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A certain college party is attended by both male and female students. [#permalink]
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08 May 2015, 05:04
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83% (01:01) correct 17% (01:15) wrong based on 171 sessions
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Re: A certain college party is attended by both male and female students. [#permalink]
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08 May 2015, 22:17
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Bunuel wrote: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24 (B) 30 (C) 48 (D) 64 (E) 80
Kudos for a correct solution. Correct answer to this question would be divisible by \(8 (3+5)\) and correct answer subtracted by \(5\) would be divisible by \(3\). Now lets put answer choices to solve the question: (A) 24 => Divisible by \(8\) but \(245=19\) is not divisible by \(3\). Incorrect (B) 30 => No divisible by \(8\). Incorrect (C) 48 => Divisible by \(8\) but \(485=43\) is not divisible by \(3\). Incorrect (D) 64 => Divisible by \(8\) but \(645=59\) is not divisible by \(3\). Incorrect (E) 80 => Divisible by \(8\) and \(805=75\) is divisible by \(3\). We have a winner. E is the correct answer.
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A certain college party is attended by both male and female students. [#permalink]
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09 May 2015, 00:54
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M/F = 3/5 5M = 3F1 Also, (M5)/F = 1/2 2M10 = F Multiply by 3 both sides 3F=6M302 from 1 and 2 M=30 F=50 Total=80 E is the answer



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Re: A certain college party is attended by both male and female students. [#permalink]
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09 May 2015, 01:52
m/f = 3/5 Assume constant = x m=3x, f=5x
Now, 3x5/5x =1/2 => 6x10 = 5x => x=10 total students = 8x = 80
Answer E



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Re: A certain college party is attended by both male and female students. [#permalink]
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09 May 2015, 06:41
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Bunuel wrote: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24 (B) 30 (C) 48 (D) 64 (E) 80
Kudos for a correct solution. Ratio of males:females=3:5 or 3x:5x Now, (3x5)/5x=1:2 6x10=5x x=10 3x=30 5x=50 Total No of males=30 and Total no of females=50 Total no of students=80 Answer E



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Re: A certain college party is attended by both male and female students. [#permalink]
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09 May 2015, 17:47
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\(\frac{M}{F}\) =\(\frac{3}{5}\) This means, 5M=3F Now after 5 male leave the party, \(\frac{(M5)}{F}\) = \(\frac{1}{2}\) Substitute F= \(\frac{5M}{3}\) \(\frac{(M5)}{(5M/3)}\)= \(\frac{1}{2}\) 2(3M 15) = 5M M= 30 \(\frac{3}{8}\)* Total = 30 Total = 80 students



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Re: A certain college party is attended by both male and female students. [#permalink]
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11 May 2015, 05:53
Bunuel wrote: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24 (B) 30 (C) 48 (D) 64 (E) 80
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:Of course, we could set up equations for the unknowns in the problem and solve them algebraically. However, it may be easier just to test the answer choices. Give this approach a try: (A) 24 students implies 9 male and 15 female students. If 5 male students left the party, the remaining ratio would be 4/14 = 2/7. INCORRECT. (B) 30 students implies 11.25 male and 18.75 female students. These numbers must be integers. INCORRECT. (C) 48 students implies 18 male and 30 female students. If 5 male students left the party, the remaining ratio would be 13/30. INCORRECT. (D) 64 students implies 24 male and 40 female students. If 5 male students left the party, the remaining ratio would be 19/40. INCORRECT. (E) 80 students implies 30 male and 50 female students. If 5 male students left the party, the remaining ratio would be 25/50 = 1/2. CORRECT. We proved that the correct answer must be (E) without doing any algebra at all. A nice thing about Testing Answer Choices is that it doesn't require any fundamental knowledge or theory. You don't need to know a special formula. Instead, it forces you to concentrate on the available answer options. It also steadily reduces your uncertainty, since you eliminate wrong answer choices one by one. A question might contain a phrase such as “Which of the following…” This is a great time to test choices
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Re: A certain college party is attended by both male and female students. [#permalink]
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20 Feb 2017, 08:33
Bunuel wrote: Bunuel wrote: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24 (B) 30 (C) 48 (D) 64 (E) 80
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:Of course, we could set up equations for the unknowns in the problem and solve them algebraically. However, it may be easier just to test the answer choices. Give this approach a try: (A) 24 students implies 9 male and 15 female students. If 5 male students left the party, the remaining ratio would be 4/14 = 2/7. INCORRECT. (B) 30 students implies 11.25 male and 18.75 female students. These numbers must be integers. INCORRECT. (C) 48 students implies 18 male and 30 female students. If 5 male students left the party, the remaining ratio would be 13/30. INCORRECT. (D) 64 students implies 24 male and 40 female students. If 5 male students left the party, the remaining ratio would be 19/40. INCORRECT. (E) 80 students implies 30 male and 50 female students. If 5 male students left the party, the remaining ratio would be 25/50 = 1/2. CORRECT. We proved that the correct answer must be (E) without doing any algebra at all. A nice thing about Testing Answer Choices is that it doesn't require any fundamental knowledge or theory. You don't need to know a special formula. Instead, it forces you to concentrate on the available answer options. It also steadily reduces your uncertainty, since you eliminate wrong answer choices one by one. A question might contain a phrase such as “Which of the following…” This is a great time to test choices Can you please explain how we are choosing values here?
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Re: A certain college party is attended by both male and female students. [#permalink]
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07 Aug 2017, 00:54
Hello anairamitch1804, Here are the detailed steps for option A. Rest follow the same approch Given: Male : Female = 3:5. Lets assume actual numbers to be 3x and 5x. Total students = 3x+5x = 8x. Now from the answer choices we get A. 8x = 24 => x = 3 => Male = 3x = 9 and female = 5x = 15. If 5 Male left, the new values of male = 95 = 4. There is no change in females. New Ratio of Male : Female = 4:15 ≠ 1:2. So, A is incorrect. I think the highlighted portion below is a Typo error. Hope this helps and this not too late a response anairamitch1804 wrote: Bunuel wrote: Bunuel wrote: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24 (B) 30 (C) 48 (D) 64 (E) 80
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:Of course, we could set up equations for the unknowns in the problem and solve them algebraically. However, it may be easier just to test the answer choices. Give this approach a try: (A) 24 students implies 9 male and 15 female students. If 5 male students left the party, the remaining ratio would be 4/14 = 2/7. INCORRECT. (B) 30 students implies 11.25 male and 18.75 female students. These numbers must be integers. INCORRECT. (C) 48 students implies 18 male and 30 female students. If 5 male students left the party, the remaining ratio would be 13/30. INCORRECT. (D) 64 students implies 24 male and 40 female students. If 5 male students left the party, the remaining ratio would be 19/40. INCORRECT. (E) 80 students implies 30 male and 50 female students. If 5 male students left the party, the remaining ratio would be 25/50 = 1/2. CORRECT. We proved that the correct answer must be (E) without doing any algebra at all. A nice thing about Testing Answer Choices is that it doesn't require any fundamental knowledge or theory. You don't need to know a special formula. Instead, it forces you to concentrate on the available answer options. It also steadily reduces your uncertainty, since you eliminate wrong answer choices one by one. A question might contain a phrase such as “Which of the following…” This is a great time to test choices Can you please explain how we are choosing values here?
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Re: A certain college party is attended by both male and female students. [#permalink]
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10 Aug 2017, 09:42
Bunuel wrote: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24 (B) 30 (C) 48 (D) 64 (E) 80 We can let the ratio of male to female = 3x to 5x and create the following equation: (3x  5)/5x = 1/2 2(3x  5) = 5x 6x  10 = 5x 10 = x So, there are 3(10) + 5(10) = 80 total students at the party. Answer: E
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