Olympiad Test: Number System - 1 - Class 7 MCQ

Numbers proportional to 4, 7, 9 and 12 are 4x ,7x, 9x, 12x respectively.
4x + 7x + 9x + 12x =128
32x = 128
x = 4
4x =16

201 is divisible by 3. So, it is not a prime number.

(125 × 5⁶) = 5³ × 5⁶ = 5³⁺⁶

Required number = (14 – 2) = 12

The sum of two odd numbers is even. So, x + y is even.

144 × 36² ÷ 432 = 144 × 1296 ÷ 432
= 144 × 3  = 432

43729 × 9999 = 43729 × (1000 – 1)
= 43729 × 1000 – 43729 × 1
= 43729000 – 43729
= 436 85271

Sum of digits = (4 + 1 + 8 + x + 3 + 4 + 2) =
(22 + x), which must be divisible by 3.
∴ x = 2

(?) – 18637 – 23994 = 9977 
(?) = 9977 + 18637 + 23994
= 52608

997 is the largest 3- digit prime number.

627 is divisible by 3. Hence it is not a prime number.

Prime numbers between 400 and 500 are:
401    409     419    421    431    433    439    443 
449    457    461    463    467    479    487    491    
499

Sum of all the first n natural numbers

Prime numbers less than 40 are:
2      3      5      7     11     13     17     19     23    29     31     37

7³ⁿ – 4²ⁿ = (7³) n – (42) n
= (343)ⁿ – (16)ⁿ
Thus 343 – 16 is a factor i.e. 327 is a factor of 7³ⁿ – 4²ⁿ

4/5 = 0.8
Hence, required number = 0.8 – 0.50  = 0.3

Additive inverse of 7.22 = – 7.22
Additive identity of 3.6   = 0
Hence, sum of – 7.22 and 0 = – 7.22

Multiplicative inverse of 

[{(3.78 + 1/5) - 2} - 1/4]

=> {(3.98) - 2} - 1/4

=> 1.98 - 1/4

=> 1.73