Question
There are four prime numbers A, B, C and D (A < B < C <
- B /C × 7D = {2(B ×
- C } + (D+26)
- D . Only A and B are consecutive prime numbers. Sum of A and B is not divisible by 2. LCM of B, C and D is 357. Sum of all the numbers is less than 30. Which of the following are true: I. The sum of A and B is 20.83% (approx.) of the sum of C and D. II. LCM of B and C is 20 more than the HCF of all the numbers. III. (A+
Solution
ATQ, ATQ, Sum of A and B is not divisible by 2 and both are prime numbers, so one of them is 2. A < B, so A = 2 A and B are consecutive prime numbers, so B = 3 LCM of B, C and D = 357 LCM of C and D = 357/3 = 119 Product of C and D = 119 = 7 × 17 Sum of all numbers < 30 and only A and B are consecutive prime numbers, so C = 7, D = 17 I => A+B = 20.83% (approx.) of (C+D) 5 = 20.83% of 24 = 4.999 (CORRECT) II => LCM of B and C = LCM(3,7) = 21 HCF of all numbers = 1 Difference = 21 – 1 = 20 (CORRECT) III => (A+B)/C × 7D = {2(B × C)} + (D+26) 5/7 × 7 × 17 = 2 × (3 × 7) + (17+26) 85 = 42 + 43 85 = 85 (CORRECT) Hence, all three are true.
More No. System Questions
- Albela Sells Chocolates in the packs of 6 chocolates, 12 chocolates, 18 chocolates and 24 chocolates etc, but the rate is necessarily uniform. One day Babl...
- Find the smallest number by which 6300 must be multiplied to make it a perfect square.
- Find the difference between minimum and maximum value of 'j' such that '7j5302' is always divisible by 3.
- Group ‘M’ comprises four even integers in order, and group ‘N’ includes four successive odd integers. If the average of their first elements is 33.5, what ...
- Which of the following number is rational number?
- When the digits are swapped, the new two-digit number equals 44 less than 120% of the original. The sum of the digits is 13. Determine the original number.
- Product of two consecutive positive even numbers is 440. Find the sum of the digits of the two numbers.
- The sum of two numbers is 144. Their LCM is 540 and HCF is 15. What is the smaller number?
- What is the average of first 28 multiples of 2.8?
- There are five numbers A, B, C, D and E. The ratio between the numbers of B and D is (y+1) : 3 respectively. The number C is 12.5% more than the number E. ...
