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The ratio of boys to girls in a certain coed school is greater than 1.
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20 Jan 2023, 06:35
20 Jan 2023, 06:35
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Question Stats:
87% (01:42) correct
12% (01:33) wrong based on 33 sessions
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The ratio of boys to girls in a certain coed school is greater than 1. When 2 boys leave and 3 girls are added to the school, the ratio still favors boys. What is the least number of boys that could have been originally enrolled in the school, assuming there was originally at least one girl?
(A) 1
(B) 4
(C) 6
(D ) 7
(E) 13
(A) 1
(B) 4
(C) 6
(D ) 7
(E) 13
Re: The ratio of boys to girls in a certain coed school is greater than 1.
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24 Jan 2023, 06:25
24 Jan 2023, 06:25
Expert Reply
OE
The original ratio can be expressed in a proportion equation:
v/c=3/1
v=3c
After the departure of 180 violinists, you have a new proportion:
v-180/c=3/2
You now have two equations and two variables and can combine and solve.
You might also notice that when the 180 violinists depart, the ratio of violinists to cellists is cut in half. Therefore, 180 must have been half of the violinists.Originally, then, there must have been 360 violinists. Since there were 3 times as many violinists as cellists, there were 360/3 =120 cellists
The original ratio can be expressed in a proportion equation:
v/c=3/1
v=3c
After the departure of 180 violinists, you have a new proportion:
v-180/c=3/2
You now have two equations and two variables and can combine and solve.
You might also notice that when the 180 violinists depart, the ratio of violinists to cellists is cut in half. Therefore, 180 must have been half of the violinists.Originally, then, there must have been 360 violinists. Since there were 3 times as many violinists as cellists, there were 360/3 =120 cellists
Re: The ratio of boys to girls in a certain coed school is greater than 1.
[#permalink]
29 Dec 2023, 17:43
29 Dec 2023, 17:43
2
To set up the information we are given, where B1 = original number of boys, G1 = original number of girls.
[(B1 - 2) / (G1 + 3)] > 1. The least number of boys requires the least number of girls, and the question tells us to assume at least 1 girl. So we should assume exactly 1 girl.
[(B1 - 2) / (G1 + 3)] > 1 ==> [(B1 - 2) / (1 + 3)] > 1 ==> [(B1 - 2) / 4] > 1 ==> B1 - 2 > 4 ==> B1 > 6
Note that it has to be greater than 6, not greater than or equal to 6. So 7 is the answer.
[(B1 - 2) / (G1 + 3)] > 1. The least number of boys requires the least number of girls, and the question tells us to assume at least 1 girl. So we should assume exactly 1 girl.
[(B1 - 2) / (G1 + 3)] > 1 ==> [(B1 - 2) / (1 + 3)] > 1 ==> [(B1 - 2) / 4] > 1 ==> B1 - 2 > 4 ==> B1 > 6
Note that it has to be greater than 6, not greater than or equal to 6. So 7 is the answer.
