Question

Two numbers are each multiplied by themselves to give two new numbers. The difference between these two new numbers is less than ten; the difference between the two original numbers was one. The two original numbers added together was more than 7. What is one of the original numbers?

Answer 1

Answer:

4 or 5.

Step-by-step explanation:

Let the numbers be represented by x and y.

x * x = mc

y * y = zq

m - c < 10

z - q < 10

x - y = 1

x + y > 7

Let's start from 0.

0

squared: 0, wrong; a new number is meant to be formed.

1

squared: 1, wrong; a new number is meant to be formed.

2

squared: 4, maybe this can work; a new number is formed.

3

squared: 9, maybe this can work; a new number is formed.

4

squared: 16, maybe this can work; a new number is formed.

5

squared: 25, maybe this can work; a new number is formed.

6

squared: 36, maybe this can work; a new number is formed.

7

squared: 49, maybe this can work; a new number is formed.

8

squared: 64, maybe this can work; a new number is formed.

9

squared: 81, maybe this can work; a new number is formed.

FROM HERE, 0 & 1 ARE OUT.

THE QUESTION STATES THAT THE DIFFERENCE BETWEEN THE TWO ORIGINAL NUMBERS WAS ONE.

NOW WE HAVE 2, 3, 4, 5, 6, 7, 8, & 9.

2 & 3.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

3^2 - 2^2

9 - 4 = 5; there's a possibility for this to work since the difference of their squares is less than 10.

3 & 4.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

4^2 - 3^2

16 - 9 = 7; there's a possibility for this to work since the difference of their squares is less than 10.

4 & 5.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

5^2 - 4^2

25 - 16 = 9; there's a possibility for this to work since the difference of their squares is less than 10.

5 & 6.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

6^2 - 5^2

36 - 25 = 11, THIS IS WRONG.

6 & 7.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

7^2 - 6^2

49 - 36 = 13, THIS IS WRONG.

7 & 8.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

8^2 - 7^2

64 - 49 = 15, THIS IS WRONG.

8 & 9.

THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.

9^2 - 8^2

81 - 64 = 17, THIS IS WRONG

THE POSSIBLE NUMBERS ARE 2&3, 3&4, AND 4&5.

THE QUESTION STATES THAT THE TWO ORIGINAL NUMBERS ADDED TOGETHER WAS MORE THAN 7.

2&3

2 + 3 = 5, WRONG, THE ADDITION OF THE TWO ORIGINAL NUMBERS SHOULD BE MORE THAN 7 FOR THIS TO WORK.

3&4

3 + 4 = 7, WRONG, THE ADDITION OF THE TWO ORIGINAL NUMBERS SHOULD BE MORE THAN 7 FOR THIS TO WORK.

4&5

4 + 5 = 9, CORRECT, THE ADDITION OF THE TWO ORIGINAL NUMBERS IS MORE THAN 7.

Therefore, the possible numbers are 4 & 5. All that is left is for you to pick which of the two is the final answer if you have options.

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