measurement mentioned is either the minimum or the maximum of this set. Therefore, if it is just one of 200 numbers in a data set, it wouldn't tell us anything. If the question had been worded, "49.5 is one of the numbers used to calculate this range" or something to that effect, it would make perfect sense to me. But as it stands, the wording seems misleading. Do you understand what I'm getting at? Thanks for your reply.

Yeah, I agree with you. A number of times, I had to verbally chastise the GRE test writers in quite a few emails. More than half the time, I successfully persuaded them to change around certain questions. This is why A) I should go to law school, and B) maybe I should take a part-time job working for ETS.

49.5 + 17 and 49.5 - 17
66.5 and 32.5

so any value between 32.5 and 66.5 would be the answer
_________________

Two cases emerge here:
1. 49.5 is the greatest value in the set of measurements; this means that 32.5 is the smallest measurement.
2. 49.5 is the smallest value in the set of measurements; this means that 66.5 is the greatest measurement.

Hence, all values between those two work. That means C and D are correct.

Just for some more proof that we can't be outside that range:
1.
If 49.5 is anywhere else in the ordered set, say in the second position with 48 in the position before it, for the range to be 17, the largest number would be 65.
That means we would have a range from 48 to 65. Both of those value are within the extremes we calculated before.

2.
In another case, if it's the second biggest item with something like 64.5 above it, that means the smallest number would be 47.5.
That means we would have a range from 47.5 to 64.5. Both of those value are within the extremes we calculated before.

3.
Let's say 49.5 is the second biggest item with 50 above it. That means that, again, as long as we have the same range value, the smallest number would be 33.
That means we would have a range from 33 to 50. Both of those value are within the extremes we calculated before.

4.
Let's say it's somewhere in the middle, around position 102 or something like that. Then, the range could be anywhere "around" it, like 40 to 57 or 34 to 51. Those values are still within the bounds we calculated previously.

Cheers!