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At an event, 4 0 % of the attendees are over 50 years old and another
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Updated on: 27 Jul 2023, 00:48
Updated on: 27 Jul 2023, 00:48
Expert Reply
00:00
Question Stats:
41% (02:05) correct
58% (01:54) wrong based on 17 sessions
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At an event, 40 % of the attendees are over 50 years old and another 20 % are under 20 years old. Which of the following statements must be true?
Indicate all such statements
A. The ratio of those over 50 to those between 20 and 50 inclusive is 2 : 3.
B. The ratio of those under 20 to those between 20 and 50 inclusive is 1 : 2.
C. 1/3 of the attendees who are not over 50 are under 20.
D. There are at least 10 attendees.
Indicate all such statements
A. The ratio of those over 50 to those between 20 and 50 inclusive is 2 : 3.
B. The ratio of those under 20 to those between 20 and 50 inclusive is 1 : 2.
C. 1/3 of the attendees who are not over 50 are under 20.
D. There are at least 10 attendees.
Re: At an event, 4 0 % of the attendees are over 50 years old and another
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25 Jan 2023, 02:43
25 Jan 2023, 02:43
Expert Reply
OE
You can see that 10 0 % - 4 0 % - 2 0 % = 4 0 % of the attendees are between 20 and 50 years old. Thus, choice (A) is not true; the real ratio is 40 : 40 =1 : 1. On the other hand, choice (B) is true, because 20 : 40 = 1 : 2.
Choice (C) is also true, because 60 % of the attendees are not over 50, and of those, 20 % (or 1/3 of 60%) are under 20.
Choice (D) requires a little more thinking. There is a hidden constraint in the problem because the number of attendees must be an integer. Expressed as fractions, the percentages of those over 50, between 20 and 50, and under 20 are 2/5,2/5, and 1/5 respectively. This means that the total number of attendees has to be divisible by 5. The smallest such number is 5. Thus, choice (D) is not necessarily true.
You can see that 10 0 % - 4 0 % - 2 0 % = 4 0 % of the attendees are between 20 and 50 years old. Thus, choice (A) is not true; the real ratio is 40 : 40 =1 : 1. On the other hand, choice (B) is true, because 20 : 40 = 1 : 2.
Choice (C) is also true, because 60 % of the attendees are not over 50, and of those, 20 % (or 1/3 of 60%) are under 20.
Choice (D) requires a little more thinking. There is a hidden constraint in the problem because the number of attendees must be an integer. Expressed as fractions, the percentages of those over 50, between 20 and 50, and under 20 are 2/5,2/5, and 1/5 respectively. This means that the total number of attendees has to be divisible by 5. The smallest such number is 5. Thus, choice (D) is not necessarily true.
Re: At an event, 4 0 % of the attendees are over 50 years old and another
[#permalink]
26 Jul 2023, 23:02
26 Jul 2023, 23:02
1
Carcass wrote:
At an event, 4 0 % of the attendees are over 50 years old and another 20 % are under 20 years old. Which of the following statements must be true?
Indicate all such statements
A. The ratio of those over 50 to those between 20 and 50 inclusive is 2 : 3.
B. The ratio of those under 20 to those between 20 and 50 inclusive is 1 : 2.
C. 1/3 of the attendees who are not over 50 are under 20.
D. There are at least io attendees.
Indicate all such statements
A. The ratio of those over 50 to those between 20 and 50 inclusive is 2 : 3.
B. The ratio of those under 20 to those between 20 and 50 inclusive is 1 : 2.
C. 1/3 of the attendees who are not over 50 are under 20.
D. There are at least io attendees.
Hi Carcass I presume option D is trying to say that there are at least 10 attendees
