The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs except one. Find that odd number-pair.

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Accepted Answer

**Solution:**

1. Analyze each pair to find the operation from first to second number.

2. Check pair 1: 5 : 128
   - $5^3 = 125$, close to 128.
   - $5^3 + 3 = 125 + 3 = 128$

3. Check pair 3: 7 : 352
   - $7^3 = 343$, close to 352.
   - $7^3 + 9 = 343 + 9 = 352$

4. Check pair 4: 1 : 4
   - $1^3 = 1$
   - $1^3 + 3 = 4$

5. Notice the pattern in pairs 1, 3, and 4:
   - The second number = first number cubed + (3 × first number)
   - For 5: $5^3 + 3 	imes 5 = 125 + 15 = 140$ (But given 128, so check again)

Let's try $x^3 + x^2$:
   - For 5: $5^3 + 5^2 = 125 + 25 = 150$ (No)

Try $x^3 + 3x$:
   - For 5: $125 + 15 = 140$ (No)

Try $x^3 + 3$:
   - For 5: 128 (matches)
   - For 7: $343 + 3 = 346$ (No, given 352)

6. Try $x^3 + 4x$:
   - For 5: $125 + 20 = 145$ (No)

7. Try $x^3 + 7x$:
   - For 5: $125 + 35 = 160$ (No)

8. Try $x^3 + x^2 + x$:
   - For 5: $125 + 25 + 5 = 155$ (No)

9. Try $x^3 + 3x^2$:
   - For 5: $125 + 75 = 200$ (No)

10. Try $x^3 + 3x + 3$:
    - For 5: $125 + 15 + 3 = 143$ (No)

11. Try $x^3 + 3x^2 + 3x + 1 = (x+1)^3$:
    - For 5: $(5+1)^3 = 6^3 = 216$ (No)

12. Check pair 2: 3 : 30
    - $3^3 = 27$, close to 30.
    - $3^3 + 3 = 30$

13. Check pair 3: 7 : 352
    - $7^3 = 343$
    - $7^3 + 9 = 352$

14. Check pair 1: 5 : 128
    - $5^3 = 125$
    - $5^3 + 3 = 128$

15. Check pair 4: 1 : 4
    - $1^3 = 1$
    - $1^3 + 3 = 4$

16. So pairs 1, 2, and 4 follow the pattern: second number = first number cubed + 3

17. Pair 3 does not follow this pattern since $7^3 + 3 = 343 + 3 = 346$ but given 352.

18. Therefore, pair 3 is the odd one out.

**Answer:** 3. 7 : 352

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