Number System - Study Mode

[#416] Let x be the product of two numbers 3, 659, 893, 456, 789, 325, 678 and 342, 973, 489, 379, 256. The number of digits in x is :
Correct Answer

(B) 34

Explanation

Solution: Sum of digits in the two numbers = 19 + 15 = 34 So, the product will have 33 or 34 digits Since 36 × 34 = 1224 (i.e., product has 2 + 2 = 4 digits) So, the number of digits in x is 34

[#417] 8899 - 6644 - 3322 = ? - 1122
Correct Answer

(A) 55

Explanation

Solution: 8899 - 6644 - 3322 = x - 1122 ⇒ 2255 - 3322 + 1122 = x ⇒ x = 3377 - 3322 ⇒ x = 55

[#418] 7 6n - 6 6n , where n is an integer > 0, is divisible by :
Correct Answer

(D) All the above

Explanation

Solution: When n is even, (x n - a n ) is divisible by both (x - a) as well as (x + a). Now, (7 6n - 6 6n ) = [(7 3 ) 2n - (6 3 ) 2n ] = [(343) 2n - (216) 2n ] ∴ (7 6n - 6 6n ) is divisible by both (7 - 6) and (7 + 6) (7 6n - 6 6n ) is divisible by 13 And, [(343) 2n - (216) 2n ] is divisible by both (343 - 216) and (343 + 216) ⇒ (7 6n - 6 6n ) is divisible by both 127 and 559

[#419] What minimum value should be assigned to *, so that 2361*48 is exactly divisible by 9 ?
Correct Answer

(B) 3

Explanation

Solution: 2361*48 will be divisible by 9 if the sum of the digits of the given number is divisible by 9 2 + 3 + 6 + 1 + * + 4 + 8 i.e., (24 + *) is divisible by 9 Clearly, * = 3 because 27 is divisible by 9

[#420] 5 (x + 3) = 25 (3x - 4) , then find the value of x
Correct Answer

(A) $$frac{{11}}{5}$$

Explanation

Solution: 5 (x + 3) = 25 (3x - 4) Or, 5 (x + 3) = 5 2 × (3x - 4) Now, comparing the powers, (x + 3) = 2 × (3x - 4) Or, x + 3 = 6x - 8 Or, 6x - x = 8 + 3 Or, 5x = 11 Hence, x = $$frac{{11}}{5}$$