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.
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
a. 12.5
b. 25
c. 31.25
d. 68.75
e. 75
Discuss the answer using comment option.Answers will be posted in 24 hrs time
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Quant-Master
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Soln to Question.1:
ReplyDeletewithout 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:
ReplyDeleteThe 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.
Hi,
ReplyDeleteThanks very much for maintaining such a useful blog.
Regarding soluntion for question 1: I could not comprehend the explanation. Can you please provide a dummied down explanation for Question 1?
Thanks....
can you post the full solution for 1?
ReplyDeleteDetailed Explanation to question 1:
ReplyDeleteTrain 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?
Let me put this in another way
Let S be speed of train B.
When Train A and B meet Train A has traveled for 50 mins and Train B has traveled for 10 mins. In this one hour, since both starting from opposite end and making contact somewhere in the middle, both the trains combined should have travelled whole distance.
Hence
100*1+(10/60)*S = distance (I have just multiplied speed into time for both the trains)
above eqn can be simplified as (600+S)/6 = distance ---(1)
We know that time traveled by both the train combined is 2 hrs therefore sum of distance/speed for both the trains is 2 hrs
since distance =(600+s)/6 we can write down the below eqn
[(600+s)/6*100]+[(600+s)/6*S] = 2 (I have just divided distance/speed for both the trains)
after cross multiplication above expression comes down to
S^2-500s+60,000=0
Above expression can be written as (s-200)(s-300)=0
Hence S = 200 or 300
When S = 200 distance = 800/6 =133.33miles (I arrived at this after substituting s in eqn 1)
When S = 300 distance = 900/6 = 150 miles
Now lets take two statements
(1) Train B arrived in New York before Train A arrived in Boston.
This will happen only when S=300
(2) The distance between New York and Boston is greater than 140 miles.
We got two possible distance one below 140 and one above 140
Hence the distance is 150 miles
Hope this is clear
Thanks,
Quant-Master