Choose the odd number out of the given options.

Question

Prepp Team · Accepted Answer

Finding the Odd Number Out: Analyzing Number Properties

The question asks us to identify the number that is different from the others in the given list: 78, 91, 24, and 65. To find the "odd number out," we need to look for a common property shared by three of the numbers, which the remaining number does not possess. Let's examine the properties of these numbers.

Analyzing Each Number

We will analyze each number based on common numerical properties such as being even or odd, and divisibility by common factors.

78: This number ends in 8, so it is an even number. It is divisible by 2, 3 (since $7+8=15$), and 13 (since $78 = 6 \times 13$).
91: This number ends in 1, so it is an odd number. It is not divisible by 2 or 3. It is divisible by 7 (since $91 = 7 \times 13$) and 13.
24: This number ends in 4, so it is an even number. It is divisible by 2, 3 (since $2+4=6$), and other factors like 4, 6, 8, 12. It is not divisible by 13.
65: This number ends in 5, so it is an odd number. It is not divisible by 2 or 3. It is divisible by 5 and 13 (since $65 = 5 \times 13$).

Comparing Number Properties

Let's summarize our findings in a table to easily compare the properties of the numbers.

Number	Even/Odd	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 7	Divisible by 13
78	Even	Yes	Yes	No	No	Yes ($6 \times 13$)
91	Odd	No	No	No	Yes ($7 \times 13$)	Yes
24	Even	Yes	Yes	No	No	No
65	Odd	No	No	Yes ($5 \times 13$)	No	Yes

Looking at the table, let's check for a property that applies to three numbers but not the fourth:

Even/Odd: There are two even numbers (78, 24) and two odd numbers (91, 65). This property doesn't isolate one number.
Divisibility by 2: 78 and 24 are divisible by 2.
Divisibility by 3: 78 and 24 are divisible by 3.
Divisibility by 5: Only 65 is divisible by 5.
Divisibility by 7: Only 91 is divisible by 7.
Divisibility by 13: Numbers 78, 91, and 65 are all divisible by 13. The number 24 is not divisible by 13.

Identifying the Odd Number Out

Based on the analysis, the property of being divisible by 13 is shared by 78, 91, and 65. The number 24 does not share this property. Therefore, 24 is the odd number out based on its divisibility characteristics compared to the other numbers in the list.

Revision Table: Key Number Properties

Term	Definition	Example
Even Number	An integer that is divisible by 2. Ends in 0, 2, 4, 6, or 8.	78, 24
Odd Number	An integer that is not divisible by 2. Ends in 1, 3, 5, 7, or 9.	91, 65
Divisibility	The ability for one number to be divided by another number without leaving a remainder.	78 is divisible by 13 because $78 \div 13 = 6$.
Factor	A number that divides into another number exactly, without leaving a remainder.	13 is a factor of 78, 91, and 65.
Multiple	A number that may be divided by another number without a remainder. It is the result of multiplying a number by an integer.	78 is a multiple of 13 ($13 \times 6$).

Additional Information: Understanding Number Patterns

Finding the odd number out in a list often requires identifying a common pattern or rule that applies to most elements but not one. This pattern can be based on:

Even or odd status
Divisibility by a specific number (like 3, 5, 7, 11, 13, etc.)
Being a prime number or a composite number
Being a perfect square, perfect cube, or other special type of number
The sum or product of digits
A mathematical sequence or progression

In this specific problem, the pattern is related to divisibility by the number 13. All numbers except 24 are multiples of 13. Recognizing common factors or multiples is a key skill in solving such numerical reasoning problems.