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Mrs. William invited 120 guests who were either her relatives or her c
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24 Mar 2023, 08:37
24 Mar 2023, 08:37
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Question Stats:
53% (02:29) correct
46% (02:04) wrong based on 13 sessions
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Mrs. William invited 120 guests who were either her relatives or her colleagues or both. If 60% of the guests were her colleagues and 20% of her relatives were her colleagues too, how many guests were her relatives?
24
36
48
60
72
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24
36
48
60
72
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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Re: Mrs. William invited 120 guests who were either her relatives or her c
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10 Apr 2023, 09:53
10 Apr 2023, 09:53
2
Expert Reply
Let's denote the number of Mrs. William's relatives as "R" and the number of her colleagues as "C".
From the given information, we know that 60% of the total guests were Mrs. William's colleagues. This can be expressed as:
0.60 * 120 = 72
So, there were 72 guests who were her colleagues.
We also know that 20% of her relatives were also her colleagues, which can be expressed as:
0.20 * R
Since these two groups overlap (some guests may be both relatives and colleagues), we need to subtract the overlapping portion to avoid double counting. Therefore, we can write the total number of guests as:
R + C - 0.20R
We are told that the total number of guests is 120, so we can set up an equation:
R + 72 - 0.20R = 120
Simplifying, we get:
0.80R = 48
Dividing both sides by 0.80, we get:
R = 60
So, there were 60 guests who were Mrs. William's relatives. Therefore, the correct answer is 60.
From the given information, we know that 60% of the total guests were Mrs. William's colleagues. This can be expressed as:
0.60 * 120 = 72
So, there were 72 guests who were her colleagues.
We also know that 20% of her relatives were also her colleagues, which can be expressed as:
0.20 * R
Since these two groups overlap (some guests may be both relatives and colleagues), we need to subtract the overlapping portion to avoid double counting. Therefore, we can write the total number of guests as:
R + C - 0.20R
We are told that the total number of guests is 120, so we can set up an equation:
R + 72 - 0.20R = 120
Simplifying, we get:
0.80R = 48
Dividing both sides by 0.80, we get:
R = 60
So, there were 60 guests who were Mrs. William's relatives. Therefore, the correct answer is 60.
Re: Mrs. William invited 120 guests who were either her relatives or her c
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10 Oct 2023, 22:55
10 Oct 2023, 22:55
1
according to given question ,
70 % of guests where Colleague (C) i.e. 72 guests [which where both only colleague and colleague +relative]
therefore, remaining would be 120 - 72 i.e. 48 would only be relatives .
But now we need to also find the guests who are relative as well as colleague
we know that 20% (R) relatives are colleague i.e. 80 % of (R) relatives would only be relatives will only be 48.
therefore, 80%R = 48 --> R=60
70 % of guests where Colleague (C) i.e. 72 guests [which where both only colleague and colleague +relative]
therefore, remaining would be 120 - 72 i.e. 48 would only be relatives .
But now we need to also find the guests who are relative as well as colleague
we know that 20% (R) relatives are colleague i.e. 80 % of (R) relatives would only be relatives will only be 48.
therefore, 80%R = 48 --> R=60
