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# Maths Quiz for KVS/NVS & CTET Exams Q1. If x and y are the two digit number in 653 xy such that this number is divisible by 80, then (x + y) = ?
(a) 2
(b) 3
(c) 4
(d) 6

Q2. If the product 4864 × 9 P 2 is divisible by 12, the value of P is:
(a) 2
(b) 5
(c) 6
(d) 1

Q3. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
(a) 553681
(b) 555181
(c) 555681
(d) 554581

Q4. Three numbers are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
(a) 75
(b) 81
(c) 85
(d) 89

Q5. Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly?
(a) 1 litre
(b) 7 litres
(c) 31 litres
(d) 41 litres

Q6. The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case is:
(a) 64
(b) 124
(c) 156
(d) 260

Q7. A motorcyclist goes from Mumbai to Pune, a distance of 192 km at an average speed of 32 km/h. Another man starts from Mumbai by car, 2 1/2 hours after the first and reaches Pune half an hour earlier. What is the rate of the speed of the motorcycle and the car?
(a) 1 : 2
(b) 1 : 3
(c) 10 : 27
(d) 5 : 4

Q8. A person sets to cover a distance of 12 km in 45 minutes. If he covers 3/4 of the distance in 2/3rd time, what should his speed to cover the remaining distance in the remaining time?
(a) 16 km/hr
(b) 8 km/hr
(c) 12 km/hr
(d) 14 km/hr

Q9. Length of a train is 287 m and it passes a bridge in 38 sec at the speed of 90 km/h. What is the length of the bridge?
(a) 665 m
(b) 663 m
(c) 680 m
(d) 580 m

Q10. A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary?
(a) Only the length of the train
(b) Only the length of the engine
(c) Either the length of the train or the length of the engine
(d) Both the length of the train and the length of the engine
Solutions

S1. Ans.(a)
Sol.
80 = 2 × 5 × 8
Since 653 xy is divisible by 2 and 5 both, so y = 0
Now, 653 x0 is divisible by 8, so 3×0 should be divisible by 8. This happens when x = 2
∴ x + y = (2 + 0) = 2

S2. Ans.(d)
Sol.
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
∴ P = 1.

S3. Ans.(c)
Sol.
987 = 3 × 7 × 47
So, the required number must be divisible by each one of 3, 7, 47
553681 → (Sum of digits = 28, not divisible by 3)
555181 → (Sum of digits = 25, not divisible by 3)
555681 is divisible by each one of 3, 7, 47.

S4. Ans.(c)
Sol.
Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common
So, middle number = H.C.F of 551 and 1073 = 29;
First number = (551/29) = 19; Third number = (1073/29) = 37
∴ Required sum = (19 + 29 + 37) = 85.

S5. Ans.(c)
Sol.
Required measurement = (H.C.F of 496, 403, 713) litres = 31 litres

S6. Ans.(a)
Sol.
Required number = H.C.F of (1356 – 12), (1868 – 12) and (2764 – 12)
= H.C.F of 1344, 1856 and 2752 = 64.
S7. Ans.(a)
Sol.
Speed of the first man = 32 km/hr
Time taken = 192 ÷ 32 = 6 hr
Second man covers 192 km in 3 hr
∴ Speed of the second man
= 192 ÷ 3 = 64 km/hr
Ratio = 32 : 64 or 1 : 2
S8. Ans.(c)
Sol.
Distance already covered = (3/4) × 12 = 9 km
Time spent = (2/3) × 45 min = 30 min
Distance left = (12-9) km = 3 km
Time left = (45-30) min = 15 min
∴ Required speed =3/ (15/60) km/hr
= 12 km/hr

S9. Ans.(b)
Sol.
Total distance covered = 90 × (5/18) × 38 = 950 m
So, length of bridge = 950 – 287 = 663

S10. Ans.(d)
Sol.
Since the sum of the length of the train and the engine is needed, so both the lengths must be known.