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1,500 individuals attended a marathon held in Town

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Carcass
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1,500 individuals attended a marathon held in Town [#permalink] New post   22 Aug 2017, 02:25
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1,500 individuals attended a marathon held in Town A. Of those, only y partic­ipated in the marathon. If x of the 1,500 individuals were from Town A, and z ofthe individiuals participated in the marathon but were not from Town A, which of the following represents the number of individuals who did not participate in the marathon and were not from Town A?

(A) 1,500 - x+ 2y
(B) 1,500 - x+ 2z
(C) 1,500 - x - y + z
(D) 1,500- x + y - z
(E) 1,500 - x - z
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Re: 1,500 individuals attended a marathon held in Town [#permalink] New post   06 May 2018, 16:42
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Carcass wrote:


1,500 individuals attended a marathon held in Town A. Of those, only y partic­ipated in the marathon. If x of the 1,500 individuals were from Town A, and z ofthe individiuals participated in the marathon but were not from Town A, which of the following represents the number of individuals who did not participate in the marathon and were not from Town A?

(A) 1,500 - x+ 2y
(B) 1,500 - x+ 2z
(C) 1,500 - x - y + z
(D) 1,500- x + y - z
(E) 1,500 - x - z



We can create the equation:

Total = from town A + participated in marathon - both + neither

From town A = x

Participated = y

Since z of the individuals participated but were not from town A, then (y - z) individuals participated and were from town A. Thus:

1500 = x + y - (y - z) + neither

1500 = x + y - y + z + neither

1500 - x - z = neither

Answer: E
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Re: 1,500 individuals attended a marathon held in Town [#permalink] New post   16 Oct 2017, 01:13
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We can proceed by taking values and check the choices: 1500 people at the marathon, 1200 from Town A, 800 marathon participants, 200 people not from Town A in the marathon. With these choices, there are 100 people not from Town A who are not participating in the marathon.

Thus we have:
y = marathon participants = 800
x = Town A population = 1200
z = Not Town A marathon participants = 200.
Answer = Not Town A Not marathon participants = 100.

All we have to do is run through the choices.

A) 1500 - x + 2y = 1500 - 1200 + 2*800 = 1900 X
B) 1500 - x + 2z = 1500 - 1200 + 2*200 = 700 X
C) 1500 - x - y + z = 1500 - 1200 - 800 + 200 = -300 X
D) 1500 - x + y - z = 1500 - 1200 + 800 - 200 = 900 X
E) 1500 - x - z = 1500 - 1200 - 200 = 100

E is the correct answer.

To see this from a set theory perspective, the people we are looking for are not from Town A and they are not marathon runners. That population is the same as the entire population minus everyone from Town A, minus everyone not from town A who is in the marathon. Translating this into the quantities we know, this is 1500 - x - z.
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1,500 individuals attended a marathon held in Town [#permalink] New post   14 Feb 2021, 04:02
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Total = \(1500\)
Participated (AUB) = \(y\)
Not Participated = \(1500 - y\)

Town A = \(x\)
Only Town B = \(z\)

Let the Intersection (Both A and B) be \(i\)
Therefore, Town B = \(z + i\)

i.e. Town A = \(x\)
Town B = \(z - i\)
Only Town A = \(x - i\)
Only Town B = \(z\)

AUB = \(y\) = only Town A + only Town B + both Town A and B
\(y = x - i + z + i = x + z\)

So, Not participated = \(1500 - y = 1500 - (x + z) = 1500 - x - z\)

Hence, option E
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1,500 individuals attended a marathon held in Town [#permalink] New post   30 Dec 2023, 19:35
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Making a chart helps for me. It looks like
[table1b=]
P N
L x
F z ?
y[/table1b]


Where P = participated, N = didn't participate, L = local, F = foreign. x, y, and z are give, and we're looking for ?

We know P+N = 1500, and L+F = 1500.

Given our info, we can see the L+F=1500 combo is the one that has the most information we need. Looking at our chart, we see L=x, and F=z + ?

So L+F=1500 ===> x + z + ? = 1500 ==> ? = 1500 - x - z
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1,500 individuals attended a marathon held in Town [#permalink]
30 Dec 2023, 19:35
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