A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
(A) 100
(B) 150
(C) 200
(D) 240
(E) 250
Source : Veritas
OA=B
A certain high school offers two foreign languages, Spanish
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Since 10% of students take no languages and 70% take only one language, the remaining 20% must take both languages.
We know that 50 people take both languages. Accordingly, the school has 250 students.
25 take no language courses.
125 take French.
75 take French and French alone (125 - the 50 overlap students).
So the number of people taking Spanish is:
250 - 25 (who take no language courses) - 75 (French alone) = 150 students.
Answer choice (B).
We know that 50 people take both languages. Accordingly, the school has 250 students.
25 take no language courses.
125 take French.
75 take French and French alone (125 - the 50 overlap students).
So the number of people taking Spanish is:
250 - 25 (who take no language courses) - 75 (French alone) = 150 students.
Answer choice (B).
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This is an EITHER/OR group problem.hazelnut01 wrote:A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
(A) 100
(B) 150
(C) 200
(D) 240
(E) 250
Every child EITHER takes Spanish OR does not.
Every child EITHER takes French OR does not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.
Let S = Spanish, NS = not Spanish, F = French, NF = not French.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.
Let the total number of students = 10x.
The following grid is yielded:
![Image](https://s24.postimg.cc/d3is92zn5/matrix_spanish_french_0.png)
10% of students do not take a foreign language class.
Half of all students are in a French class.
Students who take neither language = 10% of 10x) = x.
Students who take French = (half of 10x) = 5x.
Entering these values into the grid and completing the rest of the middle row and the rightmost column, we get:
![Image](https://s12.postimg.cc/my1p7t7ix/matrix_spanish_french_1.png)
70% of students take exactly one foreign language class.
70% of 10x = 7x.
In the grid just above, only Spanish = 4x.
Thus, only French = (total taking exactly one language) - (only Spanish) = 7x - 4x = 3x.
Entering this value into the grid and completing the remainder of the grid, we get:
![Image](https://s30.postimg.cc/c4tqga4el/matrix_spanish_french_final_2.png)
50 students take classes in both languages.
In the final grid, the number of students taking both French and Spanish = 2x.
Thus:
2x = 50
x = 25.
How many students are in a Spanish class?
In the final grid, the total number of students taking Spanish = 6x.
Thus:
6x = 6*25 = 150.
The correct answer is B.
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I thought I'd point out that Mitch's Group Grid/Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- taking Spanish or not taking Spanish
- taking French or not taking French
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
Here, we have a population of students, and the two characteristics are:
- taking Spanish or not taking Spanish
- taking French or not taking French
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
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Dear Brent,Brent@GMATPrepNow wrote:I thought I'd point out that Mitch's Group Grid/Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- taking Spanish or not taking Spanish
- taking French or not taking French
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
In general, do you offer practice questions in your website? Are they paid or free?
thanks
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We have a combination of free and paid.Mo2men wrote: Dear Brent,
In general, do you offer practice questions in your website? Are they paid or free?
thanks
For more information, see the 5th line (under the heading "Tons of Reinforcement Activities") here: https://www.gmatprepnow.com/prices
Cheers,
Brent
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To solve this problem, there are two useful formulas we can use:hazelnut01 wrote:A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
(A) 100
(B) 150
(C) 200
(D) 240
(E) 250
1) Total = French Only + Spanish Only + Both + Neither
2) Total = French + Spanish - Both + Neither
In terms of percentage of students, we will use the first formula. We are given that the "Neither" group is 10%. Even though we don't know "French Only" and "Spanish Only" individually, we know the total of these two groups is 70%; thus we have:
100% = 70% + Both + 10%
Both = 20%
We are also given that 50 students take classes in both languages. If we let t = total number of students, we have:
0.2t = 50
t = 250
Since half of all students take French and 10% take neither, we have 125 students who take French and 25 who take neither. Therefore, in terms number of students, we will use the aforementioned second formula:
250 = 125 + Spanish - 50 + 25
250 = 100 + Spanish
Spanish = 150
Answer: B
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