Placing -15, -4, 4 and 15 on the number line, only d satisfies the given conditions. Hence D

\(-4 < m < 15\)

Or, \(m = { -3 , -2 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 }\)

Thus , from the given options only (A) fits in perfectly, \(m > - 15\)

Hence, Aswer will be (A)
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I doubt the answer "A".
Answer must be D.

If m < 15 and m > –4, which of the following must be true?

A. m > –15
B. m < 4
C. m > 4
D. –4 < m < 4
E. –15 < m < 4

We have that m < 15 and m > –4, thus -4 < m < 15 (this is given to be true). Any m from this range will be for sure greater than -15.

Answer: A.

As for the other options:

B. m < 4. This is not always true. For example, x could be 10.

C. m > 4. This is not always true. For example, x could be 0.

D. –4 < m < 4. This is not always true. For example, x could be 10.

E. –15 < m < 4. This is not always true. For example, x could be 10.

Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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We note that since m is greater than -4, any possible value of m will also be greater than -15, therefore m > -15.

To see why other choices are not possible, let’s pick values for m close to upper and lower bounds, such as m = -3 and m = 14.

Answer Choice B: We see that m < 4 is not necessarily true since m can equal 14.

Answer Choice C: We see that m > 4 is not necessarily true since m can equal -3.

Answer Choice D: We see that -4 < m < 4 is not necessarily true since m can equal 14.

Answer Choice E: We see that -15 < m < 4 is not necessarily true since m can equal 14.

Answer: A
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