Number System - Study Mode

[#221] Find the multiple of 11 in the following numbers.
Correct Answer

(D) 978626

Explanation

Solution: In 978626, we have (6 + 6 + 7) - (2 + 8 + 9) = 0 Hence, 978626 is completely divisible by 11

[#222] 884697 - 773697 - 102479 = ?
Correct Answer

(C) 8521

Explanation

Solution: Given expression : = 884697 - (773697 +102479) = 884697 - 876176 = 8521

[#223] In a division sum, the remainder was 71. With the same divisor but twice the dividend, the remainder is 43. Which one of the following is the divisor ?
Correct Answer

(C) 99

Explanation

Solution: Let the dividend be (x + 71) and the divisor be y. Then, [2(x + 71) - 43] is divisible by y ⇒ (2x + 142 - 43) is divisible by y ⇒ (2x + 99) is divisible by y ∴ Divisor = 99 Shortcut method Divisor = (2 × 71 - 43) = (142 - 43) = 99

[#224] What is the number of prime factors contained in the product 30 7 × 22 5 × 34 11 ?
Correct Answer

(D) 53

Explanation

Solution: 30 7 × 22 5 × 34 11 = (2 × 3 × 5) 7 × (2 × 11) 5 × (2 × 7) 11 = 2 (7 + 5 + 11) × 3 7 × 5 7 × 11 5 × 17 11 = (2 23 × 3 7 × 5 7 × 11 5 × 17 11 ) Number of prime factors = (23 + 7 + 7 + 5 + 11) = 53

[#225] 217 × 217 + 183 × 183 = ?
Correct Answer

(B) 80578

Explanation

Solution: = (217 × 217) + (183 × 183) = (217) 2 + (183) 2 = (200 + 17) 2 + (200 - 17) 2 = (a + b) 2 + (a - b) 2 = 2(a 2 + b 2 ), where a = 200, b = 17 = 2 [(200) 2 + (17) 2 ] = 2 [40000 + 289] = (2 × 40289) = 80578