Quant Boosters  Shashank Prabhu, CAT 100 Percentiler  Set 8

Number of Questions  30
Topic  Quant Mixed Bag
Solved ? : Yes
Source : Learningroots forum

Q1) Anirudh wants to have his bath in a bathtub. There are two taps, one for hot water and one for cold water. Both the taps can individually fill the bathtub in 15 minutes. He opens both the taps simultaneously but after 6 minutes he closes the cold water tap. He lets the hot water tap run until the bathtub fills up. The temperature of the hot water is 50° and of the cold water is 25°. How many degrees is the temperature of the water in the bathtub? Assume that no heat is lost to the surrounding atmosphere.

Capacity = 15 units. So, 9 units hot water and 6 units cold water. (9 * 50 + 6 * 25)/15 = 40°.

Q2) Cocktail A contains vodka, whisky and rum in the ratio of 1 : 2 : 3 and cocktail B contains the same in the ratio of 3 : 4 : 5. A cocktail C is made by mixing the two cocktails in a certain ratio. Which of the following is an obtainable ratio of vodka, whisky and rum in the new cocktail?
a) 2 : 5 : 8
b) 3 : 5 : 7
c) 5 : 6 : 7
d) 7 : 9 : 11

Vodka will be between 2/12 and 3/12 (between 0.167 and 0.25). The only option that satisfies this is option b.

Q3) Mr. Baker runs a bakery shop. One day he made some cakes of different weights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?

100 kg total weight. Heaviest two – 12.5 kg average, lightest 5 – 9 kg average. Remaining cakes – 30 kg total. Also, as the average of the 9 < 30/x < 12.5. So, x = 3.

Q4) The arithmetic mean of a set of 20 observations is X. When three of the twenty observations, 12, 19 and 74 are discarded, the mean of the new set remains unchanged. What is the arithmetic mean, X?

20X – 105 = 17X
X = 35.

Q5) An alloy has 35% of A, 40% of B and 25% of C. In each processing step, the percentage of A and B reduces by 20% and 10% respectively and the percentage of C increases. The weight of the alloy does not change. The process stops only when the percentages of A and B become less than 25% and 33.33% respectively. What is the percentage of C at that time?

A becomes 4/5th of actual and B becomes 9/10th of actual. After the first iteration, it becomes 28, 36, 36. After the second iteration, it becomes 22.4, 32.4, 45.2. So, it will stop after 2 iterations and the percentage of C will be 45.2

Q6) A car moves with a speed of 90 km/hr with a fuel tank capacity of 100 liters. The mileage of the car is 20 km per litre without switching on the A.C. and 15 km per litre with the A.C. on. The car, with its tank filled to capacity, has to cover a distance of 1600 km without refuelling. What is the distance(in km) that the car can travel with the A.C. switched on?

a + b = 100
20a + 15b = 1600; 4a + 3b = 320
b = 80 liters. So, 15 * 80 = 1200 km.

Q7) A building is to be completed within 40 days. 40 workers started the work, each worker working 8 hours a day. After 25 days, 40% of the work is completed. How many additional workers should be added to the workforce so that the work is completed on time with each worker working for 10 hours a day?

400 units to be done. In 25 days, 160 units completed. Every day, 160/25 units done by 40 workers over 8 hours. So, 1/50 units per worker per hour. In 10 hours, 1/5 units done by each worker. 240 units to be done in 15 days. So, 16 units per day and so, 80 workers needed in total. So, 40 more workers will be added.

Q8) In a big corporate multinational firm, the employees volunteer to contribute a part of their salary for the prime minister's relief fund for flood victims. The executives each contribute Rs. 4,000 to the fund while the managers contribute twice as much. If the strength of the firm, comprising just of managers and executives, is 1000 and the net collection for the relief fund is Rs. 44,00,000; which of the following statements is true?
a. The contribution by managers is more than that by the executives by Rs. 28,00,000
b. The contribution by managers is more than that by the executives by Rs. 44,00,000
c. The contribution by managers is less than that by the executives by Rs. 28,00,000
d. The contribution by managers is less than that by the executives by Rs. 16,00,000

m + e = 1000
8000m + 4000e = 4400000
2m + e = 1100
m = 100, e = 900
Contribution by managers = 800000, contribution by executives = 3600000.
Difference is Rs. 28,00,000.

Q9) A and B are athletes. A covers a distance of 1 km in 5 minutes and 50 seconds, while B covers the same distance in 6 minutes and 4 seconds. If both of them start together and run at uniform speed, approximately by what distance will A win a 5 km marathon.
a. 220 m
b. 247 m
c. 192 m
d. 157 m

A: 1 km in 350 seconds, 5 km in 1750 seconds
B: 1 km in 364 seconds, in 1750 seconds, B will cover 4.81 km. So, A wins by approximately 192 m. Option c

Q10) Saatwik drives his car from his house to the station and picks up Seema from there every day at 7.00 p.m. and then they go to the coffeehouse. The coffeehouse is between Saatwik’s house and the station, on the road joining these two places. One day, she reached the station at 6.00 p.m. and instead of waiting for him at the station, she started walking at a speed of 10 km/hr. Saatwik left his house at the usual time and picked her up on his way to the station. If they reached the coffeehouse 20 minutes earlier than usual, what is the speed of Saatwik’s car? (in km/hr)