Question of the Day - 2nd August, 2009

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Question of the Day - 2nd August, 2009

by quant-master » Sun Aug 02, 2009 11:03 am
Question 1:
Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 2:
baseball' world series matches 2 teams against each other in a best of 7 games. The first team to win four games wins the series and no subsequent games are played. If you have no special info about either of teams what is the probability that the world series will consist of fewer than 7 games?

a. 12.5
b. 25
c. 31.25
d. 68.75
e. 75

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by real2008 » Fri Aug 07, 2009 9:42 am
anybody to answer qn2?

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by quant-master » Fri Aug 07, 2009 9:43 pm
Soln to Question.1:

without looking at the statements try to solve the problem....
by simple speed distance time equations...you would get a quadratic equation...
Solving you wud get d = 150 miles or 133.33 miles.
that is two probable answers....for these two values you will get two times....

when d =150, Train A 4:30 and train B 4:20
or you could have
when d=133.33 miles, train A 4:20 and train B 4:30....since it is a quadratic expression...

now this is where DS comes in...till here it was a PS.

from statement 1...you could pick one answer....150 miles...and time Train B arrive in New York is 4:20

from statement 2....simply trainB arrives at 4:20

So answer is D....either suffices.

Soln to Question.2:

The cases in which there will be 7 matches is when in the first 6 games both teams have won 3 each. In all other cases there will be less than 7 matches. Hence the last match doesnt matter really. The total number of ways in which 6 matches can result is 2^6 = 64 ways. The ways in which the first 6 games can be won 3 each is 6 C 3 = 20. Hence required probablity is (64 - 20) * 100 / 64 = 68.75.

Hence D.

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https://gmat-quants.blocked - My Blog Updated almost daily with new quant fundas. Find collection of quants question in my blog