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If 7 < m < 11 and -2 < n < 5

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If 7 < m < 11 and -2 < n < 5

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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.

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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.

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Hi VJesus12,

In these types of questions, there's often a fairly easy 'brute force' approach to getting the correct answer - multiply together every pair of values at the 'extremes' of the ranges and choose the least and greatest of that list.

Here, we're told that 7 < M < 11 and -2 < N < 5. The 'extreme' values of (M)(N) would be...

(7)(-2) = -14
(7)(5) = 35
(11)(-2) = -22
(11)(5) = 55

Thus, the range of (M)(N) would be -22 < (M)(N) < 55

Final Answer: D

GMAT assassins aren't born, they're made,
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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:
Quote:
If -4
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.

Similar problems:
http://www.beatthegmat.com/xy-t280232.html
http://www.beatthegmat.com/which-of-the-following-represents-the-range-of-all-possible-t213190.html
http://www.beatthegmat.com/gmat-prep-question-t279846.html
http://www.beatthegmat.com/og-129-rounding-problem-t86849.html
http://www.beatthegmat.com/modulus-ds-question-t107443.html

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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 maximum value for mn is 11 x 5 = 55 and the minimum value is 11 x -2 = -22.

Answer: D

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