Q1. The sum of remainders obtained on dividing 12112 by 11 and 13223 by 13 is
(a) 3
(b) 4
(c) 5
(d) 2
Sol.
On dividing, 12112 by 11, we get 1 as remainder
Sum of remainders 1 + 2 = 3
Q2. The difference between the place value of 6 and the face value of 4 in 56431 is
(a) 999
(b) 5600
(c) 5996
(d) 2054
Sol.
Place value of 6 in 56431 = 6000
Face value of 4 in 56431 = 4
∴ Required difference = 6000 – 4 = 5996
Q3. The product of the smallest common multiple and the biggest common factor of 30, 36 and 42 is
(a) 7460
(b) 7660
(c) 7650
(d) 7560
Sol.
Smallest common multiple of 30, 36 and 42 = 6
Biggest common factor of 30, 36 and 42
= 2 × 2 × 3 × 3 × 5 × 7 = 2160
∴ Required product = 2160 × 6 = 7560
Q4. When it is 8:49 pm, in Delhi, it is 1:19 am, on the next day in Sydney. What time will be in Sydney when it is 11:19 am in Delhi?
(a) 3:19 am
(b) 3:49 am
(c) 6:29 am
(d) 6:49 am
Sol.
When time in Delhi 8 : 49 pm, then it is 1 : 19 am is Sydney.
∴ Difference in time between Delhi and Sydney
= 8 : 49 pm – 1 : 19 am = 4 h 30 min
∴ Time is Sydney will be = 11 : 19 am to 4 : 30 = 3 : 49 pm
Q5. On a map, 1/2 cm shows 125 km on the ground. If two cities are actually 2000 km apart on the ground, then the distance between them on the map is
(a) 6 cm
(b) 8 cm
(c) 10 cm
(d) 4 cm
Ans. (b)
Sol.
According to question, 1/2 cm on a map = 125 km on the ground
⇒ If two cities are 2000 km apart on the ground,
Then the distance them on the map
=2000/125×1/2= 8 cm
Q6. There are 660 students in a school. Two-thirds of them are boys. Three-fourths of the number of boys are players and one-fourth of the girls are players. Total number of players in the school is
(a) 370
(b) 385
(c) 395
(d) 330
Sol.
Total number of students in the school = 660
Number of boys in school =2/3×660=440
∴ Number of girls of school = 660 – 440 = 220
Number of boys who are players =3/4×440=330
Number of girls who are player =1/4×220=55
Total number of players in school = 330 + 55 = 385
Q7. Renu wants to lay tiles on the floor of her house which is 9 m long and 7 m wide. Among the following sizes of tiles, which one should she buy so that the floor is tiled without cutting any tile?
(a) 40 cm × 65 cm
(b) 55 cm × 40 cm
(c) 35 cm × 45 cm
(d) 35 cm × 35 cm
Sol.
Area of the floor of the house = 9 × 7 = 63 cm2
= 630000 cm2
Using option (c),
Size of tile should she buy so that the floor is tiled without cutting any tile = 35 × 45 = 1575 cm2
Number of complete tiles =630000/1575=400
∴ Option (c) is correct.
Q8. There are four cuboidal boxes with dimensions (in cm) as given below.
Length Breadth Height
(a) 20 25 18
(b) 23 20 20
(c) 20 22 21
(d) 24 20 19
Sol.
Find out the volume of all cuboidal boxes
(i) Volume of the first cuboidal box = 20 × 25 × 18 = 9000 cm3
(ii) Volume of second cuboidal box = 23 × 20 × 20 = 9200 cm3
(iii) Volume of third cuboidal box = 20 × 22 × 21 = 9240 cm3
(iv) Volume of fourth cuboidal box = 24 × 20 × 19 = 9120 cm3
From option (a), (i) + (iii) = 9000 + 9200 = 18200 cm3
Which is not required.
From option (b), (ii) + (iii) = 9200 + 9240 = 18440 cm2
Which is correct.
Hence option (b) is correct.
Q9. The length of a rectangle is two times that of a square whose perimeter is 80 cm. If breath of the rectangle is 20 cm, then the area (in cm2) of the rectangle exceeds the area of the square by
(a) 150
(b) 300
(c) 400
(d) 100
Sol.
Perimeter of square = 4 × side
80 = 4 × side
Side of square =80/4= 20 cm
∴ Length of rectangle = 2 × side of square = 2 × 20 = 40 cm
⇒ Area of rectangle = 20 × 40 = 800 cm2
Area of square = 20 × 20 = 400 cm2
∴ Area of rectangle exceeds the area of the square by (800 – 400) = 400 cm2
Q10. Haroon went to a fruit shop. He bought 1 1/2 dozen bananas at the rate of Rs. 2.50 per banana, 3 1/2 at Rs. 57.60 per kg, 1 1/2 kg of mangoes at Rs. 75.40 per kg and 750 g of grapes at Rs. 120 per kg. If he gave a note of Rs. 500 to the fruit seller, he will get back
(a) Rs. 24.85
(b) Rs. 14.95
(c) Rs. 50.30
(d) Rs. 28.10
Sol.
Money spent on and half dozen bananas = 18 × 25 = Rs. 45
Money spent on three and a half kilogram apples =3 1/2×57.60=7/2×57.60 = Rs. 201.6
Money spent on one and half kilogram mangoes 1 1/2×75.40 = Rs. 3/2×75.40 Rs. 113.1
Money spent on 750 gram of grapes =750/1000×120 = Rs. 90
∴ Money he will get back = 500 – (45 + 201.6 + 113.1 + 90)
= 500 – 449.7 = Rs. 50.30
