In this perfect cube based odd one out question, select the number that is not a perfect cube among 2890, 3375, 1728 and 1331.

Introduction / Context:
Many numerical odd one out questions rely on basic powers such as squares and cubes. In this problem you are given four numbers, three of which are perfect cubes of integers, while one is not. Recognising standard cubes is an important skill for quantitative aptitude because it speeds up both mental calculations and pattern recognition in puzzles.

Given Data / Assumptions:

• The given numbers are 2890, 3375, 1728 and 1331.
• We use the definition of a perfect cube: a number of the form n^3 for some integer n.
• The task is to identify the number that is not a perfect cube.

Concept / Approach:
The approach here is to recall standard cube values of integers around 10, 11, 12, 13, 14 and 15 and match them with the given numbers. If a number exactly matches one of these cube values, it is a perfect cube. The number that does not correspond to any integer cube will be the odd one out. This is a direct application of memorised cube tables.

Step-by-Step Solution:
Step 1: Recall that 11^3 = 1331. Therefore, 1331 is a perfect cube. Step 2: Recall that 12^3 = 1728. So 1728 is also a perfect cube. Step 3: Recall that 15^3 = 3375. Thus 3375 is again a perfect cube. Step 4: Now consider 2890. Check nearby cube values: 13^3 = 2197, 14^3 = 2744 and 15^3 = 3375. The number 2890 does not match any integer cube among these and lies between 2744 and 3375. Step 5: Hence 2890 is not a perfect cube, while 3375, 1728 and 1331 are perfect cubes. Therefore 2890 is the odd one out.

Verification / Alternative check:
To verify, you could factor 2890. It equals 2 * 5 * 17 * 17. For a number to be a perfect cube, each prime factor must appear with an exponent that is a multiple of 3. Here, the factor 17 appears with exponent 2, which is not a multiple of 3, so 2890 cannot be a perfect cube. The other three values are standard cubes and appear frequently in cube tables, which confirms our conclusion.

Why Other Options Are Wrong:
3375 is wrong as the odd one out because it is 15^3, a perfect cube. 1728 is wrong as the odd one out because it is 12^3, another perfect cube. 1331 is wrong as the odd one out because it is 11^3, again a perfect cube.

Common Pitfalls:
Some test takers may not remember cube values and therefore start performing time consuming repeated multiplication. Others may confuse 2890 with a near cube because it lies between 14^3 and 15^3. The safest method is to recall or quickly derive nearby cubes 2197, 2744 and 3375 and notice that 2890 does not equal any of them. Practice with cube tables helps avoid these mistakes in exams.

Final Answer:
The only number that is not a perfect cube and therefore the odd one out is 2890.