Number System - Study Mode

[#541] 5358 × 51 = ?
Correct Answer

(A) 273258

Explanation

Solution: 5358 × 51 = 5358 × (50 + 1) = 5358 × 50 + 5358 × 1 = 267900 + 5358 = 273258

[#542] The sum of first five prime numbers is:
Correct Answer

(D) 28

Explanation

Solution: Required sum = (2 + 3 + 5 + 7 + 11) = 28 Note: 1 is not a prime number Definition : A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

[#543] The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Correct Answer

(B) 270

Explanation

Solution: Let the smaller number be x Then larger number = (x + 1365) ∴ x + 1365 = 6x + 15 ⇒ 5x = 1350 ⇒ x = 270 ∴ Smaller number = 270

[#544] (12) 3 × 6 4 × 432 -1 = ?
Correct Answer

(A) 5184

Explanation

Solution: $$eqalign{
& { ext{Given}},{ ext{Exp}}{ ext{.}} cr
& = frac{{{{left( {12}
ight)}^3} imes {6^4}}}{{432}} cr
& = frac{{{{left( {12}
ight)}^3} imes {6^4}}}{{12 imes {6^2}}} cr
& = {left( {12}
ight)^2} imes {6^2} cr
& = {left( {72}
ight)^2} cr
& = 5184 cr} $$

[#545] 72519 × 9999 = ?
Correct Answer

(A) 725117481

Explanation

Solution: 72519 × 9999 = 72519 × (10000 - 1) = 72519 × 10000 - 72519 × 1 = 725190000 - 72519 = 725117481