[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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Which of following satisfies the inequality (2x-49)(x^2+6x+1
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Max@Math Revolution
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The two factors must have DIFFERENT SIGNS.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
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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Max@Math Revolution
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=>
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
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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