Choose the number which is different from the others in the group based on a simple numerical property.

Introduction / Context:
This numerical reasoning question asks you to identify which number is different from the others in the group. All the numbers appear fairly ordinary, so the difference lies in a hidden arithmetic property such as divisibility by a particular number.

Given Data / Assumptions:

• The numbers are 380, 120, 290, 168 and 240.
• All the numbers are positive integers.
• Many classification questions are based on divisibility by 2, 3, 4 or other small integers.
• We are looking for a simple property shared by three of the four original numbers but not by the remaining one.

Concept / Approach:
A straightforward way to solve this type of question is to test each number for divisibility by a small integer such as 4, 6, 8 or 10. In many reasoning tests, differences based on being divisible or not divisible by 4 are common, because they can be checked quickly by looking at the last two digits of the number.

Step-by-Step Solution:
Step 1: Check divisibility by 4. A number is divisible by 4 if the number formed by its last two digits is divisible by 4.Step 2: For 380, the last two digits are 80. Since 80 ÷ 4 = 20, 380 is divisible by 4.Step 3: For 120, the last two digits are 20. Since 20 ÷ 4 = 5, 120 is divisible by 4.Step 4: For 168, the last two digits are 68. Since 68 ÷ 4 = 17, 168 is divisible by 4.Step 5: For 290, the last two digits are 90. Since 90 ÷ 4 does not give an integer (90 ÷ 4 = 22.5), 290 is not divisible by 4.Step 6: For comparison, 240 has last two digits 40, and 40 ÷ 4 = 10, so 240 is also divisible by 4.Step 7: Among the original four numbers (380, 120, 290, 168), three numbers (380, 120, 168) are divisible by 4, while 290 alone is not.Step 8: Therefore, 290 is the number that is different from the others based on divisibility by 4.

Verification / Alternative check:
You can verify this result by actually performing division. 380 ÷ 4 = 95, 120 ÷ 4 = 30, and 168 ÷ 4 = 42, all integers. But 290 ÷ 4 = 72.5, which is not an integer. For extended checking, notice that 290 is 29 × 10 and 29 is an odd prime that does not combine with 10 to produce a multiple of 4.

Why Other Options Are Wrong:
380, 120 and 168 all share the property of being multiples of 4 in addition to other divisibility features. They therefore belong naturally in one group. Any extra practice number like 240 also fits that group as it is divisible by 4. Only 290 fails this simple divisibility test, so it cannot be grouped with the others on this property.

Common Pitfalls:
Some candidates may try to use more complicated properties, such as sum of digits or prime factorisation, which are unnecessary here. Others choose the largest or smallest number without justification. The safest strategy is to look for a simple and common divisibility rule, such as divisibility by 4, which can be tested quickly from the last two digits of the number.

Final Answer:
The number which is different from the others in the group is 290.