Explanation:

Let’s get into it. You’re dealing with three-number sets, and we need to figure out how the first two numbers in each set are related to the third.

Given sets:

(168, 35, 143)

(182, 65, 127)

Let's break them down:

- 168 – 35 = 133; 133 ? 143

- 168 – 143 = 25; 25 ? 35

- 35 + 143 = 178; nope.

- If you do 168 – 143 = 25, not matching anything…

- Try 168 – 35 = 133. Doesn't fit.

- Here’s a key: 168 – 143 = 25 and 143 – 35 = 108, not matching.

- Let's try 168 – 35 = 133, now add 10 to 133 = 143? No.

- Now, what about differences between 168 and 143, and 143 and 35? Doesn't seem linked via addition or subtraction directly.

Let’s check if it’s about subtraction:

For (168, 35, 143):

- 168 – 35 = 133

- 168 – 143 = 25

- 143 – 35 = 108

For (182, 65, 127):

- 182 – 65 = 117

- 182 – 127 = 55

- 127 – 65 = 62

No clear simple relation.

But what if third number is the difference between the first two? Doesn't fit.

Let’s check:

- 168 – 143 = 25, 35 = 143 – 108? Nope.

- Check for addition: 168 = 35 + 143 = 178? Nope.

Try for squares or multiples:

- 168 = 35 + 4 × 33. No clear fit.

- Try GCD: GCD(168, 35) = 7, GCD(168, 143) = 13, GCD(35, 143) = 1.

Hmm.

Let’s compare differences:

- (168, 35, 143) ? 168 – 35 = 133, 168 – 143 = 25, 143 – 35 = 108

Check if there’s a pattern among these sets. Try (a, b, c): Maybe c = a – b? 168 – 35 = 133 (not 143)

Try a = b + c:

- 168 = 35 + 143 = 178, off by 10

- 182 = 65 + 127 = 192, off by 10

OK, now, both are off by 10. Try c = a – b + 10.

- For (168, 35, ?): a – b + 10 = 168 – 35 + 10 = 143

- For (182, 65, ?): 182 – 65 + 10 = 127

This works!

So, the relationship is:

Third number = first number – second number + 10

Let’s check the options:

- Option 1: (142, 83, 69)

142 – 83 + 10 = 69

142 – 83 = 59

59 + 10 = 69

- Option 2: (253, 99, 154)

253 – 99 + 10 = 164

But third = 154 × (doesn’t fit)

- Option 3: (203, 89, 111)

203 – 89 + 10 = 124

But third = 111 × (no match)

- Option 4: (159, 62, 87)

159 – 62 + 10 = 107

But third = 87 × (not working)

So the correct answer is:

Option 1: (142, 83, 69)

What we learned:

- The pattern is: First – Second + 10 = Third

- Each correct set fits this rule

- Option 1 is the only one matching that pattern