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Set A consists of 40 integers,

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Set A consists of 40 integers, [#permalink] New post 26 Jan 2016, 01:02
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Question Stats:

75% (00:28) correct 25% (00:29) wrong based on 32 sessions
Set A consists of 40 integers, and set B consists of 150 integers. The number of integers that are in both set A and set B is 20.

Quantity A
Quantity B
The total number of integers
that are in set A or set B,
or both
170


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




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Question: 4
Page: 465
Difficulty: hard
[Reveal] Spoiler: OA

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Re: Set A consists of 40 integers, [#permalink] New post 26 Jan 2016, 01:14
Expert's post
Solution

given that the number of integers in set A is 40, the number of integers in set B is 150, and the number of integers that are in both A
and B is 20. You are asked to compare the total number of integers that are in set A or set B, or both, with 170.

The following Venn diagram is a representation of the integers in sets A and B.

Image

Redrawing the Venn diagram so that the numbers are separated into three categories: the integers in A only, the integers in B only, and the integers in both A and B. The revised Venn diagram follows.

Image

We observe that summing the numbers of integers in set A only, set B only, and both A and B yields the total number of integers that are in set A or set B, or both. Therefore, Quantity A is 20+130+20, or 170, and the correct answer is Choice C.


[Reveal] Spoiler: Img
Attachment:
Quant.jpg
Quant.jpg [ 9.67 KiB | Viewed 4537 times ]

Attachment:
Quant.jpg
Quant.jpg [ 7.27 KiB | Viewed 4535 times ]

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Re: Set A consists of 40 integers, [#permalink] New post 04 Oct 2016, 08:39
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Also, the formula for total number of items in sets A and B is Total = A + B - A and B. We are given A, B and A and B in the question, so you can plug in the numbers 40 + 150 - 20 = 170, so the answer is C. This saves the time required for drawing venn diagrams.
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Re: Set A consists of 40 integers, [#permalink] New post 28 Jul 2017, 12:47
Expert's post
sandy wrote:
Set A consists of 40 integers, and set B consists of 150 integers. The number of integers that are in both set A and set B is 20.

Quantity A
Quantity B
The total number of integers
that are in set A or set B,
or both
170



Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of integers, and the two characteristics are:
- in Set A or not in Set A
- in Set B or not in Set B

So, we can set up our diagram as follows:
Image


Since there are 20 integers that are in BOTH set A and set B, we can add that to the diagram...
Image


This allows us to fill in two other boxes...
Image

Notice that we don't have enough information to fill in the last box, which means we also don't know the total number of integers combined.
HOWEVER, we don't need this information.

Quantity A = The total number of integers that are in set A or set B, or both
Notice that the 3 highlighted boxes represent integers that are in set A or set B, or both
Image
So, Quantity A = 20 + 20 + 130 = 170

So, Quantity A = Quantity B
Answer: C

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Re: Set A consists of 40 integers, [#permalink] New post 13 Nov 2018, 19:40
Is there any easy way?
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Re: Set A consists of 40 integers, [#permalink] New post 19 Nov 2018, 16:32
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AE wrote:
Is there any easy way?


Try the double matrix form it should make it a more straightforward approach

Quantity A asks for the highlighted part. Let me know if it is not clear
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Re: Set A consists of 40 integers,   [#permalink] 19 Nov 2018, 16:32
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Set A consists of 40 integers,

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