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.
If 7 < m < 11 and −2 < n < 5
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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
The OA is D.
I got confused. I thought it should be B. Experts, I need some help. Thanks.
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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,
Rich
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,
Rich
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To combine ranges with respect to a given operation, perform the given operation using EVERY COMBINATION OF ENDPOINTS.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
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:
Here, the given operation is SUBTRACTION.If -4<x<7 and -6<y<3, which of the following specifies all the possible values of x-y?
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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The maximum value for mn is 11 x 5 = 55 and the minimum value is 11 x -2 = -22.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
Answer: D
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