In Alba language school, 30 students study Spanish or Finnish or both.

Question

Competition Mode Question

In Alba language school, 30 students study Spanish or Finnish or both. If 10 of these students don't study Spanish, how many of these students study both Spanish and Finnish?

(1) Of the 30 students, 6 don't study Finnish.

(2) A total of 24 of the students study Finnish.

rajatchopra1994 · Answer

Explanation:

Given: 30 students study Spanish or Finnish or both
10 of these students don't study Spanish

To find: students study both Spanish and Finnish

Statement 1: Of the 30 students, 6 don't study Finnish.
S(Spanish) + F(Finnish) + B(both) = 30 
F=10
S=6
B = 30 - (S+F)
B = 14
Sufficient

Statement 2: A total of 24 of the students study Finnish
F+B = 24
10 + B = 24
B = 14
Sufficient

IMO-D

yashikaaggarwal · Answer

Students are either studying Spanish or Finnish or both of them but none of them is studying neither.
Total students = 30 (Studying S(Spanish)+F(Finnish)+B(Both Spanish and Finnish)

10 people are not studying Spanish
So 20 students are studying Spanish + Spanish and Finnish both

Statement 1: 6 students are not studying Finnish out of 20 students studying Spanish + Spanish and Finnish both
So 14 people are studying Spanish and Finnish both.
(Sufficient)

Statement 2: 24 are studying Finnish + Spanish and Finnish both
Out of which 10 are not studying Spanish.
So people studying Spanish and Finnish both = 14
(Sufficient)

Answer is D

Posted from my mobile device

stne · Answer

Please see the attached figure. GMAT DS.png Each Statement individually is SUFF. Ans- D

NiftyNiffler · Answer

In Alba language school, 30 students study Spanish or Finnish or both. If 10 of these students don't study Spanish, how many of these students study both Spanish and Finnish?

(1) Of the 30 students, 6 don't study Finnish.

(2) A total of 24 of the students study Finnish.

Stimulus:

10 of these students don't study Spanish = Finnish - Both = 10 (From the Venn Diagram)
Total = Spanish + Finnish - Both
=> 30 = Spanish + 10
=>  Spanish = 20   ----------(i)

st1) Those who don't study Finnish = Spanish - Both = 6 ---------(ii)

So, from the above equation, we can find Both = 14 SUFFICIENT

st2) Finnish = 24

From the stimulus,
Finnish - Both = 10 
=> Both = 14 SUFFICIENT

So, the answer should be  D

bidskamikaze · Answer

In Alba language school, 30 students study Spanish or Finnish or both. If 10 of these students don't study Spanish, how many of these students study both Spanish and Finnish?

Let a = no. of student who study Spanish only.
Let b = no. of students who study both Spanish and Finnish.
Let c = no. of students who study Finnish only.
Given: a+b+c = 30; c = 10
to find: b?

(1) Of the 30 students, 6 don't study Finnish.
- this statement gives the value of a = 6
therefore b= 14
 Sufficient.

(2) A total of 24 of the students study Finnish.
- this statement gives the value of b+c = 24
since c= 10, b = 14.
 Sufficient.

Answer D.

rahulbhusan · Answer

........... S.........NS..........Total
F..........X.........10...........10+X
NF........Y..........Z.............Y+Z
Total.....20......10+Z........10+X+Y+Z

From question stem, we can figure out the above information. We need to find X
Let Spanish+ Finnish+ Both + Neither = Total
We know that, 10 didn't study Spanish
So, only Finnish will be 10 and student studying Spanish will be 20

Statement I: Of the 30 students, 6 don't study Finnish.

........... S.........NS..........Total
F..........X.........10...........10+X
NF........Y..........Z.............Y+Z
Total.....20......10+Z........10+X+Y+Z

So, we know Y=6, therefore, X= 20-6= 14
Sufficient. Eliminate B, C, and E

(2) A total of 24 of the students study Finnish.

........... S.........NS..........Total
F..........X.........10...........10+X
NF........Y..........Z.............Y+Z
Total.....20......10+Z........10+X+Y+Z

Given, X+10=24 
X=24-10=14
Statement II sufficient.

Option D  is the correct answer.

Varunsawhney8 · Answer

In Alba language school, 30 students study Spanish or Finnish or both. If 10 of these students don't study Spanish, how many of these students study both Spanish and Finnish?

We Know,
Only Finnish =10
let Only Spanish= X
Let Both finnish and Spanish =Y
We need to calculate Y
We know, 
X+Y+10=30

(1) Of the 30 students, 6 don't study Finnish.
It means 
10+Y=30-6

So Y=14

(2) A total of 24 of the students study Finnish.

It Means
10+Y=24
SO 
Y=14

minustark · Answer

In Alba language school, 30 students study Spanish or Finnish or both. If 10 of these students don't study Spanish, how many of these students study both Spanish and Finnish?

(1) Of the 30 students, 6 don't study Finnish.

(2) A total of 24 of the students study Finnish.

From the stem, we can infer 10 students study Finnish only and the remaining 20 study either Spanish only or both. If we can get info on any of the two segment, we can find the other one.

1) 6 students study Spanish only. So the remaining 14 study both Spanish and Finnish. Sufficient

2) Since, 10 students study Finnish only, so the remaining (24 -10) = 14 students study both. Sufficient.

D is our answer.

exc4libur · Answer

(1) sufic

.....s......n.....t
f.....14......10......
nf...6.......0.......
t.....20.......10...30

(2) sufic

.....s......n.....t
f....14.....10......24
nf..........0.......
t.....20.......10...30

(D)

Taulark1 · Answer

GMAT question won't be framed in this way,
Per the Question 30 students speak spanish or finnish or both.
But there could very well be more than 30 students in Alba Language school.  So we cannot just not consider that fact and assume 30 students as the total

MBAB123 · Answer

We're not really concerned with the total number of students in the school. Even if they are a million kids in the school, it wouldn't change our answer. We just don't know how many students do no study finish or Spanish, but we can find the answer without that.

Taulark1 · Answer

If we consider anything as the total other than 30 , we will not get the desired answer, all answers here posted have considered 30 as total which is wrong , one can't just assume the total as 30.

MBAB123 · Answer

I get that the total should not be considered as 30, but that doesn't impact our answer. If you solve this using the 2*2 matrix, you can ignore the bottom right box. It won't change the answer. Let's say i say that the total number of students is 50, can you come up with a different answer other than 14 for any of the statements?

Taulark1 · Answer

If we take 50 as the total , using statement 1 , answer comes as 36, i'm not sure what you mean.

MBAB123 · Answer

We're not really concerned with the total number of students in the school. Even if they are a million kids in the school, it wouldn't change our answer. We just don't know how many students do no study finish or Spanish, but we can find the answer without that.

If we consider anything as the total other than 30 , we will not get the desired answer, all answers here posted have considered 30 as total which is wrong , one can't just assume the total as 30.

I get that the total should not be considered as 30, but that doesn't impact our answer. If you solve this using the 2*2 matrix, you can ignore the bottom right box. It won't change the answer. Let's says I say that the total number of students is 50, can you come up with a different answer other than 14 for any of the statements?

If we take 50 as the total , using statement 1 , answer comes as 36, i'm not sure what you mean.

X+y+z = 30 is already given in the question and out of these 30, y =10 is already given.

Taulark1 · Answer

If we consider anything as the total other than 30 , we will not get the desired answer, all answers here posted have considered 30 as total which is wrong , one can't just assume the total as 30.

I get that the total should not be considered as 30, but that doesn't impact our answer. If you solve this using the 2*2 matrix, you can ignore the bottom right box. It won't change the answer. Let's says I say that the total number of students is 50, can you come up with a different answer other than 14 for any of the statements?

If we take 50 as the total , using statement 1 , answer comes as 36, i'm not sure what you mean.

X+y+z = 30 is already given in the question and out of these 30, y =10 is already given.

gotcha ! thanks for helping me undertand

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In Alba language school, 30 students study Spanish or Finnish or both.

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