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.