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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If 7 < m < 11 and -2 < n < 5 tagged by: VJesus12 ##### This topic has 4 expert replies and 0 member replies ## If 7 < m < 11 and -2 < n < 5 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.â€‰5 < mn < 16 The OA is D. I got confused. I thought it should be B. Experts, I need some help. Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 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.â€‰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. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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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

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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.â€‰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.

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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### GMAT/MBA Expert

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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.â€‰5 < mn < 16
The maximum value for mn is 11 x 5 = 55 and the minimum value is 11 x -2 = -22.

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scott@targettestprep.com

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