Theory of Numbers Test

Result

Theory of Numbers Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

M and N are two distinct natural numbers. The HCF and LCM of M and N are K and L, respectively. If A is also a natural number, then which of the following relations is not possible?

A
K x L = A

B
K x A = L

C
L x A = K

D
K x A = M

Solution

Let the numbers be 4 and 6. Then, their LCM and HCF are 12 and 2, respectively.
That is, LCM x Natural number can never be equal to HCF. All other cases are possible.
HCF of two distinct natural numbers can never be a multiple of their LCM.
Question 2
1 / -0

If HCF of 8 numbers has to be found by the division method, then how many steps would be required?

A
8

B
7

C
6

D
4

Solution

For n numbers, we need (n –1) steps to find HCF by division method.

∴ 8 numbers will have (8 – 1) = 7 steps
Question 3
1 / -0

Which least number must be subtracted from 1856, so that the remainder is 4 when divided by 7, 12, 16?

A
137

B
1361

C
140

D
172

Solution

LCM of (7, 12, 16) = 336
If we divide 1856 by 336, then remainder is 176.
Since, it is given that remainder in this condition is 4.
Hence, the least number to be subtracted = (176 - 4) = 172
Question 4
1 / -0

If N = 1000⁸ - 8, what is the sum of its digits?

A
200

B
207

C
208

D
209

Solution

N = 1000⁸ - 8 = 10²⁴ - 8
N = Number with twenty three 9s, followed by 2.
That is, N = 9999 ... 92
The sum of digits = (23 × 9) + 2 = 207 + 2 = 209
Question 5
1 / -0

If 2^{x + y} = 4^{x – y}, then 3^x/y is

A
0

B
1

C
3

D
27

Solution

2^{x + y} = 2^{2(x – y)}

⇒ x + y = 2x – 2y

⇒ x = 3y

∴ 3^x/y = 3³ = 27