Problem Solving

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

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).

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

This is an EITHER/OR group problem.
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:


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:


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:


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.

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

Dear Brent,

In general, do you offer practice questions in your website? Are they paid or free?

thanks