According to a survey, at least 70% of students in college study Hindi

Question

According to a survey, at least 70% of students in a college study Hindi, at least 75% of students study French, and at least 80% of students study German. If x is the minimum percentage of students who study all three languages and y is the maximum percentage of students who study all three languages, then choose the appropriate values for x and y from the table given below:

samarpan.g28 · Answer

For y i.e. maximum, we have at least 70, 75 and 80. Here, the minimum of subsets is 70 so y=70%.

For x, we can get minimum if we assume students studying both subjects as the maximum.
Let, total students=100a. H=70a, F=75a, G=80a.

100a=70a+75a+80a - 100a (assuming maximum) - x
200a-225a=-x or, x=25a i.e. 25%.

x=25, y=70.

Bismuth83 · Answer

Let's say every student studies all three languages (100%). This would match all 3 requirements, however, 100% is larger than the upper bound y = 70. Maybe I misunderstood something here?

MS61 · Answer

We dont have that option in ans choices

cspatadia · Answer

I am a bit confused on the answer for the maximum. Let's say we have 100 students, and 70 study all 3 languages. That leaves 0 for (Hindi only or Hindi + other language but not all 3), 5 for (Frernch only or French + some other language but not all 3) and 25 for (German only or German + some other language but not all 3). so the total becomes 70 + 0 + 5 + 20 = 95 and not 100.

Are we supposed to assume that there are some who study none of these languages too?

Are we supposed to assume that there are some who study none of these languages too?

StacyArko · Answer

Consider the following....assuming the actual % of students studying German is 95% (note: 95% meets the condition that German >=80%), then we can have x (max)= 70%, French only =5% and German only =25%. The rest can be 0

gullyboy09 · Answer

Q is flawed, all numbers are given as "at least", so it might be possible all are studying all the three languages and y becomes 100. One can argue that 100 is not given in the option, but question is strictly asking "maximum" not which can be possible in the given options. Hard to believe one can make a question like this. One who made this Q, even if he had read it once, he would have deleted it even from his recycle bin, It clearly shows no due diligence was done on this question. WHATS MORE DIFFICULT TO BELIEVE IS AN EXPERT POSTED THIS.

WildSnow · Answer

I don't think the question is flawed, seems workable. Question says: choose the appropriate values for x and y from the table given below.
Granted, the answer will be 100, but which is more appropriate to choose for the max value: 55 or 70? I would choose 70

SuperColt · Answer

Plaese suggest what is the correct approach to solve this type of question.

egmat · Answer

Hi SuperColt,

Good question to ask, because these "at least X%" three-set problems have a clean two-step recipe. You're really solving two different things here:  x  (the minimum overlap) and  y  (the maximum overlap), and each has its own trick.

Finding y (the maximum)

The group studying  all three  can never be larger than the  smallest  of the three groups - you can't have more people in the overlap than exist in any single set.

- Hindi >=  70% , French >=  75% , German >=  80% 
- The smallest is Hindi at  70% 
- Push everyone in Hindi into French and German too (possible, since those groups are bigger)
- So the most that can study all three is  70%  ->  y = 70

Finding x (the minimum)

Here the smart move is to flip to  complements  - count who is  left out :

- At most  30%  don't study Hindi ( 100  -  70 )
- At most  25%  don't study French ( 100  -  75 )
- At most  20%  don't study German ( 100  -  80 )

Add the "left out" pieces:  30 + 25 + 20 = 75% . That's the largest possible slice of students who miss  at least one  language. Everyone else must be studying  all three :

-  100 - 75 = 25%  ->  x = 25

Therefore  the pair is  x = 25, y = 70  - and notice both fall right out of the same setup, one from the smallest group, one from the leftover complements.

Lock it in with a tiny version

Try a two-set case: at least  80%  do A, at least  90%  do B. Minimum doing both =  100  - ( 20  +  10 ) =  70% . Maximum doing both = the smaller group =  80% . Same two moves - smallest group for the max, sum of complements for the min.

Use that recipe every time and both columns drop out together.

Answer: Column 1 (x) = 25; Column 2 (y) = 70

According to a survey, at least 70% of students in college study Hindi

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According to a survey, at least 70% of students in college study Hindi

Prep Toolkit

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