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.
