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TheUltimateWinner
Joined: 23 Feb 2015
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Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,465
08 Oct 2019, 02:01
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
48% (02:40) correct
52%
(02:41)
wrong
based on 107
sessions
History
Date
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Result
Not Attempted Yet
Solve the system of inequalities:
\(3x+12≥7(x-3)\) and \(\frac{x+3}{x-7}\)≥2
A) x∈ (7, \(\frac{33}{4}\)]
B) x∈ [\(\frac{33}{4}\), 17)
C) x∈ [-\(\frac{33}{4}\), 7)
D) x∈ (-∞, \(\frac{33}{4}\)] ∪ (7, 17]
E) x∈ (7, 17]
\(3x+12≥7(x-3)\) and \(\frac{x+3}{x-7}\)≥2
A) x∈ (7, \(\frac{33}{4}\)]
B) x∈ [\(\frac{33}{4}\), 17)
C) x∈ [-\(\frac{33}{4}\), 7)
D) x∈ (-∞, \(\frac{33}{4}\)] ∪ (7, 17]
E) x∈ (7, 17]
08 Oct 2019, 05:53
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Asad
Solve the system of inequalities:
\(3x+12≥7(x-3)\) and \(\frac{x+3}{x-7}\)≥2
3x+12≥7(x-3)
3x + 12 ≥7x - 21
33 ≥ 4x
x \(\leq\) 33/4 = 8 1/4 (1)
\(\frac{x+3}{x-7}\)≥2
\(\frac{x+3}{x-7}-2\)≥0
{(x+3) - 2(x-7)}/(x-7) ≥0
(-x+17)/(x-7)≥0
\((x-17)/(x-7)\leq 0\)
\(7<x\leq 17\) (2)
Combining (1) & (2)
\(7<x<\leq 33/4\)
A) x∈ (7, \(\frac{33}{4}\)]
IMO A
General Discussion
08 Oct 2019, 05:39
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Asad
\(3x+12≥7(x-3)\) and \(\frac{x+3}{x-7}\)≥2
Looking at the choices, you can easily eliminate choices by taking x as 10 and 0..
1) x=0...
\(3x+12≥7(x-3).....0+12≥7(0-3)\)...True
and \(\frac{x+3}{x-7}\)≥2.....\(\frac{3}{-7}≥2\)...No
Eliminate choices containing 0.... C and D out
2) x=10...
\(3x+12≥7(x-3).....30+12≥7(10-3)....42≥49\)...No
and \(\frac{x+3}{x-7}\)≥2.....\(\frac{13}{3}≥2\)...Yes
Eliminate choices containing 10.... B and E also out
A left
