Question : The greater of the two numbers whose product is 900 and whose sum exceeds their difference by 30 is:
Option 1: 60
Option 2: 75
Option 3: 90
Option 4: 100
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Correct Answer: 60
Solution : Let the numbers be $x$ and $y$ where $x > y$. According to the question, ⇒ $(x + y) – (x – y) = 30$ ⇒ $x + y–x + y = 30$ ⇒ $y = \frac{30}{2} = 15$ Also, $xy = 900$ ⇒ $15x = 900$ $\therefore x = \frac{900}{15} = 60$ Hence, the correct answer is 60.
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Question : The product of two two-digit numbers is 2160, and their HCF is 12. The numbers are:
Option 1: (12 and 60)
Option 2: (72 and 30)
Option 3: (36 and 60)
Option 4: (60 and 72)
Question : The sum of two numbers is thrice their difference, their ratio is:
Option 1: 1 : 2
Option 2: 2 : 1
Option 3: 3 : 1
Option 4: 1 : 3
Question : The sum of two numbers is equal to 25 and their difference is 20. The ratio of the two numbers is:
Option 1: 9 : 1
Option 2: 7 : 9
Option 3: 3 : 5
Option 4: 2 : 7
Question : If the square of the sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, what is the largest of the three numbers?
Option 1: 5
Option 2: 6
Option 3: 3
Option 4: 8
Question : The sum of the cubes of two numbers is 793. The sum of the numbers is 13. Then the difference between the two numbers is:
Option 1: 7
Option 3: 5
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