Govt Exams
Odd numbers between 10 and 30: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.
Count = 10
Let numbers be 5x and 7x.
Then 5x + 7x = 120, so 12x = 120, x = 10.
Larger number = 7 × 10 = 70
9+8+7+6+5+4+3 = 42.
Then 4+2 = 6.
Wait, let me recalculate: Sum = 42, which reduces to 4+2=6.
The answer should be D.
Actually 9+8+7+6+5+4+3=42, 4+2=6.
Combined rate = 1/8, A's rate = 1/12. B's rate = 1/8 - 1/12 = 3/24 - 2/24 = 1/24. B takes 24 days
A completes 1/3 work in 5 days, so rate = 1/15 per day.
Remaining work = 2/3.
Days needed = (2/3)/(1/15) = (2/3) × 15 = 10 days
Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5.
Time = 5 days
A's rate = 1/12, B's rate = 1/18.
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36.
Time = 36/5 = 7.2 days
This question asks us to find the least common multiple (LCM) of two numbers using prime factorization.
Break 84 into its prime factors by dividing by smallest primes.
Break 140 into its prime factors by dividing by smallest primes.
LCM is found by taking the highest power of each prime factor that appears in either number.
The LCM of 84 and 140 is 420, which is option (A).
100 = 2² × 5², 150 = 2 × 3 × 5², 200 = 2³ × 5².
Common factors: 2¹ × 5² = 2 × 25 = 50.
Using formula: HCF × LCM = Product of two numbers. 8 × 96 = 24 × x. 768 = 24x. x = 32.