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VeritasKarishma
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In a class of 160 students, the number of students studying German and French is how much greater than the number of students studying neither German nor French?

1. The number of students studying German is 90.
2. The number of students studying French is 85.


Neither statement alone gives enough information but using both statements together, you get

Total = n(G) + n(F) - Both + None

160 = 90 + 85 - Both + None

Both - None = 15

Number of students studying both is 15 more than the number of students studying neither. Sufficient.

Answer (C)


the number of students studying German and French = n(G) + n(F) - Both
number of students studying neither German nor French = None

Question is asking 'the number of students studying ( Not written BOTH) German and French is how much greater than the number of students studying neither German nor French?'

So, Basically
[n(G) + n(F) - Both] - None =???

in that case the Ans should be E

what i am missing ?

{n(G) + n(F) - Both} is the number of students studying German OR French (including Both). It is not the number of students studying German and French.
No. of students studying German AND French = Both

So the question asks us the difference between Both and None.
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T=160

1) G=90 NS alone

2) F=85 NS alone

1&2) T=G+F-Both+Neither
Neither->160-90=70
Both->160-70=90+85-Both->Both=85
Both-Neither->85-70=15

Answer C
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