garry_arora2000 wrote:

Qs:

Every passenger on a certain airplane is from either Japan or Australia; no one is from both. Every passenger is reading either a novel or a biography; no one is reading both. If a passenger is to be selected at random, is the probability that the passenger is both from Japan and reading a novel greater than the probability that the passenger is both from Australia and reading a biography.

(1) The probability that a randomly selected passenger is either from Japan or reading a novel or both is .

(2) The probability that a randomly selected passenger is either from Australia or reading a biography or both is .

You needn't give the standard 5 options for DS questions. They are the same for every question and people know them.

Make a table:

....................Japan...........Australia

Novel.............JN....................AN

Biography.......JB.....................AB

We need to know whether JN is greater than AB. JN represents number of people from Japan and reading a novel. AB represents number of people from Australia and reading a Biography and so on.

JN + AN + JB + AB = total number of people

(1) The probability that a randomly selected passenger is either from Japan or reading a novel or both is 208/251.

....................Japan...........Australia

Novel.............JN.....................AN

Biography......JB.....................AB

JN + AN + JB represent the passengers who are either from Japan or reading a novel or both. They sum up to 208 if total number of passengers is 251. This means AB = 251 - 208 = 43. But we don't know the value of JN so we cannot compare JN with AB.

(2) The probability that a randomly selected passenger is either from Australia or reading a biography or both is 172/251.

....................Japan...........Australia

Novel.............JN.....................AN

Biography......JB......................AB

AN + AB + JB = 172

So JN = 251 - 172 = 79

We don't AB so statement 2 alone is not sufficient to answer.

Using both statements we know AB = 43 and JN = 79 so JN is greater. Sufficient.

Answer (C)

i do not understand why you say "JN + AN + JB represent the passengers who are either from Japan or reading a novel or both" . Shouldn't it be (JN+JB) + (JN+AN) + (JN) , which makes it 3JN+AN+JB. Please help!