VJesus12 wrote:If 7 < m < 11 and −2 < n < 5, then which of the following expresses the possible values of mn ?

A. −14 < mn < 35
B. −14 < mn < 55
C. −22 < mn < 35
D. −22 < mn < 55
E."‰5 < mn < 16

The OA is D.

I got confused. I thought it should be B. Experts, I need some help. Thanks.

Using the above ranges, it's possible that m = 10.99999 and that n = -1.99999. If we multiply a number slightly less than 11 and a number slightly greater than -2, we'll get a product that is slightly greater than -22. This is why -22 marks the lower bound of the interval.

VJesus12 wrote:If 7 < m < 11 and −2 < n < 5, then which of the following expresses the possible values of mn ?

A. −14 < mn < 35
B. −14 < mn < 55
C. −22 < mn < 35
D. −22 < mn < 55
E."‰5 < mn < 16

To combine ranges with respect to a given operation, perform the given operation using EVERY COMBINATION OF ENDPOINTS.

Here, the given operation is MULTIPLICATION.
Calculating the value of mn using every combination of endpoints, we get:
(7)(-2) = -14.
(7)(5) = 35.
(11)(-2) = -22.
(11)(5) = 55.
The SMALLEST result gives us the LOWER limit of mn: -22.
The GREATEST result gives us the UPPER limit of mn: 55.
Thus:
-22 < mn < 55.

The correct answer is D.

Another example:

If -4<x<7 and -6<y<3, which of the following specifies all the possible values of x-y?

Here, the given operation is SUBTRACTION.
Calculating the value of x-y using every combination of endpoints, we get:
-4 - (-6) = 2.
-4 - 3 = -7.
7 - (-6) = 13.
7 - 3 = 4.
Thus:
-7 < x-y < 13.

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