Question : The sum of the two numbers is 37 and the difference between their squares is 185, then the difference between the two numbers is:
Option 1: 10
Option 2: 4
Option 3: 5
Option 4: 3
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Correct Answer: 5
Solution : Let the two numbers be X and Y. Given: X + Y = 37 and X2 – Y2 = 185 According to the question X2 – Y2 = 185 ⇒ (X + Y)(X – Y) = 185 ⇒ 37(X – Y) = 185 $\therefore$ X – Y = 5 Hence, the correct answer is 5.
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Question : If the sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.
Option 1: 4
Option 2: 8
Option 3: 1
Option 4: 2
Question : If the difference between the two numbers is 20 percent of their sum, then what is the ratio of larger number and smaller number?
Option 1: 6 : 5
Option 2: 5 : 4
Option 3: 4 : 3
Option 4: 3 : 2
Question : The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are:
Option 1: 2, 3 and 5
Option 2: 10, 15 and 25
Option 3: 8, 12 and 20
Option 4: 4, 6 and 10
Question : The sum of the cubes of two given numbers is 10234, while the sum of the two given numbers is 34. What is the positive difference between the cubes of the two given numbers?
Option 1: 3484
Option 2: 3488
Option 3: 3356
Option 4: 8602
Question : The sum of the two numbers is 75, and their difference is 25. The product of the two numbers is:
Option 1: 1350
Option 2: 1250
Option 3: 410
Option 4: 1000
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