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Tammy's friends

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Tammy's friends

by kevincanspain » Thu Apr 25, 2013 2:19 pm
If Tammy has 80 Spanish-speaking and 70 English-speaking friends, does she have more than 100 friends in all?

(1) Among Tammy's friends, for every 9 friends who speak both English and Spanish, there are 2 who speak neither English nor Spanish.
(2) 40 of Tammy's friends speak at least two languages.
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by gaurav_gaur » Thu Apr 25, 2013 6:12 pm
The question is to find out if Tammy has at least 100 friends.
My initial analysis is more the number of people common between the 2 groups fewer will be Tammy's friend.

1) Among Tammy's friends, for every 9 friends who speak both English and Spanish, there are 2 who speak neither English nor Spanish

The first statement states that the number of people who falls in both the groups should be a multiple of 9. Hence
People who speak both the languages = 9*7 = 63 (as the max number of English speaking people is 70).
People who don't speak any language = 2*7 = 14
People who speak English = 7
People who speak Spanish = 17

Total number of friends = 101
So Tammy has more than 100 friends.


2)40 of Tammy's friends speak at least two languages.
I am confused here whether statement wants to state
a) At least 40 people speak 2 languages or
b) There are 40 people who speak at least 2 languages hopefully which includes English and Spanish.

I am going with the second option:
People who speak both the languages = 40
People who speak English = 30
People who speak Spanish = 40

Total number of friends = 110
So Tammy has more than 100 friends.

Therefore the answer should be D


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by Anju@Gurome » Thu Apr 25, 2013 9:13 pm
kevincanspain wrote:If Tammy has 80 Spanish-speaking and 70 English-speaking friends, does she have more than 100 friends in all?

(1) Among Tammy's friends, for every 9 friends who speak both English and Spanish, there are 2 who speak neither English nor Spanish.
(2) 40 of Tammy's friends speak at least two languages.
For two overlapping sets, total = number of elements in 1st set + number of elements in 2nd set - number of elements that are in both set + number of elements that are in none of the sets

Here, total number of friends (T) = number of friends speaking Spanish (S) + number of friends speaking English (E) - number of friends speaking both (B) + number of friends speaking none (N)
So, T = S + E - B + N

Now, S = 80 and E = 70
And, B cannot be greater than 70.
So, T = 80 + 70 - B + N = 150 - B + N = 150 - (B - N)
--> If T > 100 ---> 150 - (B - N) > 100 ---> (B - N) < 50
--> We need to determine whether (B - N) less than 50 or not

Statement 1: B:N = 9:2
Let us assume B = 9x and N = 2x
So, B is an integral multiple of 9 which is not greater than 70.
--> Maximum value of B is 63
--> If B = 63, N = (63/9)*2 = 14
--> Maximum value of (B - N) = (63 - 14) = 49 < 50
--> (B - N) is always less than 50

Sufficient

Statement 2: This means 40 of Tammy's friends speaks 2 languages or more.
So, number of friends speaking both English and Spanish cannot be more than 40.
So, B < 40
--> (B - N) ≤ 40 < 50

Sufficient

The correct answer is D.
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by kevincanspain » Thu Apr 25, 2013 9:55 pm
Fantastic! OA=D
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