Answer:
4 or 5.
Step-by-step explanation:
<u>Let the numbers be represented by </u><u>x</u><u> and </u><u>y</u><u>.</u>
x * x = mc
y * y = zq
m - c < 10
z - q < 10
x - y = 1
x + y > 7
<u>Let's start from 0.</u>
0
squared: 0, <u>wrong; a new number is meant to be formed.</u>
1
squared: 1, <u>wrong; a new number is meant to be formed.</u>
2
squared: 4, <u>maybe this can work; a new number is formed.</u>
3
squared: 9, <u>maybe this can work; a new number is formed.</u>
4
squared: 16, <u>maybe this can work; a new number is formed.</u>
5
squared: 25, <u>maybe this can work; a new number is formed.</u>
6
squared: 36, <u>maybe this can work; a new number is formed.</u>
7
squared: 49, <u>maybe this can work; a new number is formed.</u>
8
squared: 64, <u>maybe this can work; a new number is formed.</u>
9
squared: 81, <u>maybe this can work; a new number is formed.</u>
<u />
<u><em>FROM HERE, 0 & 1 ARE OUT.</em></u>
<u><em>THE QUESTION STATES THAT THE DIFFERENCE BETWEEN THE TWO ORIGINAL NUMBERS WAS ONE.</em></u>
<u><em>NOW WE HAVE 2, 3, 4, 5, 6, 7, 8, & 9.</em></u>
<u>2 & 3.</u>
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.
<u>3 & 4.</u>
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.
<u>4 & 5.</u>
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.
<u>5 & 6.</u>
THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.
6^2 - 5^2
36 - 25 = 11, THIS IS WRONG.
<u>6 & 7.</u>
THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.
7^2 - 6^2
49 - 36 = 13, THIS IS WRONG.
<u>7 & 8.</u>
THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.
8^2 - 7^2
64 - 49 = 15, THIS IS WRONG.
<u>8 & 9.</u>
THE DIFFERENCE BETWEEN THEIR SQUARES SHOULD BE LESS THAN 10 IF THEY CAN WORK.
9^2 - 8^2
81 - 64 = 17, THIS IS WRONG
<u><em>THE POSSIBLE NUMBERS ARE 2&3, 3&4, AND 4&5.</em></u>
<u><em>THE QUESTION STATES THAT THE TWO ORIGINAL NUMBERS ADDED TOGETHER WAS MORE THAN 7.</em></u>
<u>2&3</u>
2 + 3 = 5, WRONG, THE ADDITION OF THE TWO ORIGINAL NUMBERS SHOULD BE MORE THAN 7 FOR THIS TO WORK.
<u>3&4</u>
3 + 4 = 7, WRONG, THE ADDITION OF THE TWO ORIGINAL NUMBERS SHOULD BE MORE THAN 7 FOR THIS TO WORK.
<u>4&5</u>
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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