If 'X' is a multiple of 4 and 'Y' is a multiple of 6, can we conclude that 'X +

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Question: If \'X\' is a multiple of 4 and \'Y\' is a multiple of 6, can we conclude that \'X + Y\' is a multiple of 10?

Options:

Correct Answer: No, not necessarily.

Solution:

\'X + Y\' being a multiple of 10 cannot be concluded from the given information.

If 'X' is a multiple of 4 and 'Y' is a multiple of 6, can we conclude that 'X + Y' is a multiple of 10?

If 'X' is a multiple of 4 and 'Y' is a multiple of 6, can we conclude that 'X + Y' is a multiple of 10?

Step 1: Understand what a multiple is. A multiple of a number is the result of multiplying that number by an integer. For example, multiples of 4 are 4, 8, 12, 16, etc.
Step 2: Identify what 'X' and 'Y' are. 'X' is a multiple of 4, which means it can be written as 4n (where n is an integer). 'Y' is a multiple of 6, which means it can be written as 6m (where m is an integer).
Step 3: Write the expression for 'X + Y'. Since 'X' is 4n and 'Y' is 6m, we can write 'X + Y' as 4n + 6m.
Step 4: Check if 'X + Y' can be a multiple of 10. A number is a multiple of 10 if it ends in 0. We need to see if 4n + 6m can end in 0.
Step 5: Analyze the possible values of 'X + Y'. Since 'X' and 'Y' can take many values, we can test some examples. For example, if n = 1 (X = 4) and m = 1 (Y = 6), then X + Y = 10, which is a multiple of 10. But if n = 1 (X = 4) and m = 2 (Y = 12), then X + Y = 16, which is not a multiple of 10.
Step 6: Conclude that 'X + Y' being a multiple of 10 cannot be guaranteed because it depends on the specific values of n and m.

Multiples and Divisibility – Understanding how multiples of different numbers interact and the conditions under which their sums are also multiples.