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Chapter 10: Problem 3

If the product of two distinct integers is \(91,\) then which of the following could be the sum of the two integers? Indicate all such sums. A. $$-92$$ B. $$-91$$ C. $$7$$ D. $$13$$ E. $$20$$

Short Answer

Expert verified
The possible sums are -92 and 20.

Step by step solution

01

Listing the factors of 91

First identify all the factors of 91. Factors of 91 are pairs of numbers that you could multiply together to get 91. Since 91 equals 7 times 13, the pairs of integers that multiply to become 91 are: (1,91), (-1,-91),(7,13), (-7,-13).
02

Compute the sums

Now, add each pair of factors to compute their sums. The sum of (1,91) is 92; the sum of (-1,-91) is -92; the sum of (7,13) is 20; the sum of (-7,-13) is -20.
03

Match the sums

From Step 2, we found four sums: 92, -92, 20, -20. Now compare these to the given options (A. -92, B. -91, C. 7, D. 13, E. 20). From this comparison, we find that the sums that match the options are -92 (option A) and 20 (option E). These are the possible sums of two distinct integers that multiply to 91.

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