PS Quant doubt questions

Hi,

Please help with these questions-

Ratio and Proportion-
1. 5 cups of equal capacity contain water in the ratio 2 : 3 : 4 : 5 : 6. If total
water in these cups equal 40% of their total capacity, how many of the cups are
at least half filled?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

2.if p/q= 1/3; q/3= 2; r/s= 1/2; s/t= 1/3; and t/u= 1/4, what is pqr/stu ?

Distance Speed and Time-
Mr. Ghosh usually arrives at his office 15 min late. On a particular day, he
reduces his speed by 25% and hence arrives 45 min late instead. If Mr. Ghosh has
to reach office on time, by what percentage should he increase his usual speed?

Time Work Rate-
1. A and B can build a wall alone in 12 days and 20 days respectively, working 8
hr/day in two shifts, from 9 AM – 1 PM and then 2 AM – 6 PM. If the work is
started on Jan 1, on which day and at what time will the work be completed if
i. both of them work together on all days
ii. A works alone on Jan 1, followed by B alone on Jan 2, and cycle repeats
iii. B works alone on Jan 1, followed by A alone on Jan 2, and cycle repeats
iv. A is assisted by B in the first half every day, but leaves in the second half

2. A and B, working together, take 12 days to complete a work. B and C, working
together, take 20 days to complete the same work. C and A, working together, take
15 days to complete the same work. In how many days can A, B and C, working
together, complete the same work?

3. A can build an entire wall in 6 days. However, B the demolition man can break
the entire wall in 15 days. In how many days will the wall be built if
i. they work together
ii. A starts alone on first day and they continue to work alone on alternate days

4. 15 men can complete a construction work in 20 days. 5 days into the project,
10 more men who are equally efficient join the work. The project was completed
how many days before its scheduled date?

5. A team of 2 men and 5 women finish a work in 42 days. The same work is
done by a team of 3 men and 2 women in 50 days. How many women need to join
1 man in order to complete the same work in 75 days?

6. A team of 35 equally efficient men are scheduled to build a tunnel in certain
days, working 8 AM – 6 PM. They start on Jan 1. But each subsequent day, 1 man
leaves the team until the last man completes the tunnel working alone till EOD.
i. By what day and time was the tunnel scheduled to be built?
ii. On evening of Jan 6, a strict penalty of not showing to work is declared.
Hence, no man leaves. On what day and time will the tunnel be built?
iii. Post Jan 6, the project manager still wants to complete the project on time.
To achieve this, each man must increase his efficiency by what percentage
to the nearest integer?

Permutation and Combination-
1. How many 6-digit numbers have their digits either all odd or all even?
(A) 31,250 (B) 25,000 (C) 28,125 (D) 15,625 (E) 25,200

2. Devi wants to plan a party by inviting at least 4, but not more than 6 friends. If Devi has
a total of 9 friends, in how many ways can she plan the party?
(A) 252 (B) 90 (C) 336 (D) 216 (E) NOTA

3. Six couples are invited to play a game of cards, which needs 4 players at a time. In how
many ways can the players be selected, if no couple should be included?
(A) 256 (B) 384 (C) 240 (D) 320 (E) 60

4. A committee of 3 people needs to be formed by selecting from 7 men and 5 women.
What is the ratio of the number of all possible committees that have at least one man, to the
number of all possible committees that have at least one woman?
(A) 42 : 37 (B) 12 : 7 (C) 1 : 5 (D) 5 : 7 (E) NOTA

5. At an office party, a game is being played that needs a team of 4 people. There are 8
couples present, and the 4 people must be chosen from these 16 people so that no couple is
chosen in the team. In how many ways can the selection be made?
(A) 1,120 (B) 495 (C) 700 (D) 840 (E) 1,820

Probability-
1. The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will get an electric contract is 7/12. If the probability to get exactly one contract is 5/8, the probability that he does not get any contract is- ?

2. Two persons A and B roll a fair dice alternately, till one of them gets a 6. If
A makes the first roll, the probability that B wins is- ?