Number System - Study Mode

[#146] The LCM of two numbers is 1890 and their HCF is 30. If one of them is 270, the other will be
Correct Answer

(A) 210

Explanation

Solution: HCF of the numbers × LCM of the numbers = Multiplication of the numbers Or, 30 × 1890 = 270 × N Or, N = $$30 imes frac{{1890}}{{270}}$$ Or, N = 210

[#147] Find the least number of five digits which when divided by 40, 60, and 75, leave remainders 31, 51 and 66 respectively.
Correct Answer

(C) 10191

Explanation

Solution: Difference, 40 - 31 = 9 60 - 51 = 9 75 - 66 = 9 Difference between numbers and remainder is same in each case. Then, The answer = {(LCM of 40, 60, 75) - 9} 40 = 2 × 2 × 2 × 5 60 = 2 × 2 × 3 × 5 75 = 3 × 5 × 5 LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600 But, the least number of 5 digits = 10000 $$frac{{10000}}{{600}},$$ xa0 we get remainder as 400 Then, the answer = 1000 - (600 - 400) - 9 = 10191

[#148] There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed?
Correct Answer

(C) 16

Explanation

Solution: 576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 448 = 2 × 2 × 2 × 2 × 2 × 2 × 7 HCF = 2 × 2 × 2 × 2 × 2 × 2 = 64 Hence, number of classes required $$frac{{576}}{{64}} + frac{{448}}{{64}}$$ = 9 + 7 = 16 Shortcut: The numbers (3 × 3) and 7 are not a part of HCF. And sum of multiplication of these number is the required answer.

[#149] Which of following can never be ending of a perfect square?
Correct Answer

(B) 000

Explanation

Solution: A perfect square never ends with odd number of zeros.

[#150] The smallest whole number that is to be multiplied with 59535 to make a perfect square number is x. The sum of digits of that number is?
Correct Answer

(A) 6

Explanation

Solution: $$59535 = 3 imes 5 imes x08oxed{3 imes 3} imes x08oxed{3 imes 3} imes 7 imes 7$$ ⇒ To make a perfect square we should multiply by = 3 × 5 = 15 x = 15 [given] ⇒ Sum of digits of number = 1 + 5 = 6