Number System - Study Mode

[#336] A boy multiplies 987 by a certain number and obtains 559981 as his answer. If in the answer both 9's are wrong but the other digits are correct, then the correct answer will be :
Correct Answer

(C) 555681

Explanation

Solution: Clearly, 7261 must be replaced by 2961, which is possible if 6648 is replaced by 6218, which in turn is possible if 5599 is replaced by 5556. Thus, the correct number is 555681

[#337] The product of any three consecutive natural numbers is always divisible by :
Correct Answer

(B) 6

Explanation

Solution: Let the required product be n (n + 1) (n + 2) Then, n = 1 ⇒ n (n + 1) (n + 2) = (1 × 2 × 3) = 6 n = 2 ⇒ n (n + 1) (n + 2) = (2 × 3 × 4) = 24 n = 3 ⇒ n (n + 1) (n + 2) = (3 × 4 × 5) = 60 So, each such product is divisible by 6

[#338] If (67 67 + 67) is divided by 68, the remainder is :
Correct Answer

(C) 66

Explanation

Solution: (x n + a n ) is divisible by (x + a) when n is odd ∴ (67 67 + 1 67 ) is divisible by (67 + 1) ⇒ (67 67 + 1) is divisible by 68 ⇒ On dividing (67 67 + 67) by 68, we get (67 - 1) = 66 as remainder.

[#339] If 11,109,999 is divided by 1111, then what is the remainder ?
Correct Answer

(C) 1110

Explanation

Solution: On dividing 11109999 by 1111, we get 9999 So, the required remainder is 1110

[#340] How many 3-digit numbers are there in between 100 and 300, having first and the last digit as 2 ?
Correct Answer

(B) 10

Explanation

Solution: Such numbers are 202, 212, 222, 232, 242, 252, 262, 272, 282, 292. There are 10 such numbers.