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The ratio of the number of boys to the number of girls in

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The ratio of the number of boys to the number of girls in

by AAPL » Sat Jul 20, 2019 6:55 am

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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.

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Source: — Data Sufficiency |
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by swerve » Sat Jul 20, 2019 11:06 am

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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.

Therefore, the correct answer is __C__.
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