From the following numbers, which one is the odd one out based on divisibility by 25?

Introduction / Context:
This odd one out question is based on divisibility properties of numbers. Four of the given numbers share a common factor, while one number does not. You are required to identify that special number. Recognising divisibility by 25 is particularly useful in such problems, because it is linked to numbers ending in 00, 25, 50 or 75.

Given Data / Assumptions:

• Numbers given: 700, 250, 350, 640 and 900.
• You need to find which number does not share a key divisibility property with the others.
• We recall that a number is divisible by 25 if its last two digits form 00, 25, 50 or 75.
• We aim for a clean and simple numerical property that explains the pattern.

Concept / Approach:
Look at the last two digits of each number. For 700, the last two digits are 00, so 700 is divisible by 25. For 250, the last two digits are 50, which again indicates divisibility by 25. For 350, the last two digits are also 50, so it is again a multiple of 25. For 900, the last two digits are 00, so it is divisible by 25 as well. Now check 640: the last two digits are 40, which do not match 00, 25, 50 or 75. Therefore, 640 is not divisible by 25. This makes it different from the others and hence the odd one out.

Step-by-Step Solution:

Write the last two digits of 700, 250, 350, 640 and 900. 700 ends with 00, so 700 / 25 is an integer. 250 ends with 50, so 250 / 25 is 10, an integer. 350 also ends with 50, so 350 / 25 is 14, an integer. 900 ends with 00, so 900 / 25 is 36, an integer. 640 ends with 40, which is not 00, 25, 50 or 75, so 640 is not divisible by 25.

Verification / Alternative check:
If you actually divide, 700 / 25 = 28, 250 / 25 = 10, 350 / 25 = 14 and 900 / 25 = 36, all neat whole numbers. However, 640 / 25 equals 25.6, which is not an integer. This confirms that only 640 fails the test of divisibility by 25. No other simple property like parity or divisibility by 10 distinguishes only one number as clearly as this property does.

Why Other Options Are Wrong:
700, 250, 350 and 900 all share the common feature of being multiples of 25. Because we are looking for the number that does not share the group property, these cannot be the odd one out. Only 640 lacks this shared factor and hence fits the requirement.

Common Pitfalls:
A common mistake is to focus on even and odd status or to pick the smallest or largest number without checking divisibility patterns. Many reasoning questions use factors like 5, 10 or 25 as the hidden link, so checking these quickly can save time and prevent confusion.

Final Answer:
The only number not divisible by 25 is 640, so it is the odd one out.