Direction: Read the following information carefully and answer the qu...
Question: Minimum how many of these integers can be even?
Given:
- P, Q, R, S, T, U, and V are seven positive integers
- (P x Q x R x S x T x U x V) is odd
Solution:
- In order for the product of seven positive integers to be odd, we need an odd number of odd integers
- Let's assume that all seven integers are odd
- The product of seven odd integers is also odd, which contradicts the given information that the product is odd
- Therefore, we must have at least one even integer
- Let's assume that we have only one even integer, say P
- In this case, the product would be even, which again contradicts the given information that the product is odd
- Therefore, we must have at least two even integers
- Let's assume that we have only two even integers, say P and Q
- In this case, the product would be even, which again contradicts the given information that the product is odd
- Therefore, we must have at least three even integers
- Let's assume that we have only three even integers, say P, Q, and R
- In this case, the product would be odd, which satisfies the given information
- Therefore, the minimum number of integers that can be even is 0
Answer: Option D (0)
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