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21 Nov 2024, 01:30
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49% (02:22) correct
51%
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At a certain school 60% of the students are studying French and 70% are studying German, What percent of the students are studying neither language?
(1) The percent of students studying French only is equal to percent of students studying neither language
(2) The percent of students studying both German and French exceeds the percent of students studying neither language by 30% of the total number of students
(1) The percent of students studying French only is equal to percent of students studying neither language
(2) The percent of students studying both German and French exceeds the percent of students studying neither language by 30% of the total number of students
21 Nov 2024, 01:57
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Let number of students in the school be 100x.
Notations for Only French - F; Only german - G; Both french and german - B; Neither - N.
We have F+G+B+N = 100x ---- 1.
We also have:
F+B = 60x ---- 2
G+B = 70x ---- 3
Adding 2 & 3 - you get F+G+2B = 130x. So F+B+G = 130x - B. Substituting F+B+G in 1,
we get B-N = 30x.
St 1 -
This means, F = N. Substituting in 2, we get 2 equations with B and N - B+N = 60x and B-N = 30x. We can solve to get N. So, St 1 alone is sufficient.
St 2 -
We already know B-N = 30x. Doesn't add any value.
So, answer is A. St 1 alone is sufficient.
Notations for Only French - F; Only german - G; Both french and german - B; Neither - N.
We have F+G+B+N = 100x ---- 1.
We also have:
F+B = 60x ---- 2
G+B = 70x ---- 3
Adding 2 & 3 - you get F+G+2B = 130x. So F+B+G = 130x - B. Substituting F+B+G in 1,
we get B-N = 30x.
St 1 -
Quote:
This means, F = N. Substituting in 2, we get 2 equations with B and N - B+N = 60x and B-N = 30x. We can solve to get N. So, St 1 alone is sufficient.
St 2 -
Quote:
We already know B-N = 30x. Doesn't add any value.
So, answer is A. St 1 alone is sufficient.
21 Nov 2024, 08:22
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A simpler approach to this is if we just take 100 students since all the figures to calculate are given as % only.
Therefore, 100 students total, a total of 70 learn french & a total of 60 learning German. Since its clear that this is an overlapping set problem, we need 2 additional variables called studying both (F+G) and studying neither (0).
This leads to 40 not studying German and 30 not studying French.
Statement 1)
Percent of students who study French only = Percent of student who study neither. Let these be X.
Refer to the matrix below.
By substituting X as the value for both the number of students who study French only and not German & neither French not German, we can clearly see that X = 15, 2X = 30 and thus X = 15%. A is Sufficient. Cross off BCE
Statement 2)
The percent of students studying both German and French exceeds the percent of students studying neither language by 30% of the total number of students.
This tells us that the number of kids who study both languages (marked in the matrix below by "?" exceeds the number of those that study neither language by 30% of the total number of students (30 students in our case since our assumed total is 100 students). But we aren't sure of what the value of those who study neither language is (marked by "K")
To give some context, the number of students who study neither languages can be 0 or 1 or 10 or 20.
In each case, substituting K for the above values, the number of students who study both in this case will be 0 + 30 = 30 or 1 + 30 = 31 or 10 + 30 = 40 or 20 + 30 = 50.
Since theres multiple values that Statement B could have, we boot Option D.
STATEMENT (1) alone is sufficient.
Therefore, 100 students total, a total of 70 learn french & a total of 60 learning German. Since its clear that this is an overlapping set problem, we need 2 additional variables called studying both (F+G) and studying neither (0).
This leads to 40 not studying German and 30 not studying French.
Statement 1)
Percent of students who study French only = Percent of student who study neither. Let these be X.
Refer to the matrix below.
| Study French | Not French | Total | |
| Study German | - | - | 70 |
| Not German | (x) | (x) | 30 |
| Total | 60 | 40 | 100 |
By substituting X as the value for both the number of students who study French only and not German & neither French not German, we can clearly see that X = 15, 2X = 30 and thus X = 15%. A is Sufficient. Cross off BCE
Statement 2)
The percent of students studying both German and French exceeds the percent of students studying neither language by 30% of the total number of students.
This tells us that the number of kids who study both languages (marked in the matrix below by "?" exceeds the number of those that study neither language by 30% of the total number of students (30 students in our case since our assumed total is 100 students). But we aren't sure of what the value of those who study neither language is (marked by "K")
To give some context, the number of students who study neither languages can be 0 or 1 or 10 or 20.
In each case, substituting K for the above values, the number of students who study both in this case will be 0 + 30 = 30 or 1 + 30 = 31 or 10 + 30 = 40 or 20 + 30 = 50.
Since theres multiple values that Statement B could have, we boot Option D.
| Study French | Not French | Total | |
| Study German | K + 30 | - | 70 |
| Not German | - | K | 30 |
| Total | 60 | 40 | 100 |
STATEMENT (1) alone is sufficient.
