Real Numbers Test

Result

Real Numbers Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container which can measure the petrol of each tanker in exact number of times is

A
200 litres

B
180 litres

C
190 litres

D
170 litres

Solution

Here, maximum capacity of measuring container = HCF(680, 850)

∴ Applying Euclid’s division algorithm to 850 and 680,
850 = 680 × 1 + 170

⇒ 680 = 170 × 4 + 0 [Zero remainder]

∴ HCF = (680, 850) = 170
Question 2
1 / -0

Two tankers contain 135 and 225 litres of water respectively. The maximum capacity of a container which can measure the water of each tanker in exact number of times is

A
25 litres

B
45 litres

C
35 litres

D
55 litres

Solution

Here, maximum capacity of measuring container = HCF (135, 225)

∴ Applying Euclid’s division algorithm to 225 and 135,

225 = 135 × 1 + 90

⇒ 135 = 90 ×1 + 45

90 = 45 × 2 + 0 [Zero remainder]

∴HCF = (135, 225) = 45

Therefore, the maximum capacity of a container which can measure the water of each tanker in exact number of times is 45 liters.
Question 3
1 / -0

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of ‘m’ is

A
1

B
2

C
3

D
4

Solution

First, find the HCF of 65 and 117

117 = 65 × 1 + 52

65 = 52 × 1 + 13

52 = 13 × 4 + 0 (zero remainder)

Therefore, HCF (117 , 65) is 13

Now,

∴ 65m – 117 = 13

⇒ 65m = 13 + 117

⇒ 65m = 130

r ⇒ m = 2
Question 4
1 / -0

Which of the following is false?

A
H.C.F.(a,b) × L.C.M. (a,b) = a × b

B
L.C.M. (p,q,r) = p × q × r; if p,q,r are prime numbers

C
H.C.F. (p,q,r) = 1; if p,q,r are prime numbers

D
H.C.F. (p,q,r) × L.C.M. (p,q,r) = p × q × r

Solution

H.C.F. (p,q,r) × L.C.M. (p,q,r) ≠ p × q × r

This condition is applied on HCF and LCM of two numbers (either (p , q ) or (q , r ) or (r , p))

For three numbers p,q and r the formula is different.