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

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

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New post 01 Mar 2019, 00:58
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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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Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?  [#permalink]

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New post 01 Mar 2019, 01:16
MathRevolution wrote:
[GMAT math practice question]

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

\(A. 24\)
\(B. 25\)
\(C. 50\)
\(D. 51\)
\(E. 99\)



All choices are positive, so \((x^2+6x+10)>0\) for all positive x...
For \((2x-49)(x^2+6x+10) < 0\), 2x-49<0 as \((x^2+6x+10)>0\).
So, 2x-49<0....2x<49...x<49/2 or x<24.5

Only 24 is in the range ..

A
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Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?  [#permalink]

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New post 01 Mar 2019, 01:31
MathRevolution wrote:
[GMAT math practice question]

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

\(A. 24\)
\(B. 25\)
\(C. 50\)
\(D. 51\)
\(E. 99\)



Either (2x - 49) or \((x^2 + 6x + 10)\) must be negative.

but if you scan the answer choices , you see that there is no negative answer choices.

Thus, \(( x^2 + 6x + 10)\) can not be negative in this case.

So, (2x - 49) is negative.

2x - 49<0

2x <49

scanning the option it's visible that only available value of x is 24.

2*24 <49.

The correct answer is A.
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Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?  [#permalink]

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New post 01 Mar 2019, 05:44
MathRevolution 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

.
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Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?  [#permalink]

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New post 03 Mar 2019, 18:36
=>

\(x^2+6x+10 = x^2+6x+9 + 1 = (x+3)^2+1 ≥ 1 > 0\).
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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Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?   [#permalink] 03 Mar 2019, 18:36
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