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The range of set X is 9 and the range of set Y is 18. Which of the fol

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Math Revolution GMAT Instructor
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The range of set X is 9 and the range of set Y is 18. Which of the fol  [#permalink]

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New post 14 Nov 2018, 00:32
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[Math Revolution GMAT math practice question]

The range of set \(X\) is \(9\) and the range of set \(Y\) is \(18\). Which of the following cannot be the range of the union of sets \(X\) and \(Y\)?

\(A. 9\)
\(B. 18\)
\(C. 27\)
\(D. 36\)
\(E. 45\)

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Re: The range of set X is 9 and the range of set Y is 18. Which of the fol  [#permalink]

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New post 14 Nov 2018, 00:44
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set \(X\) is \(9\) and the range of set \(Y\) is \(18\). Which of the following cannot be the range of the union of sets \(X\) and \(Y\)?

\(A. 9\)
\(B. 18\)
\(C. 27\)
\(D. 36\)
\(E. 45\)



Good question!!Here is my approach.

The minimum range will be the max of range of the two sets.

The max range is 18 of the sets so minimum range of two sets is 18.

Now notice the options all are greater than equal to 18 except option A.Bingo ..that's are option.

Hence,OA is A
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Re: The range of set X is 9 and the range of set Y is 18. Which of the fol  [#permalink]

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New post 16 Nov 2018, 02:19
=>

The range of a union is greater than or equal to the maximum of the ranges of the two sets. Thus, the range of the union of \(X\) and \(Y\) is greater than or equal to \(18\).

Therefore, the answer is A.
Answer: A
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Re: The range of set X is 9 and the range of set Y is 18. Which of the fol  [#permalink]

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New post 21 Jan 2019, 08:07
MathRevolution wrote:
=>

The range of a union is greater than or equal to the maximum of the ranges of the two sets. Thus, the range of the union of \(X\) and \(Y\) is greater than or equal to \(18\).

Therefore, the answer is A.
Answer: A


Can you please explain this with an example?
I did not understand the concept.
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Re: The range of set X is 9 and the range of set Y is 18. Which of the fol  [#permalink]

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New post 21 Jan 2019, 08:22
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set \(X\) is \(9\) and the range of set \(Y\) is \(18\). Which of the following cannot be the range of the union of sets \(X\) and \(Y\)?

\(A. 9\)
\(B. 18\)
\(C. 27\)
\(D. 36\)
\(E. 45\)


Range is Highest term - Lowest term.

Now i considered some cases for both set X and Y

Set X [1,10] & Set Y [10,28]
Union will be [1,10,28] => Range will be 27

Set X [1,10] & Set Y[1,19]
Union will be [1,10,19] => Range will be 18

SO from the above examples, i realized it can never be less than 18

IMO A
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Re: The range of set X is 9 and the range of set Y is 18. Which of the fol  [#permalink]

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New post 26 Jan 2019, 02:00
Without the mathematical notation.

Let's say set x has the numbers 1 through 10 (10-1=9)
Let's say set y has the numbers 100 through 118 (118-100=18)

The union of two sets is combining the two sets and lets call it set u. Set u (118-1=117).
This shows that the range of the union of the two sets is as big as we want it to be. Thus, the difficulty is in making it small as explained in above posts.

Just for completeness, let's say Set X is 1 through 9 and Set Y is -100 through -118 [-100-(-118)=-100+118=18]
Set u is -118 through to 9 [9-(-118)=127]
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Re: The range of set X is 9 and the range of set Y is 18. Which of the fol   [#permalink] 26 Jan 2019, 02:00
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