AbdurRakib wrote:

Did a train arrive at station X no earlier than 4:00 p.m. and no later than 8:00 p.m. on Tuesday?

(1) 36 hours after the train arrived, it was between 6 a.m. and 10:00 a.m. on Thursday.

(2) 36 hours before the train arrived, it was between 3:00 a.m. and 7:30 a.m. on Monday

Dear

AbdurRakibI'm happy to help.

This is a clever question.

Statement #1:

36 hours after the train arrived, it was between 6 a.m. and 10:00 a.m. on Thursday.

Well, 24 hours before that, 12 hours after the train, was between 6 a.m. and 10:00 a.m. on Wednesday. Then, 12 hours before that, the time of the train, would have been between 6 p.m. and 10:00 p.m. on Tuesday.

The train could have left at 7:15 pm on Tuesday, which would give a "yes" to the prompt question.

The train could have left at 9:30 pm on Tuesday, which would give a "no" to the prompt question.

Because two answers to the prompt are possible, we do not have the information we need to give a definitive answer. The first statement, alone and by itself, is

not sufficient.

Now, forget all about statement #1.

Statement #2:

36 hours before the train arrived, it was between 3:00 a.m. and 7:30 a.m. on Monday.

Well, 24 hours after that, 12 hours before the train, was between 3:00 a.m. and 7:30 a.m on Tuesday. Then, 12 hours after that, the time of the train, would have been between 3:00 p.m. and 7:30 p.m. on Tuesday.

The train could have left at 7:15 pm on Tuesday, which would give a "yes" to the prompt question.

The train could have left at 3:15 pm on Tuesday, which would give a "no" to the prompt question.

Because two answers to the prompt are possible, we do not have the information we need to give a definitive answer. The first statement, alone and by itself, is

not sufficient.

Combined statement.

Statement #1:

36 hours after the train arrived, it was between 6 a.m. and 10:00 a.m. on Thursday.

Statement #2:

36 hours before the train arrived, it was between 3:00 a.m. and 7:30 a.m. on Monday.

The only region allowed by both is the overlap, 6 p.m. and 7:30 p.m. on Tuesday. The train's departure time has to be within that region, and everything in that region is after 4:00 pm and before 8:00 pm, so we can give a definitive "yes" to the prompt question. Because we can give a definitive answer, we must have

sufficient information.

Both statements sufficient together but not separately. OA =

(C) Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)