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12 May 2021, 21:00
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C
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Difficulty:
25%
(medium)
Question Stats:
79% (01:15) correct
21%
(01:27)
wrong
based on 102
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The ratio of the number of boys to the number of girls in Washington High School is 5:3. What is the number of teachers in the school?
(1) In the same school, the ratio of the number of girls to the number of teachers is 4:17
(2) There are less than 55 teachers in the school
(1) In the same school, the ratio of the number of girls to the number of teachers is 4:17
(2) There are less than 55 teachers in the school
12 May 2021, 21:40
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Bunuel
Let number of Boys = B, Girls = G, and Teachers = T
Given: B:G = 5:3
T = ?
Statement 1:
G:T = 4:17
But we have no information about total number of boys or girls or teachers.
Statement 1 is Not Sufficient.
Statement 2:
T < 55
T can be any number below 55.
Statement 2 is also Not Sufficient.
Statement 1 and Statement 2 combined:
G:T = 4:17 and T < 55
=> B:G:T = 20:12:51
=> Number of teachers is a multiple of 51 and T < 55.
=> Smallest multiple of 51 below 55 is 51.
=> T = 51.
Statement 1 and Statement 2 together are Sufficient.
So, correct answer is option C.
16 May 2021, 08:30
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The ratio of the number of boys to the number of girls in Washington High School is 5:3. What is the number of teachers in the school?
Boys:Girls = 5:3.
(1) In the same school, the ratio of the number of girls to the number of teachers is 4:17.
Girls:Teachers = 4:17 = 12:51;
Boys:Girls = 5:3 = 20:12 (from the stem).
Boys:Girls:Teachers = 20:12:51. So, we know that the number of teachers must be a multiple of 51. Not sufficient.
(2) There are less than 55 teachers in the school. Clearly insufficient.
(1)+(2) The least positive multiple of 51 less than 55 is 51, thus there are 51 teachers. Sufficient.
Answer: C.
Boys:Girls = 5:3.
(1) In the same school, the ratio of the number of girls to the number of teachers is 4:17.
Girls:Teachers = 4:17 = 12:51;
Boys:Girls = 5:3 = 20:12 (from the stem).
Boys:Girls:Teachers = 20:12:51. So, we know that the number of teachers must be a multiple of 51. Not sufficient.
(2) There are less than 55 teachers in the school. Clearly insufficient.
(1)+(2) The least positive multiple of 51 less than 55 is 51, thus there are 51 teachers. Sufficient.
Answer: C.
