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# In a certain school, teachers who lecture English and Spanish are ther

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
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In a certain school, teachers who lecture English and Spanish are ther  [#permalink]

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08 Jun 2016, 17:02
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:17) correct 51% (01:23) wrong based on 95 sessions

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In a certain school, teachers who lecture English and Spanish are there. If 2 teachers are selected randomly, what is the probability that at least one teacher selected lectures Spanish?
1) The ratio of Spanish teachers’ number to English teachers’ number is 3 to 1.
2) The sum of Spanish teachers’ number and English teachers’ number is less than 20.

*An answer will be posted in 2 days.

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Re: In a certain school, teachers who lecture English and Spanish are ther  [#permalink]

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08 Jun 2016, 19:17
MathRevolution wrote:
In a certain school, teachers who lecture English and Spanish are there. If 2 teachers are selected randomly, what is the probability that at least one teacher selected lectures Spanish?
1) The ratio of Spanish teachers’ number to English teachers’ number is 3 to 1.
2) The sum of Spanish teachers’ number and English teachers’ number is less than 20.

*An answer will be posted in 2 days.

2 teachers are selected, so we require to know the numbers of each to know the probability..

1) The ratio of Spanish teachers’ number to English teachers’ number is 3 to 1.

Important- you can find probability of picking one teacher but not 2 techer as it will vary depending on the number..
if there are 8.. 6 spanish and 2 English.... ans = 6/8*5/7
if there are 4.. 3 spanish and 1 English.... ans = 3/4*2/4
Insuff

2) The sum of Spanish teachers’ number and English teachers’ number is less than 20.
nothing about individual number of teachers in each language
Insuff..

Combined..
still teachers can be 4, 8, 12, or 16..
Insuff

E
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Re: In a certain school, teachers who lecture English and Spanish are ther  [#permalink]

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10 Jun 2016, 22:59
1
If we modify the original condition and the question, there are two variables (E and S). In order to match the number of variables and the number of equations, we need 2 equations. Hence, there is high chance that the correct answer is C. Using the condition 1) and the condition 2), since (E,S)=(2,6),(3,9),(4,12), the answer is not unique and the conditions are not sufficient. Thus, the correct answer is E.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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In a certain school, teachers who lecture English and Spanish are ther  [#permalink]

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26 Mar 2018, 00:55
Hi chetan2u,

Though i got E. My understanding of the question was different.

Question says , teachers who teach spanish and english are there. From these wordings, I assumed, there could be teachers who teach both spanish and english among other teachers who teach only english or spanish.
So question i thought was P(S U E) = P(S) + P(E) - P(S AND E) ?

And one more thing i assumed, there could teachers who teach neither. Based on this, i saw combining both the statements insuff.

do you think the question should have been worded as teachers teach either english or spanish?

I was lucky to get correct answer even after i misunderstood, but not to be true always.

Thanks
In a certain school, teachers who lecture English and Spanish are ther   [#permalink] 26 Mar 2018, 00:55
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