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Bunuel
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The ratio of male employees to female employees among the regular staf 09 Nov 2021, 03:00
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65% (hard)

Question Stats:

61% (02:25) correct 39% (02:38) wrong based on 406 sessions

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The ratio of male employees to female employees among the regular staff at a bookstore is 1:3. In addition to regular staff members, the bookstore retains two female employees and one male employee who are “on call.” If one of the regular staff members is replaced by an “on call” employee, what is the probability that the ratio of male employees to female employees working in the store remains unchanged?

(A) \(\frac{1}{3}\)

(B) \(\frac{1}{2}\)

(C) \(\frac{7}{12}\)

(D) \(\frac{2}{3}\)

(E) \(\frac{3}{4}\)
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C
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GMAT Focus 1: 735 Q90 V89 DI81
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The ratio of male employees to female employees among the regular staf 09 Nov 2021, 19:44
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Bunuel
The ratio of male employees to female employees among the regular staff at a bookstore is 1:3. In addition to regular staff members, the bookstore retains two female employees and one male employee who are “on call.” If one of the regular staff members is replaced by an “on call” employee, what is the probability that the ratio of male employees to female employees working in the store remains unchanged?

(A) \(\frac{1}{3}\)

(B) \(\frac{1}{2}\)

(C) \(\frac{7}{12}\)

(D) \(\frac{2}{3}\)

(E) \(\frac{3}{4}\)
Show more


There are two possibilities for the ratio to remain the same.

1) Regular male staff changed with an ‘on call’ male staff
P of Regular male staff = \(\frac{1}{1+3}\)
P of on call male staff = \(\frac{1}{1+2}\)
Overall P = \(\frac{1}{4}*\frac{1}{3}=\frac{1}{12}\)

2) Regular female staff changed with an ‘on call’ female staff
P of Regular female staff = \(\frac{3}{1+3}\)
P of on call female staff = \(\frac{2}{1+2}\)
Overall P = \(\frac{3}{4}*\frac{2}{3}=\frac{1}{2}\)

Final P = \(\frac{1}{12}+\frac{1}{2}=\frac{7}{12}\)


C
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The ratio of male employees to female employees among the regular staf 28 Aug 2024, 19:53
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Did not get the answer and question wording clearly
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The ratio of male employees to female employees among the regular staf 15 Oct 2024, 20:39
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chetan2u
Bunuel
The ratio of male employees to female employees among the regular staff at a bookstore is 1:3. In addition to regular staff members, the bookstore retains two female employees and one male employee who are “on call.” If one of the regular staff members is replaced by an “on call” employee, what is the probability that the ratio of male employees to female employees working in the store remains unchanged?

(A) \(\frac{1}{3}\)

(B) \(\frac{1}{2}\)

(C) \(\frac{7}{12}\)

(D) \(\frac{2}{3}\)

(E) \(\frac{3}{4}\)


There are two possibilities for the ratio to remain the same.

1) Regular male staff changed with an ‘on call’ male staff
P of Regular male staff = \(\frac{1}{1+3}\)
P of on call male staff = \(\frac{1}{1+2}\)
Overall P = \(\frac{1}{4}*\frac{1}{3}=\frac{1}{12}\)

2) Regular female staff changed with an ‘on call’ female staff
P of Regular female staff = \(\frac{3}{1+3}\)
P of on call female staff = \(\frac{2}{1+2}\)
Overall P = \(\frac{3}{4}*\frac{2}{3}=\frac{1}{2}\)

Final P = \(\frac{1}{12}+\frac{1}{2}=\frac{7}{12}\)


C
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Although I could mathematically prove that replacing a person with opposite gender will change ratio.
x+1/3x-1 = 1/3 => 4=0 not possible
or
x-1/3x+1 = 1/3 => 4=0 not possible.

Is there any intuitive way to reach this conclusion?
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The ratio of male employees to female employees among the regular staf 16 Oct 2024, 01:04
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Adarsh_24
chetan2u
Bunuel
The ratio of male employees to female employees among the regular staff at a bookstore is 1:3. In addition to regular staff members, the bookstore retains two female employees and one male employee who are “on call.” If one of the regular staff members is replaced by an “on call” employee, what is the probability that the ratio of male employees to female employees working in the store remains unchanged?

(A) \(\frac{1}{3}\)

(B) \(\frac{1}{2}\)

(C) \(\frac{7}{12}\)

(D) \(\frac{2}{3}\)

(E) \(\frac{3}{4}\)


There are two possibilities for the ratio to remain the same.

1) Regular male staff changed with an ‘on call’ male staff
P of Regular male staff = \(\frac{1}{1+3}\)
P of on call male staff = \(\frac{1}{1+2}\)
Overall P = \(\frac{1}{4}*\frac{1}{3}=\frac{1}{12}\)

2) Regular female staff changed with an ‘on call’ female staff
P of Regular female staff = \(\frac{3}{1+3}\)
P of on call female staff = \(\frac{2}{1+2}\)
Overall P = \(\frac{3}{4}*\frac{2}{3}=\frac{1}{2}\)

Final P = \(\frac{1}{12}+\frac{1}{2}=\frac{7}{12}\)


C
Although I could mathematically prove that replacing a person with opposite gender will change ratio.
x+1/3x-1 = 1/3 => 4=0 not possible
or
x-1/3x+1 = 1/3 => 4=0 not possible.

Is there any intuitive way to reach this conclusion?
Show more

When there are x men and y women, and you replace a man with a woman, the number of men decreases while the number of women increases, yet the total number of employees stays the same. Naturally, the ratio of men to women will decrease since the number of men goes down and the number of women goes up, which disrupts the balance of the original ratio.
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The ratio of male employees to female employees among the regular staf 16 Oct 2024, 02:57
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Bunuel
Adarsh_24
chetan2u
There are two possibilities for the ratio to remain the same.

1) Regular male staff changed with an ‘on call’ male staff
P of Regular male staff = \(\frac{1}{1+3}\)
P of on call male staff = \(\frac{1}{1+2}\)
Overall P = \(\frac{1}{4}*\frac{1}{3}=\frac{1}{12}\)

2) Regular female staff changed with an ‘on call’ female staff
P of Regular female staff = \(\frac{3}{1+3}\)
P of on call female staff = \(\frac{2}{1+2}\)
Overall P = \(\frac{3}{4}*\frac{2}{3}=\frac{1}{2}\)

Final P = \(\frac{1}{12}+\frac{1}{2}=\frac{7}{12}\)


C
Although I could mathematically prove that replacing a person with opposite gender will change ratio.
x+1/3x-1 = 1/3 => 4=0 not possible
or
x-1/3x+1 = 1/3 => 4=0 not possible.

Is there any intuitive way to reach this conclusion?

When there are x men and y women, and you replace a man with a woman, the number of men decreases while the number of women increases, yet the total number of employees stays the same. Naturally, the ratio of men to women will decrease since the number of men goes down and the number of women goes up, which disrupts the balance of the original ratio.
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Thank you, Bunuel. I forgot about the total remaining same.
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The ratio of male employees to female employees among the regular staf 17 Dec 2025, 07:28
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