Select the triad in which the numbers are related in the same way as are the numbers of the given triads: (11, 1, 10) and (13, 7, 90). Operations should be performed on the whole numbers without breaking them into digits.

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Accepted Answer

Step 1: Analyze the given triads (11, 1, 10) and (13, 7, 90).

Step 2: Check the relationship between the first two numbers and the third number in each triad.

For (11, 1, 10):
- 11 - 1 = 10

For (13, 7, 90):
- 13 * 7 = 91 (close to 90 but not exact)
- 13 + 7 = 20 (not 90)
- 13^2 - 7^2 = 169 - 49 = 120 (not 90)
- 13^2 - 7 = 169 - 7 = 162 (not 90)
- 13 * (7 - 1) = 13 * 6 = 78 (not 90)
- (13 - 7) * (13 + 7) = 6 * 20 = 120 (not 90)

Try another approach:
- 11 - 1 = 10 (difference)
- 13 - 7 = 6, but the third number is 90, which is 13 * 7 - 1 = 91 - 1 = 90

So, the pattern could be:
- For the first triad: 11 - 1 = 10
- For the second triad: 13 * 7 - 1 = 90

This suggests the third number is either the difference or product minus 1.

Step 3: Check options for similar pattern:

Option 1: (1, 2, 15)
- 1 - 2 = -1 (not 15)
- 1 * 2 - 1 = 2 - 1 = 1 (not 15)

Option 2: (4, 5, 19)
- 4 - 5 = -1 (not 19)
- 4 * 5 - 1 = 20 - 1 = 19 (matches)

Option 3: (2, 6, 28)
- 2 - 6 = -4 (not 28)
- 2 * 6 - 1 = 12 - 1 = 11 (not 28)

Option 4: (3, 6, 23)
- 3 - 6 = -3 (not 23)
- 3 * 6 - 1 = 18 - 1 = 17 (not 23)

Step 4: Reconsider the pattern with the first triad (11, 1, 10) as difference and second triad (13, 7, 90) as product minus 1.

Since the pattern is inconsistent, check if the third number equals the sum of the first two numbers minus 2:

- 11 + 1 - 2 = 10 (matches first triad)
- 13 + 7 - 2 = 18 (not 90)

Try sum of squares minus something:

- 11^2 - 1^2 = 121 - 1 = 120 (not 10)
- 13^2 - 7^2 = 169 - 49 = 120 (not 90)

Try sum of squares minus product:

- 11^2 + 1^2 - 11*1 = 121 + 1 - 11 = 111 (not 10)
- 13^2 + 7^2 - 13*7 = 169 + 49 - 91 = 127 (not 90)

Try product minus sum:

- 11*1 - (11 + 1) = 11 - 12 = -1 (not 10)
- 13*7 - (13 + 7) = 91 - 20 = 71 (not 90)

Try product minus difference:

- 11*1 - (11 - 1) = 11 - 10 = 1 (not 10)
- 13*7 - (13 - 7) = 91 - 6 = 85 (not 90)

Try product minus 1:

- 11*1 - 1 = 11 - 1 = 10 (matches first triad)
- 13*7 - 1 = 91 - 1 = 90 (matches second triad)

So the pattern is: third number = (first number * second number) - 1

Check options with this pattern:

Option 1: (1, 2, 15)
- 1*2 - 1 = 2 - 1 = 1 (not 15)

Option 2: (4, 5, 19)
- 4*5 - 1 = 20 - 1 = 19 (matches)

Option 3: (2, 6, 28)
- 2*6 - 1 = 12 - 1 = 11 (not 28)

Option 4: (3, 6, 23)
- 3*6 - 1 = 18 - 1 = 17 (not 23)

Therefore, the correct triad is (4, 5, 19).

Final Answer: Option 2.

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