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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

Add 8 times x to 2 times x and then subtract 5 from the sum. If x is a positive integer, the result must be an integer multiple of

Answer Choices

Right-o!

Explanation

The mathematical expression given in the question is (8 times x) + (2 times x) minus 5, which is equivalent to (10 times x) minus 5. The expression (10 times x) minus 5 can be factored as 5 times ((2 times x) minus 1). For every positive integer x, 5 times ((2 times x) minus 1) must be a multiple of 5. If x = 1, then 5 times ((2 times x) minus 1) = 5, which is not an integer multiple of  2, 8, 10, or 15. Therefore, the correct answer is 5.

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