CSAT 2024 Solutions - Consider the following statements in respect of the sum S = x + y + z, where x, y, and z are distinct prime numbers each less than 10

Consider the following statements in respect of the sum S = x + y + z, where x, y, and z are distinct prime numbers each less than 10:

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1. The unit digit of S can be 0.
2. The unit digit of S can be 9.
3. The unit digit of S can be 5.

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Which of the statements given above are correct?

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A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1, 2 and 3

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Answer: C. 1 and 3 only

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‍Explanation

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The distinct prime numbers less than 10 are: 2, 3, 5, and 7.

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We will check all possible sums of three distinct primes to find all the possible value of unit digit.

- 2 + 3 + 5 = 10 (unit digit is 0)

- 2 + 3 + 7 = 12 (unit digit is 2)

- 2 + 5 + 7 = 14 (unit digit is 4)

- 3 + 5 + 7 = 15 (unit digit is 5)

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Therefore, the unit digit of S can be 0 and 5 but not 9.