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

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Intern
Joined: 04 Jul 2013
Posts: 16
Location: Switzerland
Concentration: General Management, Sustainability
GMAT 1: 690 Q46 V35
WE: Information Technology (Consulting)
The ratio of the number of boys to the number of girls in Wa  [#permalink]

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Updated on: 03 Mar 2014, 06:51
1
2
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:33) correct 29% (01:48) wrong based on 196 sessions

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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

Originally posted by dennis14 on 03 Mar 2014, 06:48.
Last edited by Bunuel on 03 Mar 2014, 06:51, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 50572
Re: The ratio of the number of boys to the number of girls in Wa  [#permalink]

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03 Mar 2014, 06:59
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.

_________________
Intern
Joined: 04 Jul 2013
Posts: 16
Location: Switzerland
Concentration: General Management, Sustainability
GMAT 1: 690 Q46 V35
WE: Information Technology (Consulting)
Re: The ratio of the number of boys to the number of girls in Wa  [#permalink]

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03 Mar 2014, 07:23
The problem i had in this question is that What if the school has

15 boys , 8 girls and 34 teachers ? But now i see that its not possible.

Thanks,
Den
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Joined: 09 Sep 2013
Posts: 8757
Re: The ratio of the number of boys to the number of girls in Wa  [#permalink]

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04 Dec 2017, 05:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The ratio of the number of boys to the number of girls in Wa &nbs [#permalink] 04 Dec 2017, 05:36
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# The ratio of the number of boys to the number of girls in Wa

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