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Which of following satisfies the inequality (2x-49)(x^2+6x+1

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by Max@Math Revolution » Thu Feb 28, 2019 11:40 pm

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[GMAT math practice question]

Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?

A. 24
B. 25
C. 50
D. 51
E. 99
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by GMATGuruNY » Fri Mar 01, 2019 4:30 am
Max@Math Revolution wrote:[GMAT math practice question]

Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?

A. 24
B. 25
C. 50
D. 51
E. 99
The two factors must have DIFFERENT SIGNS.
Each of the answer choices will yield a positive value for x² + 6x + 10.
Thus, the correct answer must yield a negative value for 2x-49.
Only A is viable:
(2*24) - 49 = -1.

The correct answer is A.
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by Max@Math Revolution » Sun Mar 03, 2019 5:16 pm
=>

x^2+6x+10 = x^2+6x+9 + 1 = (x+3)^2+1 ≥ 1 > 0.
Since x^2+6x+10 > 0, we have (2x-49)(x^2+6x+10) ≤ 0, which implies that 2x - 49 < 0.
So, 2x < 49, and x < 24.5.

Therefore, the answer is A.
Answer: A
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