In the set of four numbers given, select the odd one out.
67
For an odd-one-out among numbers, the key is to test a shared numerical property; here the deciding property is whether each number is prime or composite.
A composite number can be written as a product of smaller factors beyond 1 and itself, whereas a prime number has exactly two divisors, namely 1 and the number itself.
Check 12: it factorises as \(12=2\times2\times3\), so it has factors other than 1 and 12 and is composite.
Check 9 and 56 in the same way: \(9=3\times3\) is composite, and \(56=2\times2\times2\times7=2^{3}\times7\) is composite as well.
Now check 67: testing the small primes, it is not divisible by 2, 3, 5 or 7, and since \(8^{2}=64 \lt 67 \lt 81=9^{2}\) we need test no divisor beyond 8, so 67 has only the factors 1 and 67 and is prime.
Thus 12, 9 and 56 all belong to the composite family, while 67 stands apart as the only prime, so it does not fit with the others.
Hence the odd one out is 67.
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Important Questions from Classification
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(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
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(The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)
