Data Sufficiency

In the following questions each question is followed by three statements I, II and III. Read the question and the statements carefully and choose your answer according to which set of statement(s) is/are sufficient to answer the question.

6.What is the present age of Rakesh? 
I.The ratio of the ages of Ramesh and Rakesh, three years ago, was 4 : 5. 
II.The ratio of the ages of Rajesh and Rakesh, after two years, will be 4 : 5. 
III.Two years ago the ratio of the ages of Rajesh and Ramesh was 12 : 13.

1 : I and II only

2 : II and III only

3 : I and III only

4 : All I, II and III

5 : None of these

7.What is the length of the train travelling at uniform speed? 
I.The train crossed a bridge of length 400 m in 35 seconds. 
II.The train overtook a man riding a motor bike at a speed of 54 kmph in one minute. 
III.The train crossed another train moving in the opposite direction in 16 seconds.

1 : I and II only

2 : II and III only

3 : I and III only

4 : All I, II and III

5 : None of these

8.In how many days can two men and three women, together, complete the work? I.Three men and three women can complete the work in eight days. 
II.The ratio of efficiencies of a man, a woman and a boy is 15 : 10 : 8. 
III.A boy takes 15 days more than a woman to complete the work.

1 : I and II only

2 : II and III only

3 : Any two of the three statements

4 : All I, II and III

5 : None of these

9.What is the cost of three kg of rice and two kg of wheat together? 
I.The cost of four kg of rice, five kg of wheat and three kg of sugar together is Rs.416. 
II.The ratio of prices of one kg of rice to that of wheat is 2 : 3. 
III.The cost of seven kg of rice, seven kg of wheat and three kg of sugar, together, is Rs.608

1 : I and II only

2 : I and III only

3 : II and III only

4 : Any two of the three

5 : None of these

10.How many men watched the show in the auditorium? 
I.The ratio of the number of men to the number of women who watched the show is 7 : 5. 
II.Had there been 12 more men, the ratio of the number of the men to the number of women who watched the show would be 3 : 2. 
III.The capacity of the auditorium is 300.

1 : I and II only

2 : II and III only

3 : I and III only

4 : All I, II and III

5 : None of these

Cube roots of perfect cubes

Here are eight poets, namely, A, B, C, D, E, F, G and H in respect of whom questions are being asked in the examination. The first four are ancient poets and the last four are modern poets. The question on ancient and modern poets is being asked in alternate years. Those who like H also like G, those who like D like C also. The examiner who sets question is not likely to ask question on D because he has written an article on him. But he likes D. Last year a question was asked on F. Considering these facts, on whom the question is most likely to be asked this year? 

a. B
b. C
c. D
d. G

Points to remember  for speedy  calculation of cube roots of perfect cubes

1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of 1 to 10 which is given below.

1³	=	1
2³	=	8
3³	=	27
4³	=	64
5³	=	125
6³	=	216
7³	=	343
8³	=	512
9³	=	729
10³	=	1000

2. From the above cubes of 1 to 10, we need to remember an interesting property.

1³	=	1	=>	If the last digit of the perfect cube = 1, the last digit of the cube root = 1
2³	=	8	=>	If the last digit of the perfect cube = 8, the last digit of the cube root = 2
3³	=	27	=>	If the last digit of the perfect cube = 7, the last digit of the cube root = 3
4³	=	64	=>	If the last digit of the perfect cube = 4, the last digit of the cube root = 4
5³	=	125	=>	If the last digit of the perfect cube =5, the last digit of the cube root = 5
6³	=	216	=>	If the last digit of the perfect cube = 6, the last digit of the cube root = 6
7³	=	343	=>	If the last digit of the perfect cube = 3, the last digit of the cube root = 7
8³	=	512	=>	If the last digit of the perfect cube = 2, the last digit of the cube root = 8
9³	=	729	=>	If the last digit of the perfect cube = 9, the last digit of the cube root = 9
10³	=	1000	=>	If the last digit of the perfect cube = 0, the last digit of the cube root = 0

Time and Distance – Trains

1. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
   A.310 m
   B.350 m
   C.600 m
   D.490 m
   E.None of these
   
   Answer

   Answer – B (350 m)
   Explanation – when it cross a pole actually it is crossing itself
   so, S = 300/18
   let length of platform be “p”
   relative speed = total lengths/time
   speed of train = [300 + p ]/39
   (300/18)x39=300 +p
   650 -300=p
   p=350 m
   Note : in this type of question one thing is pole,man and other is of considerable length like platform ,bridge.
   when train crosses pole,man it crosses itself

2.Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A.1 : 3
B.3 : 4
C.3 : 2
D.Data inadequate
E.None of these

Answer

Answer – C (3 : 2)
Explanation – Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
relative speed = total lengths/time
y – x = [27x + 17 y ]/23
23y -23x = 27x + 17 y
27x+23x= 23 y-17y
4x=6y
x/y=6/4=3/2= 3:2

3.Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
A. 1: 2
B. 4 : 3
C. 7 : 8
D. 3 : 4
E. none of these

Answer

Answer- B (4:3)
Explanation:
Let us name the trains as A and B. Then,
trick formula
(A’s speed) : (B’s speed) = square root of b : square-root of a =square-root of 16 : square-root of 9 = 4 : 3.

Arithmetical Reasoning

1.A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes ?
32 rolls 54 rolls 108 rolls 120 rolls

2.Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?
20 years 22 years 25 years 27 years

3.Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?
23 years 25 years 33 years 35 years

4.In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
18 36 45 None of these

5.Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?
32 years, 23 years 32 years, 29 years 35 years, 29 years 35 years, 33 years

Classification

1.Find the odd one out
crusade campaign expedition cruise

2.Find the odd one out
Flower : Petal Circle : Arc Cover : Page Chair : Leg

3.Choose the number pair/group which is different from others?
7:22 12:37 8:33 15:46

4.Choose the number which is different from others in the group?
64 162 27 144

5.Choose out the odd one
Lion Bear Cheetah Leopard

Time and Distance

1. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
   A.9 : 28
   B.11 : 9
   C.11 : 8
   D.9 : 22
   E.None of these
   
   Solution

   Answer – B (11 : 9)
   Explanation – In the same time, they cover 110 km and 90 km respectively.Ratio of their speeds = 110 : 90 = 11 : 9

2. A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m.?
A.15
B.8
C.7
D.10
E.None of these

Solution

Answer – C (7)
Explanation – Relative speed = (2 + 3) = 5 rounds per hourSo, they cross each other 5 times in an hour and 2 times in half an hourHence, they cross each other 7 times before 9.30 a.m.

3.The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
A.10:30 am
B.10:45 am
C.11 am
D.11:25 am
E.None of these

Solution

Answer – C (11 am)
Explanation – Suppose they meet x hrs after 8 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330
60x + 75(x – 1) = 330
x = 3
So, they meet at (8 + 3), i.e. 11 a.m

4.The speed of a car increases by 2 kms after every one hour. If the distance travelled in the first one hour was 35 kms, what was the total distance traveled in 12 hours?
A.456 kms
B.482 kms
C.552 kms
D.556 kms
E.None of these

Solution

Answer – C (552 kms)
Explanation – Total distance travelled in 12 hours = (35 + 37 + 39 + …… upto 12 terms) This is an A.P. with first term,
a = 35, number of terms, n = 12, common difference, d =2.
Required distance =12/2 (2 x 35 + (12 – 1) x 2) = 6(70 + 22) = 552 kms

5.A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
A.100 m
B.150 m
C.190 m
D.200 m
E.None of these

Solution

Answer- A(100m)
Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =[(1/60)*6] km = (1/10)km = 100 m.
Distance between the thief and policeman = (200 – 100) m = 100 m.

Alphabet Test

1.A B C D E F G H I J K L M N O P Q R S T U V W X Y Z . Which letter in this alphabet is the eighth letter to the right of the letter and which is tenth letter to the left of the last but one letter of the alphabet?
X W I H

2.From the word 'LAPAROSCOPY' how many independent meaningful words can be made without changing the order of the letters and using each letter only once ?
3 4 1 2

3.How many pairs of letters are there in the word " CASTRAPHONE" which have as many letters between them in the word as in the alphabet?
2 3 4 5

4.If the first and second letters in the word DEPRESSION' were interchanged, also the third and the fourth letters, the fifth and the sixth letters and so on, which of the following would be the seventh letter from the right ?
R O S P

5.What should come next in the following letter sequence?A A B A B C A B C D A B C D E A B C D
A E C B

Partnership Quiz

1.A starts business with Rs. 7000 and after 5 months, B joins with A as his partner. After 1 year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital?
A)Rs 13000
B)Rs 12000
C)Rs 15000
D)Rs 18000
None of these
Answer – D (Rs 18000)
Explanation –
Let B’s capital be Rs. x. Then.
(7000 x 12) / 7x = 2/3 [ capital ratio= profit ratio] 14x = 252000 x = 18000

2.shikha started a business investing Rs. 50,000 in 1999, In 2000, she invested an additional amount of Rs. 20,000 and Raju joined him with an amount of Rs. 70,000. In 2001, Shikha invested another additional amount of Rs. 20,000 and Jolly joined them with an amount of Rs. 70,000. What will be Raju’s share in the profit of Rs. 300,000 earned at the end of 3 years from the start of the business in 1999?
A)Rs Rs. 250,000.
B)Rs Rs. 120,000.
C)Rs Rs. 100,000.
D)Rs Rs. 150,000.
E)None of these
Answer – C (Rs. 100,000)
Explanation –
Shikha : Raju : Jolly
= (50000 x 12 + 70000 x 12 + 90000 x 12) : (70000 x 24) : (70000 x 12)
= 2520000 : 1680000 : 840000 = 3 : 2 : 1
Raju’s share = Rs.300,000 x 2/6 = Rs. 100,000.

3.A, B and C started a business. They invest Rs. 80,000, Rs. 160,000 and Rs. 2,40,000 respectively. At the end of the first year, B withdraws Rs. 80,000, while at the end of the second year, C withdraws Rs. 160,000. In what ratio will the profit be shared at the end of 3 years?
A)2:3:4
B)3:4:7
C)3:2:5
D)3:1:4
E)None of these
Answer – D (3:4:7)
Explanation – A : B : C = (80000 x 36) : (160000 x 12 + 80000 x 24)
(240000 x 24 + 80000 x 12) =144 : 192 : 336 = 3: 4 : 7