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15 Sep 2009, 08:24
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C
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25%
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Question Stats:
76% (02:07) correct
24%
(02:12)
wrong
based on 492
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If Set Z has a median of 19, what is the range of Set Z?
(1) Z = {18, 28, 11, x, 15, y}
(2) The average (arithmetic mean) of Set Z is 20.
(1) Z = {18, 28, 11, x, 15, y}
(2) The average (arithmetic mean) of Set Z is 20.
Hi everyone,
I saw this question in the practice problems of Kaplan GMAT book, but I am not sure if the answer they gave is right....so any help in this regard shall be highly appreciated. The question is as follows:
If set Z has a median of 19, what is the range of set Z?
(1) Z = { 18, 28, 11, x, 15, y}
(2) The average (arithmetic mean) of the members of set Z is 20.
The book gives the answer as C (BOTH statements TOGETHER are sufficient), but I think the answer is E(BOTH are not sufficient)
The reasoning in the book is as follows:
Statements (1) and (2) together: From statement (1), we know the set has 6 elements and that either x or y must be 20. From (2), we know the average is 20. For a set of 6 elements with an average of 20, the sum of the numbers must be 6x20 = 120.
So, it must be the case that 11 + 15 + 18 + 28 + x + y = 120, or x + y = 48. Since we know that either x or y must be equal to 20, let's say that x = 20. So, we have 20 + y = 48 or y=28. Thus the set is {11, 15, 18, 20, 28, 28}. The range must be 28-17 = 11, so the statements together are sufficient. (C) is correct.
Now, my question is.....the answer takes the set to be {11, 15, 18, 20, 28, 28} and comes to the conclusion C. As per the definition of a set, there should not be any repetitive elements. So the set cannot be {11, 15, 18, 20, 28, 28} with the element 28 being repeated. So the set can be {11, 15, 18, 20, 28}, in which case we cannot determine the value of y. So I am not sure if this question is right.
Please let me know if my thought process is wrong....and what should be the right answer?
Thank you for your time. I shall look forward to hearing from all of you.
regards,
Rahul
I saw this question in the practice problems of Kaplan GMAT book, but I am not sure if the answer they gave is right....so any help in this regard shall be highly appreciated. The question is as follows:
If set Z has a median of 19, what is the range of set Z?
(1) Z = { 18, 28, 11, x, 15, y}
(2) The average (arithmetic mean) of the members of set Z is 20.
The book gives the answer as C (BOTH statements TOGETHER are sufficient), but I think the answer is E(BOTH are not sufficient)
The reasoning in the book is as follows:
Statements (1) and (2) together: From statement (1), we know the set has 6 elements and that either x or y must be 20. From (2), we know the average is 20. For a set of 6 elements with an average of 20, the sum of the numbers must be 6x20 = 120.
So, it must be the case that 11 + 15 + 18 + 28 + x + y = 120, or x + y = 48. Since we know that either x or y must be equal to 20, let's say that x = 20. So, we have 20 + y = 48 or y=28. Thus the set is {11, 15, 18, 20, 28, 28}. The range must be 28-17 = 11, so the statements together are sufficient. (C) is correct.
Now, my question is.....the answer takes the set to be {11, 15, 18, 20, 28, 28} and comes to the conclusion C. As per the definition of a set, there should not be any repetitive elements. So the set cannot be {11, 15, 18, 20, 28, 28} with the element 28 being repeated. So the set can be {11, 15, 18, 20, 28}, in which case we cannot determine the value of y. So I am not sure if this question is right.
Please let me know if my thought process is wrong....and what should be the right answer?
Thank you for your time. I shall look forward to hearing from all of you.
regards,
Rahul
05 Feb 2014, 15:28
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goodyear2013
Dear goodyear2013
I'm happy to help with this.
Here's an article about mean & median:
https://magoosh.com/gmat/2012/common-gma ... tatistics/
Here's an article about Data Sufficiency strategies:
https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/
At the outset, we know nothing about Set Z but the median. As usual, we have no way to answer the questions without the statements.
Statement #1: Z = {18, 28, 11, x, 15, y}
We have three numbers less than 19, so they only way we can have a median of 19 is to have one of the variables x = 20, and the other equal something greater than or equal to 20. If x = 20 and y = 3000, then the set would have a median of 19 and a very large range, and because we could pick whatever we want for the value of y, we have no way to determine an exact value of the range. This statement, along and by itself, is not sufficient.
Statement #2: The average (arithmetic mean) of Set Z is 20.
The tricky thing about this statement is that we need to ignore statement #1 completely and just focus on this. Right now, we know median = 19, mean = 20, and absolutely nothing else about the situation. We don't even know how many members are in the set --- 6, or 10, or 500. We know nothing, so we certainly don't know the range. This statement, along and by itself, is not sufficient.
Combined Statements
From the first statement, we know x = 20 and y > 20. If the six numbers have an average of 20, then they have a sum of 120.
18 + 28 + 11 + 20 + 15 + y = 120
We could solve this for y, but we won't be daft enough actually to perform that calculation. This is GMAT Data Sufficiency! We don't actually need to solve for y. All we need to do is determine that y has a unique value, and we are able to create a simple equation for it, then we could solve. At that point, we would know all six numbers in the set, and we would know the range. The combined statements are sufficient.
Answer = (C)
BTW, y = 28, but that's irrelevant for answering the question.
Does all this make sense?
Mike
General Discussion
15 Sep 2009, 10:06
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The GMAT will never try to trick you about technicalities of the definition of a set. It is exceptionally rare for a GMAT question to even mention a 'set' at all; most stats questions are about 'lists', or provide real world data, so that it's clear that repetition of elements is permitted. See Questions 133, 134 and 136 from the DS section of OG12 for typical examples of GMAT-style stats questions. Among all of the 452 questions in the Official Guide, only one (Q67 in the PS section) simply mentions a 'set', and in that question, the sets are given to you, so it doesn't matter if you know whether repetition is permitted in a set. Note that Q199 mentions 'data sets' (though again, the sets are provided, and clearly repetition is allowed), and Q9 and Q31 in the Diagnostic Test at the beginning of the book mention a 'set of performance scores' and a 'set of measurements', respectively, each phrase just another way of saying 'data set'. Again, repetition of elements is clearly allowed in Q31 (it's the only way Statement 2 can be true), and isn't relevant to consider in Q9.
In general, on the GMAT, you're extremely unlikely to see a question even mention a 'set' without some sort of qualification, and in general you should assume that repetition of elements *is* allowed in sets on the GMAT, since in pretty much every GMAT stats question, the question will describe a list or real world situation in which repetition of elements is permitted. The question quoted above from the Kaplan book is not worded in the way a real GMAT question would be; a real GMAT question would call the set 'a set of test scores' or something similar, to make clear that they don't intend the definition of 'set' used in mathematical set theory.
In general, on the GMAT, you're extremely unlikely to see a question even mention a 'set' without some sort of qualification, and in general you should assume that repetition of elements *is* allowed in sets on the GMAT, since in pretty much every GMAT stats question, the question will describe a list or real world situation in which repetition of elements is permitted. The question quoted above from the Kaplan book is not worded in the way a real GMAT question would be; a real GMAT question would call the set 'a set of test scores' or something similar, to make clear that they don't intend the definition of 'set' used in mathematical set theory.
