1. The total number of digits used in numbering the pages of a book having 366 pages is
a) 732
b) 990
c) 1098
d) 1305
Explanation: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.
2. In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family ?
a) 2
b) 3
c) 4
d) 5
Explanation: Let d and s represent the number of daughters and sons respectively.
Then, we have :
d - 1 = s and 2 (s - 1) = d.
Solving these two equations, we get: d = 4, s = 3.
3. At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ?.
a) 60
b) 65
c) 90
d) None of these
Explanation:
4. 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 ?
a) 23 years
b) 25 years
c) 33 years
d) 35 years
Explanation: Ayush's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years
5. A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly ?
a) 12
b) 16
c) 18
d) 24
Explanation: Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 48 ⇔ 3x = 48 ⇔ x = 16.
6. A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
a) 2
b) 3
c) 6
d) 12
Explanation: Since B and D are twins, so B = D.
Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3 ⇔ D + 3 = C-3 ⇔ C - D = 6.
7.The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?
a) 15
b) 29
c) 61
d) None of these
Explanation: Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 29.
8. In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
a) 20 m
b) 22 m
c) 24 m
d) 26 m
Explanation: Each row contains 12 plants.
There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.
Therefore Length = (22 + 2) m = 24 m.
9. 12 year old Manick is three times as old as his brother Rahul. How old will Manick be when he is twice as old as Rahul ?
a) 14 years
b) 16 years
c) 18 years
d) 20 years
Explanation: Let Manick be twice as old as Rahul after x years from now.
Then, 12 + x = 2 (4 + x) ⇔ 12 + x = 8 + 2x ⇔ x = 4.
Hence, Manick's required age = 12 + x = 16 years.
10. 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 ?
a) 32 rolls
b) 54 rolls
c) 108 rolls
d) 120 rolls
Explanation: Number of cuts made to cut a roll into 10 pieces = 9.
Therefore Required number of rolls = (45 x 24)/9 = 120.
11. In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
a) 6
b) 12
c) 18
d) 24
Explanation: Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.
12. A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
a) 12
b) 15
c) 18
d) 20
Explanation: Let son's age be x years. Then, father's age = (3x) years.
Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.
So, 3x - 5 = 4 (x - 5) ⇔ 3x - 5 = 4x - 20 ⇔ x = 15.
13. A waiter's salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips ?
a) 4/9
b) 5/4
c) 5/8
d) 5/9
Explanation:
14. If you write down all the numbers from 1 to 100, then how many times do you write 3 ?
a) 11
b) 18
c) 20
d) 21
Explanation: Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 10 + 10 = 20.
15. If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?
a) 1 day
b) 4 days
c) 40 days
d) 100 days
Explanation:
16. Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What fraction of the bill did Veena pay ?
a) 1/3
b) 3/11
c) 12/13
d) 5/8
Explanation:
17. In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements ?
a) Only 20% of the total members own three cars each
b) 48% of the total members own only one car each.
c) 60% of the total members own at least two cars each.
d) 80% of the total members own at least one car.
Explanation: Let total number of members be 100,
Then, number of members owning only 2 cars = 20.
Number of members owning 3 cars = 40% of 80 = 32.
Number of members owning only 1 car = 100 - (20 + 32) = 48.
Thus, 48% of the total members own one car each.
18. When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
a) 7 years
b) 10 years
c) 14 years
d) 19 years
Explanation:When Rahul was born, his brother's age = 6 years;
His father's age = (6 + 32) years = 38 years,
His mother's age = (38 - 3) years = 35 years;
His sister's age = (35 - 25) years = 10 years.
19. A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there ?
a) 10
b) 12
c) 14
d) 16
Explanation:et number of horses = number of men = x.
Then, number of legs = 4x + 2 x (x/2) = 5x.
So, 5X = 70 or x = 14.
20. 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 ?
a) 32 years, 23 years
b) 32 years, 29 years
c) 35 years, 29 years
d) 35 years, 33 years
Explanation: When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.
Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.
21. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
a) 19
b) 28
c) 30
d) 37
Explanation:
22. I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
a) 25
b) 37
c) 54
d) 65
Explanation: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.
23. If a clock takes seven seconds to strike seven, how long will it take to strike ten ?
a) 7 seconds
b) 9 seconds
c) 10 seconds
d) None of these
Explanation:
24. In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is
a) 5
b) 7
c) 10
d) 12
Explanation: Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 14 ⇔ 4x + 2y = 2x + 2y + 14 ⇔ 2x = 14 ⇔ x = 7.
25. A father tells his son, "I was of your present age when you were born". If the father is 36 now, how old was the boy five years back ?
a) 13
b) 15
c) 17
d) 20
Explanation: Let the father's age be x and the son's age be y.
Then, x - y = y or x = 2y,
Now, x = 36. So, 2y = 36 or y = 18.
Therefore Son's present age = 18 years.
So, son's age 5 years ago = 13 years.
26. A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is
a) 2
b) 3
c) 4
d) Data inadequate
Explanation:
27. A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is
a) 23 years
b) 34 years
c) 45 years
d) None of these
Explanation: Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then, woman's age = (10X + y) years; husband's age = (10y + x) years.
Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)
⇔ (9y-9x) = (1/11)(11y + 11x) = (x + y) ⇔ 10x = 8y ⇔ x = (4/5)y
Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.
28. A girl counted in the following way on the fingers of her left hand : She started by calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5 and then reversed direction calling the ring finger 6, middle finger 7 and so on. She counted upto 1994. She ended counting on which finger ?
a) Thumb
b) Index finger
c) Middle finger
d) Ring finger
Explanation: Clearly, while counting, the numbers associated to the thumb will be : 1, 9,17, 25,.....
i.e. numbers of the form (8n + 1).
Since 1994 = 249 x 8 + 2, so 1993 shall correspond to the thumb and 1994 to the index finger.
29. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
a) 45
b) 60
c) 75
d) 90
Explanation: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 480 ⇔ 16x = 480 ⇔ x = 30.
Hence, total number of notes = 3x = 90.
30. What is the product of all the numbers in the dial of a telephone ?
a) 1,58,480
b) 1,59,450
c) 1,59,480
d) None of these
Explanation: Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.