This problem is a variation of a group problem. the basic formul is Group 1 +Group 2 - Both + Neither = total but here you ahve three groups (English, Spanish and German)and a neither as well as additional restrictions. Because you can't have anyone with all three languages and if they speak German they must speak English you have the formula
Eonly+ES+GE+Sonly + neither = 200
The stem tells you that Sonly=70 so that means Eonly+ES+GE+70=200 - you have one equation and three variables so you cannot solve the problem yet.
Statement 1 only gives you one of the variables - so that is not enough -- BCE
Statement 2 only gives you one of the variables - again not enough -- CE
If you put the equations together you have two additional varibables and can therefore solve th problem - answer is C.
Sets prob
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Source: Beat The GMAT — Data Sufficiency |
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sumanr84
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Just to make it more clear to someone who is yet in doubt.
Easiest way to solve this is using a venn diagram.
1. Draw a circle for english
2. Draw german inside of english ( since all those who speak german speak english as well)
3. Draw a spanish that overlaps with english but does not touch German (since no one speaks all 3)
Now, shade the portion of the circle where data is given and you'll find that the inner german circle and the english to spanish overlap is the only remaining and since both represent 2 languages, that's your answer.
Eonly+ES+GE+Sonly + neither = 200
ES + GE = 200 - Eonly - Sonly - neither
200 - 60 - 70 - 20 = 50
So, answer is C
Easiest way to solve this is using a venn diagram.
1. Draw a circle for english
2. Draw german inside of english ( since all those who speak german speak english as well)
3. Draw a spanish that overlaps with english but does not touch German (since no one speaks all 3)
Now, shade the portion of the circle where data is given and you'll find that the inner german circle and the english to spanish overlap is the only remaining and since both represent 2 languages, that's your answer.
Eonly+ES+GE+Sonly + neither = 200
ES + GE = 200 - Eonly - Sonly - neither
200 - 60 - 70 - 20 = 50
So, answer is C
I am on a break !!
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Patrick_GMATFix
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This is a really difficult question that tests your ability to handle overlapping sets. Whenever I have 2 overlapping sets, I use the group formula to solve (Total = group1 + group2 + neither - both). However when there are three overlapping sets as there are here, I use the Venn Diagram to solve. Therefore I agree with sumanr84.
You must keep your work neat to do this at a good GMAT pace. The solutions above are excellent. If you're still struggling to understand, have a look at a video solution: this is is GMATPrep question 1386.
You can practice similar questions if you have access to the Solutions Engine drill generator by selecting topic="Sets & Groups" and difficulty="700+"
Good luck,
-Patrick
You must keep your work neat to do this at a good GMAT pace. The solutions above are excellent. If you're still struggling to understand, have a look at a video solution: this is is GMATPrep question 1386.
You can practice similar questions if you have access to the Solutions Engine drill generator by selecting topic="Sets & Groups" and difficulty="700+"
Good luck,
-Patrick
You are right Suman and other experts.
The main point of this problem is figuring the venn diagram. Once that is made the equations that you have writen can be sorted out. Can any expert please draw a venn diagram to describe the situation?
Thanks in advance.
The main point of this problem is figuring the venn diagram. Once that is made the equations that you have writen can be sorted out. Can any expert please draw a venn diagram to describe the situation?
Thanks in advance.
sumanr84 wrote:Just to make it more clear to someone who is yet in doubt.
Easiest way to solve this is using a venn diagram.
1. Draw a circle for english
2. Draw german inside of english ( since all those who speak german speak english as well)
3. Draw a spanish that overlaps with english but does not touch German (since no one speaks all 3)
Now, shade the portion of the circle where data is given and you'll find that the inner german circle and the english to spanish overlap is the only remaining and since both represent 2 languages, that's your answer.
Eonly+ES+GE+Sonly + neither = 200
ES + GE = 200 - Eonly - Sonly - neither
200 - 60 - 70 - 20 = 50
So, answer is C
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Patrick_GMATFix
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A detailed Venn diagram illustrates this situation at GMATPrep question 1245. Hit the "Swap Views" button above the question to bring up the solution & diagram. Let me know if you have any problem seeing it.tata wrote:You are right Suman and other experts.
The main point of this problem is figuring the venn diagram. Once that is made the equations that you have writen can be sorted out. Can any expert please draw a venn diagram to describe the situation?
Thanks in advance.
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
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nikhilkatira
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Gr8 explanation..sumanr84 wrote:Just to make it more clear to someone who is yet in doubt.
Easiest way to solve this is using a venn diagram.
1. Draw a circle for english
2. Draw german inside of english ( since all those who speak german speak english as well)
3. Draw a spanish that overlaps with english but does not touch German (since no one speaks all 3)
Now, shade the portion of the circle where data is given and you'll find that the inner german circle and the english to spanish overlap is the only remaining and since both represent 2 languages, that's your answer.
Eonly+ES+GE+Sonly + neither = 200
ES + GE = 200 - Eonly - Sonly - neither
200 - 60 - 70 - 20 = 50
So, answer is C
Best,
Nikhil H. Katira
Nikhil H. Katira
Thanks for the solution. Infact I also got the same answer. But I have one doubt regarding the solution. The question says nothing about the number of people who can speak both Spanish and Enlish or Spanish and German. So, if the question does not say anything about this , can we assume that the values for both the possibilites is zero. Dosent it make any sense to choose option E
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Patrick_GMATFix
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That's a great question Bikash. No we cannot make this assumption. If in a group question, it's logically possible for one item to belong to multiple groups, you must account for that possibility. For instance a problem that talks about what languages people speak or what courses people take allows the logical possibility that someone belongs to multiple groups, so our math must account for this. On the other hand, a question that talks about what colors marbles are or what age ranges people belong to does not allow for the possibility of group overlap; thus in this latter case our math can ignore this possibility.bikash123 wrote:I have one doubt regarding the solution. The question says nothing about the number of people who can speak both Spanish and Enlish or Spanish and German. So, if the question does not say anything about this , can we assume that the values for both the possibilites is zero.
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
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