Tata Steel Management Trainee Sample Paper Problems

Couple of quick and simple questions on areas I haven't studied in detail. I would appreciate it if you could provide a few methods to calculate the solutions. Thanks in advance.

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11.N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N?
A. 4
B. 3
C. 6
D. 5
(Solved)

12.A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?
A. 156
B. 199
C. 211
D. 231
(Solved)

15.The ratio of two numbers is 4 : 5. If the HCF of these numbers is 6, what is their LCM?
A. 30
B. 60
C. 90
D. 120
(Solved)

19.A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road?
A. 5 m
B. 4 m
C. 2 m
D. 3 m
(Solved)

21.The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
A. 18 cm
B. 16 cm
C. 22 cm
D. 20 cm
(Solved)

23. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, what was the son’s age five years back?
A. 20 years
B. 18 years
C. 14 years
D. 22 years
(Solved)

24. Six years ago, the ratio of the ages of Vimal and Saroj was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Saroj’s age at present?
A. 18
B. 17
C. 16
D. 15
(Solved, this question was bull)

25. Sobha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A. 6 years
B. 5 years
C. 4 years
D. 3 years
(Solved)

26. The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. What is father’s present age?
A. 30 years
B. 31 years
C. 32 years
D. 33 years
(Solved)

28. A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
A. 38 sec
B. 35 s
C. 44 sec
D. 40 s
(Solved)

29.A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
A. 79.2 km/hr
B. 69 km/hr
C. 74 km/hr
D. 61 km/hr
(Solved)
30.Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
A. 10.30 a.m
B. 10 a.m.
C. 9.10 a.m.
D. 11 a.m.
(Solved)

(edited 9 years ago)

Reply 1

atsruser

Original post by Ocelot60

Couple of quick and simple questions on areas I haven't studied in detail.

There are more than a couple here. No one is going to do all this work for you.

12.A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?

This is poorly worded. I guess it means that there is a largest number found to give the same remainder, and no larger number does so.

Hint: Suppose the largest number is

x

. Now express 7654, 8506, and 9997 in quotient/remainder form via the division theorem, and then figure out what

x

is the HCF of.

Reply 2

Ocelot60

Original post by atsruser

There are more than a couple here. No one is going to do all this work for you.

This is poorly worded. I guess it means that there is a largest number found to give the same remainder, and no larger number does so.

Hint: Suppose the largest number is

x

. Now express 7654, 8506, and 9997 in quotient/remainder form via the division theorem, and then figure out what

x

is the HCF of.

I'm not asking anyone to give me the answers, I'm just asking for methods for a few quick 1 mark questions that I can't afford to spend more than a minute on each.

I used your method on question 12 and indeed got the answer of B, thanks. The HCF was 213. These questions are rather simple once you get the gist. I just... Don't quite have the gist on these particular.

(edited 9 years ago)

Reply 3

brianeverit

Original post by Ocelot60

Couple of quick and simple questions on areas I haven't studied in detail. I would appreciate it if you could provide a few methods to calculate the solutions. Thanks in advance.

------------------------------------------------------------------------------------------------
11.N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N?
A. 4
B. 3
C. 6
D. 5
(Solved)

12.A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?
A. 156
B. 199
C. 211
D. 231
(Solved)

15.The ratio of two numbers is 4 : 5. If the HCF of these numbers is 6, what is their LCM?
A. 30
B. 60
C. 90
D. 120
(Solved)

19.A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road?
A. 5 m
B. 4 m
C. 2 m
D. 3 m

21.The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
A. 18 cm
B. 16 cm
C. 22 cm
D. 20 cm

23. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, what was the son’s age five years back?
A. 20 years
B. 18 years
C. 14 years
D. 22 years

24. Six years ago, the ratio of the ages of Vimal and Saroj was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Saroj’s age at present?
A. 18
B. 17
C. 16
D. 15

25. Sobha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A. 6 years
B. 5 years
C. 4 years
D. 3 years

26. The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. What is father’s present age?
A. 30 years
B. 31 years
C. 32 years
D. 33 years

28. A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
A. 38 sec
B. 35 s
C. 44 sec
D. 40 s

29.A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
A. 79.2 km/hr
B. 69 km/hr
C. 74 km/hr
D. 61 km/hr

30.Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
A. 10.30 a.m
B. 10 a.m.
C. 9.10 a.m.
D. 11 a.m.
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Answers: (Highlight to reveal)
11: A
12: B
15: D
19: D
21: A
23: C
24: B
25: C
26: A1: A

28: C
29: D
30: A

The test has a 90 minute time limit and 60 questions in total.

Do you just mean numbers 19 & 21 since they are the only ones involving area?
If so
19 Total area of paths=60x+40x-x^2 where mx is the width of the path, which must equal 291.
Solve for x.
20. Original area=2x^2 (If beeadth is x) New area=(2x-5)(x+5) equate difference to 75 and solve.
Incidentally the given answer is incorrect.

Reply 4

Ocelot60

Original post by brianeverit

I thought there was something 'off' about this paper, some of the answers are incorrect. Question 31-60 is nearly completely wrong too. I'll give this a try in a moment, thanks for your input.

Oh, I didn't just mean 19 and 21, my bad.

(edited 9 years ago)

Reply 5

Ocelot60

Okay, that's 19 and 21 complete, thanks.

Though, I find question 19 to be a little bothering. This is what I had originally.
Park Area = 2400
Lawn Area = 2109
Road Area = 291

291/60 = 4.85

This was because I had assumed the roads went straight down the middle of the park, therefore having the same length as the park itself; 60.

Quick question, how was this equation derived?

291 = 60x + 40x - x^2

With a bit of quick trial and error, the answer is obviously 3, but how would one piece together such an equation?

Reply 6

Ocelot60

Okay, this is ridiculous, turns out I was correct on most questions, the answers are just WRONG.

Thanks for the help on the few questions I wasn't so sure about.

/thread