Number properties

The units digit of powers of 7 follows a repeating four-step pattern of 7, 9, 3, and 1. Since the exponent 100 is a multiple of 4, the units digit of 7^100 is 1, which leaves a remainder of 1 when divided by 5. A remainder of 4 is incorrect because it corresponds to powers ending in 9, such as 7^2.

To select the committee, we find the combinations of choosing 2 men from 4, which is 6, and 2 women from 5, which is 10. Multiplying these independent choices yields 6 * 10 = 60 total ways. A common error is calculating permutations instead of combinations, which would incorrectly yield 120.

The units digit of powers of 7 follows a repeating four-step pattern of 7, 9, 3, and 1. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !A remainder of 4 is incorrect because it corresponds to powers ending in 9, such as 7^2.
• !The greatest common divisor is the largest integer that divides both numbers without a remainder, which is 12 since 24/12 = 2 and 36/12 = 3.
• !A common error is calculating permutations instead of combinations, which would incorrectly yield 120.
• !Option B is incorrect because 3 is an odd prime, while Option D is incorrect because most prime numbers are odd.

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