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Jefferson School

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by BlueDragon2010 » Fri Jan 24, 2014 9:34 am
In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

1) Of the 300 students, 60 do not study Spanish.

2) A total of 240 of the students study Spanish
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by Patrick_GMATFix » Fri Jan 24, 2014 9:44 am
There are several ways to solve this type of question, including groups table, venn diagram, and group formula. The solution below is taken from the GMATFix App.

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by GMATGuruNY » Fri Jan 24, 2014 11:57 am
For more practice with overlapping sets, try the following:

https://www.beatthegmat.com/three-set-ve ... 68125.html
Last edited by GMATGuruNY on Fri Jan 24, 2014 5:58 pm, edited 1 time in total.
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by ceilidh.erickson » Fri Jan 24, 2014 4:02 pm
Mitch, it looks like you've accidentally posted the solution to the wrong problem here.

There are two easy ways to solve an OVERLAPPING SETS problem like this: a matrix or a Venn diagram

MATRIX:
Students can either take French or not, and they can take Spanish or not. Set up your categories like this:

Image

Then, fill in the given information, and make inferences:

Image

It's important to note here that students can only take French, Spanish, or both - no one is taking NEITHER. We can put a 0 in the "no French, no Spanish" box, and extrapolate from there:

Image

Now, fill in the information from the statements. If 60 do not study Spanish, we can add that to the "no Spanish" total, but we can also add it to the "French but no Spanish" box. We can infer from there that 140 students take both. Sufficient:

Image

The second statement allows us to fill in that 240 student take Spanish, from which we can infer that 60 do not study Spanish... the same thing that statement 1 told us. This is also sufficient.

The answer is D.
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by ceilidh.erickson » Fri Jan 24, 2014 4:10 pm
VENN DIAGRAM:

Because in this problem, students can take only French, Spanish, or both - but not neither - a Venn diagram would also work well.

We have 300 total students. If 100 do not take French, they must take only Spanish:

Image

In order to find how many students take both, we need to find the number that take French only, or total for Spanish.

Statement 1:
If 60 do not study Spanish, they must take French only. That means that the "both" section must be 140, because 60 + 140 + 100 = 300

Image

Statement 2:
If 240 study Spanish, then 140 must study both, because 140 + 100 = 240

Image


Both statements are sufficient.
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by ceilidh.erickson » Fri Jan 24, 2014 4:12 pm
For more on OVERLAPPING SETS, see:
https://www.beatthegmat.com/rainbow-trou ... tml#555603
https://www.beatthegmat.com/ds-question- ... tml#677080
https://www.beatthegmat.com/survery-resu ... tml#576105
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by GMATGuruNY » Fri Jan 24, 2014 6:00 pm
ceilidh.erickson wrote:Mitch, it looks like you've accidentally posted the solution to the wrong problem here.
Thanks for pointing this out. I've edited my post accordingly.
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by sanju09 » Sat Jan 25, 2014 1:34 am
BlueDragon2010 wrote:In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

1) Of the 300 students, 60 do not study Spanish.

2) A total of 240 of the students study Spanish
Gear up with the Group Formula: Total = Group 1 + Group 2 - Both (+ Neither, not applicable in this case)

"¢ We know 300 = Group 1 (#French) + Group 2 (#Spanish) - Both (#French and Spanish).
"¢ We also know that 100 of those study Spanish only. It means that the size of Group 1 (#French) is 300 - 100 = 200.
"¢ Now, we know 300 = 200 + Group 2 (#Spanish) - Both (#French and Spanish).

Wish we also know the real size of Group 2 (#Spanish) somehow, and then the target question can be answered with conviction.

(1) If 60 do not study Spanish, it means those 60 study French only, and the remaining 200 - [spoiler]60 = 140[/spoiler] French students also study Spanish, that's the "Both (#French and Spanish)" answered. Sufficient

(2) This is what we were already wishing for. It supplies the missing "Group 2 (#Spanish)". Now, we know 300 = 200 + 240 - Both (#French and Spanish) or Both (#French and Spanish) = [spoiler]140. Sufficient

Take D[/spoiler]
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by Brent@GMATPrepNow » Sun Jan 26, 2014 9:42 am
ceilidh.erickson has done a great job demonstrating the Double Matrix Method.

This technique 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:
- studying French or not studying French
- studying Spanish or not studying Spanish

If anyone is interested in learning this technique, we have a free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with the Double Matrix Method, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html

Difficult Problem Solving questions
- 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.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://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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