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The range of set A is 24 and the range of set B is 20. What is the sma

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The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 22 Oct 2018, 23:43
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[Math Revolution GMAT math practice question]

The range of set A is 24 and the range of set B is 20. What is the smallest possible range of sets A and B, combined?

A. 20
B. 24
C. 40
D. 44
E. 48

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Re: The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 23 Oct 2018, 00:53
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set A is 24 and the range of set B is 20. What is the smallest possible range of sets A and B, combined?

A. 20
B. 24
C. 40
D. 44
E. 48


Let A = {1,2.......24,25}

The range of set A is 24

Let B = {1,2.......21}

the range of set B is 20

the smallest possible range of sets A and B, combined is the overlap of A & B(Here we need to minimize the range)

A & B = {1,2.......24,25}

Hence B
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The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 23 Oct 2018, 01:30
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set A is 24 and the range of set B is 20. What is the smallest possible range of sets A and B, combined?

A. 20
B. 24
C. 40
D. 44
E. 48


The smallest possible range for 2 sets is when the lowest value in both the sets is the same.

Also, the minimum range for both the sets combined when the lowest value in
both the sets is the same is at least equal to the range of more widely spread set - set A.

Therefore, the smallest possible range of the sets A and B is 24(Option B)
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Re: The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 23 Oct 2018, 02:08
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set A is 24 and the range of set B is 20. What is the smallest possible range of sets A and B, combined?

A. 20
B. 24
C. 40
D. 44
E. 48


Lets assume SET A and SET B
SET A
elements 4 and 28 (gives range as 28-4=24)
SET B
elements 4 and 24 (gives range as 24-4=20)

Since we have to find the SMALLEST POSSIBLE range so we are trying to have a subset.

There combing A and B ..
We need to have a minimum of 4 and 28 that is a range of 24


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Re: The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 23 Oct 2018, 05:48
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set A is 24 and the range of set B is 20. What is the smallest possible range of sets A and B, combined?

A. 20
B. 24
C. 40
D. 44
E. 48


If the range of set A is 24, and we add more values (from set B) to set A, then the range of the resulting set must be greater than or equal to 24 (that is, the range of a set cannot get smaller upon adding MORE numbers to that set).
For this reason, we can ELIMINATE answer choice A.

From here, if we can show that it's possible for sets A and B combined to have a range of 24, then the correct answer will be B, since 24 is the smallest possible answer choice (once we have eliminated answer choice A).
Well, if set A = {0, 24} and set B = {1, 21}, then sets A and B combined = {0, 1, 21, 24}, which has range 24
DONE!

Answer: B

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Re: The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 25 Oct 2018, 00:21
=>

Note that the range of the combined set can’t be less than the maximum of the ranges of the two sets.

The maximum of the ranges of the two sets is \(24\). So, the range of the combined set must be greater than or equal to \(24\).
For example, if \(A = {0, 24}\) and \(B = { 0, 20 }\), the combined set \({ 0, 20, 24 }\), has range \(24\).
\(24\) is the smallest possible range of the set \(A ⋃ B.\)

Therefore, B is the answer.
Answer: B
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Re: The range of set A is 24 and the range of set B is 20. What is the sma  [#permalink]

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New post 25 Oct 2018, 08:32
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The range of set A is 24 and the range of set B is 20. What is the smallest possible range of sets A and B, combined?

A. 20
B. 24
C. 40
D. 44
E. 48


The smallest range is when all the numbers in set B are between the smallest number and the largest number of set A, inclusive. For example, if the smallest number of set A is 0, and the largest number of set A is 24, and the smallest number of set B is 2, and the largest number of set B is 22, we see that the range of sets A and B combined is still 24 - 0 = 24.

Answer: B
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Re: The range of set A is 24 and the range of set B is 20. What is the sma &nbs [#permalink] 25 Oct 2018, 08:32
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