Question : The product of two numbers is 24 times the difference between these two numbers. If the sum of these numbers is 14, the larger number is:
Option 1: 9
Option 2: 8
Option 3: 7
Option 4: 10
Correct Answer: 8
Solution : Let the first number be $a$. So, second number $=(14-a)$ Product of two numbers = 24 × difference of two numbers $a(14-a) = 24(a-14+a)$ ⇒ $14a-a^{2} = 48a-336$ ⇒ $a^{2}+34a-336=0$ ⇒ $a^{2}+42a-8a-336=0$ ⇒ $a(a+42)-8(a+42)=0$ ⇒ $(a+42)(a-8)=0$ Since $a$ cannot be negative, $a=8$ So, second number = (14 – 8) = 6 So, the larger number is 8. Hence, the correct answer is 8.
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Question : If the square of the sum of two numbers is equal to 4 times their product, then the ratio of these numbers is:
Option 1: 2 : 1
Option 2: 1 : 3
Option 3: 1 : 1
Option 4: 1 : 2
Question : The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of the four numbers?
Option 1: 17
Option 2: 14
Option 3: 21
Option 4: 24
Question : The ratio between the two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. What is the difference of the numbers?
Option 1: 1
Option 2: 3
Option 3: 6
Option 4: 8
Question : Two positive numbers differ by 3951. When the larger number is divided by the smaller number, the quotient is 12 and the remainder is 13. The sum of the digits of the larger number is:
Option 1: 12
Option 2: 16
Option 3: 18
Option 4: 14
Question : The sum of two numbers is 16 and the difference is 2. What is the product of the two numbers?
Option 1: 35
Option 2: 56
Option 3: 63
Option 4: 42
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