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A safari is held twice in a day either in the morning or in the evenin

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A safari is held twice in a day either in the morning or in the evenin  [#permalink]

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New post 10 Jul 2017, 04:28
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Question Stats:

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A safari is held twice in a day either in the morning or in the evening. A person is allowed to participate in the safari in both the timings. A total of 108 people participate in the safari. The number of men and women in the safari are in the ratio 5 : 4. The total number of men who participate in the safari in the morning is 50 percent of the total number of men who participate in the safari. If every person participated in the safari at least once, what is the number of people who participate in the safari both in the morning and in the evening?


(1) The number of men who participate in the safari only in the morning is 80 percent of the women who participate in the safari only in the morning. Also, the number of men who participate in the safari only in the evening is double the number of women who participate in the safari only in the evening.

(2) The number of women who participate in the safari only in the evening is 60 percent of the girls who participate in the safari only in the morning.

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A safari is held twice in a day either in the morning or in the evenin  [#permalink]

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New post 10 Jul 2017, 09:52
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Let the men participating in the safari only in the morning be x, and only in the evening be y.
Let the women participating in the safari only in the morning be a, and only in the evening be b.

From question stem,
Total guests : 108
Since they are in ratio 5:4, Men are 60 and Women are 48.
Men(morning) = 1/2*Men(Total)
Therefore, Men(morning) = x + Both = 30
x + y + Both = 60, so y = 30.
a + b + Both = 48

1. The number of men who participate in the safari only in the morning is 80 percent of the women who participate in the safari only in the morning. Also, the number of men who participate in the safari only in the evening is double the number of women who participate in the safari only in the evening.

\(x = \frac{4a}{5}\)
\(y = 2b\) -> \(b = 15\)
This information is not enough to determine the total number of people who participated in both the morning and evening safari(Insufficient)

2. The number of women who participate in the safari only in the evening is 60 percent of the girls who participate in the safari only in the morning.

\(b = \frac{3a}{5}\)
This information is not enough to determine the total number of people who participated in both the morning and evening safari(Insufficient)

Combining the information from both the statements,

a = 25,b=15
\(x = \frac{4a}{5} = 20\) | \(y = \frac{6a}{5} = 30\)

Both(men) = 10
Both(women) = 8
From this information, we can find out the total number of people who participated in both safaris are 18(Option C)
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Re: A safari is held twice in a day either in the morning or in the evenin  [#permalink]

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New post 10 Jul 2017, 15:05
pushpitkc wrote:
Let the men participating in the safari only in the morning be x, and only in the evening be y.
Let the women participating in the safari only in the morning be a, and only in the evening be b.

From question stem,
Total guests : 108
Since they are in ratio 5:4, Men are 60 and Women are 48.
Men(morning) = 1/2*Men(Total)
Therefore, Men(morning) = x + Both = 30
x + y + Both = 60, so y = 30.
a + b + Both = 48

1. The number of men who participate in the safari only in the morning is 80 percent of the women who participate in the safari only in the morning.
Also, the number of men who participate in the safari only in the evening is double the number of women who participate in the safari only in the evening.
x = 4a/5
y = 2b => b = 15
This information is not enough to determine the total number of people who participated in both the morning and evening safari(Insufficient)

2. The number of women who participate in the safari only in the evening is 60 percent of the girls who participate in the safari only in the morning.
b = 3a/5
This information is not enough to determine the total number of people who participated in both the morning and evening safari(Insufficient)

Combining the information from both the statements,
a = 25,b=15
x=4a/5=20
y=6a/5=30
Both(men) = 10
Both(women) = 8
From this information, we can find out the total number of people who participated in both safari's are 18(Option C)


How did you arrive at a = 25 and b = 15?
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A safari is held twice in a day either in the morning or in the evenin  [#permalink]

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New post 10 Jul 2017, 15:46
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Bunuel wrote:
A safari is held twice in a day either in the morning or in the evening. A person is allowed to participate in the safari in both the timings. A total of 108 people participate in the safari. The number of men and women in the safari are in the ratio 5 : 4. The total number of men who participate in the safari in the morning is 50 percent of the total number of men who participate in the safari. If every person participated in the safari at least once, what is the number of people who participate in the safari both in the morning and in the evening?


(1) The number of men who participate in the safari only in the morning is 80 percent of the women who participate in the safari only in the morning. Also, the number of men who participate in the safari only in the evening is double the number of women who participate in the safari only in the evening.

(2) The number of women who participate in the safari only in the evening is 60 percent of the girls who participate in the safari only in the morning.


I struggled a lot with this question, is there a simpler way to solve it? It took me a really long time.

Let:
Men:
- X = only in the morning
- Y = only in the evening
- XY = both (note that it's not a multiplication, just a convenient notation)
- M = X + Y + XY
Women:
- A = only in the morning
- B = only in the evening
- W = A + B + AB (same here)

We want AB + XY

Info from stimulus:
4 M = 5 W -> 1 ~unit~ = \(\frac{108}{9}\) = 12
Therefore M = 5 * 12 = 60, W = 48
Men that participate in the morning = X + XY = 30


(1) 5 X = 4 A
Y = 2 B
We have far more variables than equations (it's easy to plug in some numbers and get viable results)

(2) 5 B = 3 A
The same

(1) + (2):
To combine 5 X = 4 A and 5 B = 3 A, we multiply the first by 3 and the second by 4. Y = 2 B can than be inserted by mathing the B = Y/2
15 X = 12 A = 20 B = 10 Y (3 equations)

Combine with:
X + XY = 30 (1 eq)
AB+XY = 108 - (A+B+X+Y) (1 eq)

Variables: X, Y, XY, A, B, AB -> 6
We need one more equation. Maybe taking into account that te solution needs to comprise only of integers:
Solution 1: X = Y = A = B = 0
Solution 2: X = 4

Therefore, E.
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Re: A safari is held twice in a day either in the morning or in the evenin  [#permalink]

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New post 17 Jul 2017, 02:30
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Question Stem: Xb + Yb?
Let total men be X
divided as Xm, Xe, Xb such that m is morn, e is eve, b is both
Xm + Xe + Xb = 60

Similarly for women as Y
Ym + Yb + Ye = 48

Also, Xm + Xb = 1/2* 60 = 30
thus, Xe = 30

Statement 1: Xm = 0.8*Ym
Xe = 2Ye
Thus Ye = 15
and Ym + Yb = 33

No value of Xb or Yb - hence insufficient

Statement 2: Ye = 0.6*Ym
Insufficient as for different values of Ye, different values of Ym and Yb are possible
Further, no info on Xb

Combining:
Ye = 15 and = 0.6*Ym
Ym = 25
if Ym = 25,
Yb = 8

Further, Xm = 0.8*25 (Ym) = 20
and Xb = 30-20 = 10

Hence, Xb + Yb = 18
Sufficient

Answer C

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Re: A safari is held twice in a day either in the morning or in the evenin  [#permalink]

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New post 12 Feb 2019, 19:47
pushpitkc wrote:
Let the men participating in the safari only in the morning be x, and only in the evening be y.
Let the women participating in the safari only in the morning be a, and only in the evening be b.

From question stem,
Total guests : 108
Since they are in ratio 5:4, Men are 60 and Women are 48.
Men(morning) = 1/2*Men(Total)
Therefore, Men(morning) = x + Both = 30
x + y + Both = 60, so y = 30.
a + b + Both = 48

1. The number of men who participate in the safari only in the morning is 80 percent of the women who participate in the safari only in the morning.
Also, the number of men who participate in the safari only in the evening is double the number of women who participate in the safari only in the evening.
x = 4a/5
y = 2b => b = 15
This information is not enough to determine the total number of people who participated in both the morning and evening safari(Insufficient)

2. The number of women who participate in the safari only in the evening is 60 percent of the girls who participate in the safari only in the morning.
b = 3a/5
This information is not enough to determine the total number of people who participated in both the morning and evening safari(Insufficient)

Combining the information from both the statements,
a = 25,b=15
x=4a/5=20
y=6a/5=30
Both(men) = 10
Both(women) = 8
From this information, we can find out the total number of people who participated in both safari's are 18(Option C)





Thanks for the great explanation! It is really good structured and easy to follow!

Towards the questions about b=15 and a=25,
It is from:
y=30 and in (1) y=2b, so b=15
and from (2) b=3/5a, so a=25
Subsequently, 25+15+ab=48, so ab=8

x=4/5a=20, y=30, therefore from 20+30+xy=60, xy=10

We were asked the sum of xy and ab, and its 10+8=18

The answer choice C
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Re: A safari is held twice in a day either in the morning or in the evenin   [#permalink] 12 Feb 2019, 19:47
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