Number System - Study Mode
[#181] The remainder when (15 23 + 23 23 ) is divided by 19, is :
Correct Answer
(A) 0
Explanation
Solution: (x n + a n ) is divisible by (x + a) when n is odd ∴ (15 23 + 23 23 ) is divisible by (15 + 23) ⇒ (15 23 + 23 23 ) is divisible by 38 and hence by 19 ⇒ On dividing (15 23 + 23 23 ) by 19, we get 0 as remainder.
[#182] Which one of the following numbers is divisible by 15 ?
Correct Answer
(A) 17325
Explanation
Solution: Consider the number is 17325 Its unit digit is 5, so it is divisible by 5 Sum of its digits = (5 + 2 + 3 + 7 + 1) = 18, which is divisible by 3 So, the given number is divisible by 3 And since 5 and 3 are co-primes, So the given number is divisible by (5 × 3), i.e., 15
[#183] How many numbers will be there between 300 and 500, where 4 comes only one time ?
Correct Answer
(B) 99
Explanation
Solution: From 300 to 399, we note that when '4' comes only one time = 19 such instances. From 400 to 499, we note that when '4' comes only one time = 80 such instances. So, total = (19 + 80) = 99 such instances.
[#184] A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :
Correct Answer
(B) 10, 1, 6
Explanation
Solution: z = 13 × 1 + 8 = 21 y = 11 × z + 9 = 11 × 21 + 9 = 240 x = 9 × y + 8 = 9 × 240 + 8 = 2168 Now, when order of divisor is reversed, we have : ∴ Respective remainders are 10, 1 and 6
[#185] The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, then the dividend is :
Correct Answer
(D) 6480
Explanation
Solution: Quotient = 16, Divisor = (25 × 16) = 400 5 × Remainder = Divisor ⇒ Remainder = $$frac{400}{5}$$ = 80 Divided = (400 × 16) + 80 = 6480