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CAT Standard Multiple-choice Question Papers 05 |
Speed, Time and Distance
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
60 km/hr
90 km/hr
120 km/hr
135 km/hr
Ans : C
Two trains, 200 and 160 meters long take a minute to cross each other while traveling in the same direction and take only 10 seconds when they cross in opposite directions. What are the speeds at which the trains are traveling?
21 m/s; 15 m/s
30 m/s; 24 m/s
18 m/s; 27 m/s
15 m/s; 24 m/s
Ans : A
An express train traveling at 72 km/hr speed crosses a goods train traveling at 45 km/hr speed in the opposite direction in half a minute. Alternatively, if the express train were to overtake the goods train, how long will it take to accomplish the task. Assume that the trains continue to travel at the same respective speeds as mentioned in case 1.
Cannot be determined
30 seconds
150 seconds
130 seconds
Ans : D
A train travels at an average speed of 90 km/hr without any stoppages. However, its average speed decrease to 60km/hr on account of stoppages. On an average, how many minutes per hour does the train stop?
12 minutes
18 minutes
24 minutes
20 minutes
Ans : D
Two trains A and B start simultaneously from stations X and Y towards each other respectively. After meeting at a point between X and Y, train A reaches station Y in 9 hours and train B reaches station X in 4 hours from the time they have met each other. If the speed of train A is 36 km/hr, what is the speed of train B?
24 km/hr
54 km/hr
81 km/hr
16 km/hr
Ans : B
A man moves from A to B at the rate of 4 km/hr. Had he moved at the rate of 3.67 km/hr, he would have taken 3 hours more to reach the destination. What is the distance between A and B?
33 kms
132 kms
36 kms
144 kms
Ans : B
A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards the shore at a speed of 8 km/hr. However, the ship can stay afloat only for 20 minutes. If a rescue vessel were to leave from the shore towards the ship, and it takes 4 minutes to evacuate the crew and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully rescue the people aboard the ship?
53 km/hr
37 km/hr
28 km/hr
44 km/hr
Ans : B
A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven 25% faster on an average he would have reached 4 minutes earlier than the scheduled time. How far is his office?
24 km
72 km
18 km
Data Insufficient
Ans : C
When an object is dropped, the number of feet N that it falls is given by the formula N = ½gt2 where t is the time in seconds from the time it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?
64.4
96.6
161.0
257.6
Ans : D
If the wheel of a bicycle makes 560 revolutions in travelling 1.1 km, what is its radius?
31.25 cm
37.75 cm
35.15 cm
11.25 cm
Ans : A
Probability
A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?
17/30
2/5
11/30
4/15
Ans : B
What is the probability of getting at least one six in a single throw of three unbiased dice?
1 / 6
125 / 216
1 / 36
91 / 216
Ans : D
What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?
2 / 15
4 / 15
1 / 15
4 / 90
Ans : B
A man bets on number 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the number 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes? (Roulette has numbers 1 to 36)
16; 22 : 14
12; 72 : 1
12; 7 : 1
Either; 35 : 1
Ans : D
Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
1 / 18
64 / 4032
63 / 64
1 / 9
Ans : A
When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?
5 / 6
11 / 12
1 / 6
1 / 12
Ans : B
When 4 dice are thrown, what is the probability that the same number appears on each of them?
1/36
1/18
1/216
1/5
Ans : C
An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?
0
(2/3)^4
5*((2/3)^4)*(1/3)
((2/3)^4)*(1/3)
Ans : C
An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?
0.084
0.916
0.036
0.964
Ans : A
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
18 days
27 days
26.67 days
16 days
Ans : A
Miscellaneous
Which amongst the following investments has the lowest return?
a. 7% Rs.100 shares at Rs.120
b. 8% Rs.10 shares at 13.50
c. 9% Rs.50 shares at Rs.54
a
b
c
a and c
Ans : A
The classic problem of a monkey and the greased flag pole . The height of a certain flag pole is 30 feet. Grease is applied to the pole. A monkey attempts to climb the pole. It climbs 3 feet every second but slips down 2 ft in the next second. When will the monkey reach the top of the flag pole?
56 secs
27 secs
60 secs
55 secs
Ans : D
How many squares can be formed using the checkered 1 * 1 squares in a normal chessboard?
64
204
1296
65
Ans : B
Solve for real 'x' if :
x > 9
0 < x < 9
x < 0
None of these
Ans : B
If log 2 = 0. 3010, then find how many digits are contained in the number 256.
15
16
17
Cannot be determined
Ans : C
A gentleman buys every year Bank's cash certificates of value exceeding the last year's purchase by Rs. 300. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 83,000. Find the value of the certificates purchased by him in the 13th year.
Rs. 4900
Rs. 6900
Rs. 1300
None of these.
Ans : A
From the following choices what is the equation of a line whose x intercept is half as that of the line 3x + 4y = 12 and y intercept is twice as that of the same line.
3x + 8y = 24
8x + 3y = 24
16x + 3y = 24
3x + y = 6
Ans : D
Pipe A can fill a tank completely in 5 hours. However, on account of a leak at the bottom of the tank, it takes 3 more hours to fill the tank. How long will the leak take to empty a full tank, when pipe A is shut?
13 hours 20 minutes
7.5 hours
14 hours 40 minutes
None of these
Ans : A
The sum of the first 50 terms common to the series 15,19,23 ... and 14,19,24 ... is
25450
24550
50900
Cannot be determined
Ans : A
For what values of 'x' will the function be defined in the real domain?
-10 < x < 4
4 < x < 10
x does not lie between the closed interval 10 and 4
x does not lie between the open interval 4 and 10
Ans : D
Quantitative Ability : Miscellaneous
Find the sum of all the integers which are multiples of 7 and lie between 200 and 400.
8729
8700
8428
None of these
Ans : A
How many digits will the number 3 200 have if the value of log 3 = 0.4771?
95
94
96
None of these
Ans : C
A and B enter in to a partnership and A invests Rs. 10,000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If B receives Rs.9600 as his share of the total profit of Rs.19,100 for the year, how much did B invest in the company?
12,000
96,000
8000
6000
Ans : C
The sum of the first and the 9th of an arithmetic progression is 24. What is the sum of the first nine terms of the progression?
216
108
54
None of these
Ans : B
What is the equation of the line that is parallel to the line 3x + 7y = 10 and passes through the point (4, 8)
7x - 3y = 46
3x + 7y = 44
9x + 21y - 184 = 0
3x + 7y = 68
Ans : D
Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?
36 days
14 days
29 days
Cannot be determined.
Ans : C
Ram buys Rs.100 shares at Rs.112. If he sells the shares after a year at Rs.132 after receiving a dividend of 8% just before selling, what is the net yield on his investment?
17.85%
6.06%
32%
25%
Ans : D
The sum of 20 terms of the series 12 + 22, 32 + 42, 52 + 62 is:
210
519
190
None of these.
Ans : A
A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?
2
4
6
5
Ans : B
If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?
20 days
40 days
30 days
24 days
Ans : C
Profit and Loss
A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?
33.33%
75%
300%
150%
Ans : C
A merchant buys two articles for Rs.600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?
Rs. 404.80
Rs. 440
Rs. 536.80
Rs. 160
Ans : A
A trader professes to sell his goods at a loss of 8% but weights 900 grams in place of a kg weight. Find his real loss or gain per cent.
2% loss
2.22% gain
2% gain
None of these
Ans : B
Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?
Rs. 40
Rs. 45
Rs. 36
Rs. 28
Ans : A
A trader buys goods at a 19% Aount on the label price. If he wants to make a profit of 20% after allowing a Aount of 10%, by what % should his marked price be greater than the original label price?
+8%
-3.8%
+33.33%
None of these
Ans : A
If apples are bought at the rate of 30 for a rupee. How many apples must be sold for a rupee so as to gain 20%?
28
25
20
22
Ans : B
One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and recieves Rs. 120 and a shirt. Then find the price of the shirt.
Rs. 80
Rs. 100
Rs. 120
Cannot be determined
Ans : C
Two merchants sell, each an article for Rs.1000. If Merchant A computes his profit on cost price, while Merchant B computes his profit on selling price, they end up making profits of 25% respectively. By how much is the profit made by Merchant B greater than that of Merchant A?
Rs.66.67
Rs. 50
Rs.125
Rs.200
Ans : B
A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?
25%
50%
100%
66.67%
Ans : C
A merchant marks his goods up by 75% above his cost price. What is the maximum % Aount that he can offer so that he ends up selling at no profit or loss?
75%
46.67%
300%
42.85%
Ans : D
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