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If 7 < m < 11 and −2 < n < 5, then which of the following expresses th

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If 7 < m < 11 and −2 < n < 5, then which of the following expresses th [#permalink]

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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
[Reveal] Spoiler: OA

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Re: If 7 < m < 11 and −2 < n < 5, then which of the following expresses th [#permalink]

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New post 19 Apr 2017, 11:56
SajjadAhmad 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


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If 7 < m < 11 and −2 < n < 5, then which of the following expresses th [#permalink]

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To find range of product mn, minimize lowest product and maximize highest product.

Here, to minimize, take the negative value of n and multiply by the higher positive value of m:

-2 * 11 = -22

To maximize, take the higher positive value of m, and the positive value of n:

11 * 5 = 55

Hence -22 < mn < 55

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Re: If 7 < m < 11 and −2 < n < 5, then which of the following expresses th [#permalink]

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New post 03 Dec 2017, 20:07
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Hi All,

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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D


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Re: If 7 < m < 11 and −2 < n < 5, then which of the following expresses th   [#permalink] 03 Dec 2017, 20:07
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