Number System - Study Mode

[#396] What is the minimum number of four digits formed by using the digits 2, 4, 0, 7 ?
Correct Answer

(A) 2047

Explanation

Solution: Required number = 2047

[#397] When 2 256 is divided by 17, the remainder would be :
Correct Answer

(A) 1

Explanation

Solution: When n is even, (x n - a n ) is divisible by (x + a) Now, 2 256 = (2 4 ) 64 = (16) 64 ∴ (16 64 - 1 64 ) is divisible by (16 + 1) ⇒ (16 64 - 1) is divisible by 17 ⇒ (2 256 - 1) is divisible by 17 ⇒ On dividing 2 256 by 17, we get 1 as remainder.

[#398] 5566 - 7788 + 9988 = ? + 4444
Correct Answer

(C) 3322

Explanation

Solution: Let, 5566 - 7788 + 9988 = x + 4444 Then, (5566 + 9988) - 7788 = x + 4444 ⇒ 15554 - 7788 = x + 4444 ⇒ x + 4444 = 7766 ⇒ x = (7766 - 4444) ⇒ x = 3322

[#399] The sum of the digits of a 3-digit number is subtracted from the number. The resulting number is always :
Correct Answer

(B) Divisible by 9

Explanation

Solution: Let the hundreds, tens and unit digits be x, y and z respectively. Then, (100x + 10y + z) - (x + y + z) = 99x + 9y = 9 (11x + y) So, the resulting number is divisible by 9

[#400] The number of zeros at the end of the product 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 is :
Correct Answer

(C) 8

Explanation

Solution: Let N = 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 = 5 10 × ( 1 × 2 × 3 × 4 × ..... × 10) = 5 10 × 10! Highest power of 2 in 10! $$ = left[ {frac{{10}}{2}}
ight] + left[ {frac{{10}}{{{2^2}}}}
ight] + left[ {frac{{10}}{{{2^3}}}}
ight]$$ = 5 + 2 + 1 = 8 Highest power of 5 in 10! = $$left[ {frac{{10}}{5}}
ight]$$ = 2 ∴ N = 2 8 × 5 12 × k Since highest power of 2 is less than that of 5, So, required number of zeros = 8