Number Sequence Analysis: Finding the Outlier in 21, 29, 12, 27, 23

Q: Why isn't the answer based on prime numbers since some are prime?

While $ 23 $ and $ 29 $ are prime, this creates 2 primes vs 3 composites - no clear single outlier. The even/odd property gives a clearer 1 vs 4 pattern, making $ 12 $ the obvious choice.

Q: Could there be multiple correct answers to this type of question?

Technically yes, but look for the most obvious pattern first. Even/odd classification is simpler than prime analysis, digit sums, or other complex properties. Choose the pattern that creates the clearest single outlier.

Q: How do I quickly identify even and odd numbers?

Check the last digit: if it's 0, 2, 4, 6, or 8, the number is even. If it's 1, 3, 5, 7, or 9, it's odd. So $ 12 $ ends in 2 (even), while others end in 1, 9, 7, 3 (all odd).

Q: What if I see other patterns like all numbers being in the 20s except 12?

Good observation! $ 12 $ is indeed the only number not in the twenties. When multiple patterns exist, choose the most fundamental mathematical property - even/odd classification is more basic than digit ranges.

Q: Should I always check multiple properties before answering?

Start simple, then expand if needed. Check even/odd first, then factors, then primes, then digit patterns. Stop when you find a clear 1 vs all others pattern. Don't overcomplicate when a simple solution exists!

Even-Odd Classification with Prime Number Analysis

Which number is the odd one out?

$21,29,12,27,23$

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Step-by-step written solution

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Understand the problem

Which number is the odd one out?

$21,29,12,27,23$

Step-by-step solution

To solve this problem, we'll investigate which given number does not fit with the others based on the concept of prime numbers.

First, identify which numbers are prime:
$21$ is not prime (divisible by $3$ ).
$29$ is prime (divisors are 1 and 29).
$12$ is not prime (divisible by $2, 3,$ and $4$ ).
$27$ is not prime (divisible by $3$ ).
$23$ is prime (divisors are 1 and 23).

Among the given numbers, $29$ and $23$ are prime, making 21, 12, and 27 non-prime. However, upon reviewing the numbers again, reconsider the common trivial property: whether they are even or odd numbers.

Now examine a simpler property:

$21$ : Odd
$29$ : Odd
$12$ : Even
$27$ : Odd
$23$ : Odd

With this assessment, $12$ is the only even number, thereby making it the odd one out.

Therefore, the solution to the problem is $12$ .

Final Answer

$12$

Key Points to Remember

Essential concepts to master this topic

Rule: Look for the simplest distinguishing property first
Technique: Classify by even/odd: 12 is even, others are odd
Check: Count categories: 4 odd numbers, 1 even number confirms answer ✓

Common Mistakes

Avoid these frequent errors

Overcomplicating with prime number analysis
Don't jump to complex properties like prime factorization when simpler patterns exist = missed obvious answer! Prime analysis shows 2 primes vs 3 composites, creating confusion. Always check basic properties like even/odd first before exploring advanced concepts.

Practice Quiz

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What number do the blue squares below represent?

FAQ

Everything you need to know about this question

Why isn't the answer based on prime numbers since some are prime?

While $23$ and $29$ are prime, this creates 2 primes vs 3 composites - no clear single outlier. The even/odd property gives a clearer 1 vs 4 pattern, making $12$ the obvious choice.

Could there be multiple correct answers to this type of question?

Technically yes, but look for the most obvious pattern first. Even/odd classification is simpler than prime analysis, digit sums, or other complex properties. Choose the pattern that creates the clearest single outlier.

How do I quickly identify even and odd numbers?

Check the last digit: if it's 0, 2, 4, 6, or 8, the number is even. If it's 1, 3, 5, 7, or 9, it's odd. So $12$ ends in 2 (even), while others end in 1, 9, 7, 3 (all odd).

What if I see other patterns like all numbers being in the 20s except 12?

Good observation! $12$ is indeed the only number not in the twenties. When multiple patterns exist, choose the most fundamental mathematical property - even/odd classification is more basic than digit ranges.

Should I always check multiple properties before answering?

Start simple, then expand if needed. Check even/odd first, then factors, then primes, then digit patterns. Stop when you find a clear 1 vs all others pattern. Don't overcomplicate when a simple solution exists!

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