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12 May 2021, 21:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:14) correct
20%
(01:27)
wrong
based on 103
sessions
History
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Not Attempted Yet
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
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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
Kudos
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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.
