The table below shows the result of survey of 100 students

Question

Topics.png The table attached shows the result of survey of 100 students who responded with “For” or “Against” or “Not sure” when asked about the Debate choice of the Topic A and Topic B. What was the number of students who responded “For” for both Topics? (1) The number of students who did not respond “For” for either Topic was 40. (2) The number of students who responded “Against” for both Topics was 20.

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=18845 
 The table attached shows the result of survey of 100 students who responded with “For” or “Against” or “Not sure” when asked about the Debate choice of the Topic A and Topic B. What was the number of students who responded “For” for both Topics?

{Total # of students who responded "For"} = {"For" A} + {"For" B} - {"For" both} ;
 {Total # of students who responded "For"} = 30 + 40 - {"For" both} 
 {"For" both} = 70 - {Total # of students who responded "For"} .

(1) The number of students who did not respond “For” for either Topic was 40 --> since 40 students did NOT respond "For", then the remaining 60 students DID respond "For" for either Topic, thus  {Total # of students who responded "For"} = 60 . Therefore,  {"For" both} = 70 - 60 = 10 . Sufficient.

(2) The number of students who responded “Against” for both Topics was 20. Not sufficient.

Answer: A.

carcass · Answer

Bunuel but the first statement could be solved by the unknown multiplier and a ratio strategy ?? I came to A with this logic or is wrong ??

Thanks

gmatbull · Answer

Carcas, can you please show how you applied the "ratio strategy"?

carcass · Answer

because you have (make the things simple) FOR 3x + 7x = 100 so your UM is 7x (70 of bunuel): with 7x we have not real number but 1) provide us with.

IF 7x is the total number of students AND 40 not respond so 60 respond. IF you have 7x = 60 (real number) you CAN calculate the number of student (remember: we are talking of integers, so even you have 14.5 is not possible, is a constraint not written but you have to take in account for). However, it depens a lot from the context.

BE careful : this is totally an inference and intuitive approach, that come up after several time of study and that you develope instinctively. Similar native speakers have about SC

Marcab · Answer

Carcass....you definitely have GMAT EAR.

mcwoodhill · Answer

expand the tablet will lead fast and direct solution:

For only For both||| Against only Against both||| Not sure for only Not sure for neither|||

A 30-x x 40-y y 30-z z

B 40-x x 20-y y 40-z z

now it's very graphic:

the question is x=?

(1) not for either is 100-(30-x+x+40-x)=40

sufficient

(2) y=20

insufficient

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The table below shows the result of survey of 100 students

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