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18 Aug 2020, 22:40
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Hi Folks,
I am currently reviewing the material from Manhattan GMAT. This is related to compound inequalities.
Here is the question:
If x>8, x<17, x+5<19, what is the range of possible values of x?
Solution:
Solving the above individual inequalities and making the equalities to point in the same direction we get these - 8<x, x<17, x<14
I see two possibilities: 8<x<14 OR 8<x<17
But the book prefers 8<x<14 as this is a tighter range than 8<x<17
Let's say x=15. This would not fall in the inequality 8<x<14 but x=15 still satisfies the individual inequality x<17 (given in the question).
Is it correct to conclude 8<x<17 would be a better option than 8<x<14 OR is there something I am missing?
I am currently reviewing the material from Manhattan GMAT. This is related to compound inequalities.
Here is the question:
If x>8, x<17, x+5<19, what is the range of possible values of x?
Solution:
Solving the above individual inequalities and making the equalities to point in the same direction we get these - 8<x, x<17, x<14
I see two possibilities: 8<x<14 OR 8<x<17
But the book prefers 8<x<14 as this is a tighter range than 8<x<17
Let's say x=15. This would not fall in the inequality 8<x<14 but x=15 still satisfies the individual inequality x<17 (given in the question).
Is it correct to conclude 8<x<17 would be a better option than 8<x<14 OR is there something I am missing?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
19 Aug 2020, 07:02
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If you know that x < 14 is true, then x cannot be equal to 15. So if you know, say, that x < 14 is true, and x < 17 is also true, then that second inequality, "x < 17", is useless, since you already know it's true from the inequality "x < 14".
If you know several inequalities are all true, and you want to combine them into a single inequality, you are trying to find where the inequalities overlap. So if you knew these inequalities were all true, say:
a > -4
a < 7
-11 < a < 5
then we know -4 < a < 5, because that is the only range of values for a that works with all three inequalities.
If you know several inequalities are all true, and you want to combine them into a single inequality, you are trying to find where the inequalities overlap. So if you knew these inequalities were all true, say:
a > -4
a < 7
-11 < a < 5
then we know -4 < a < 5, because that is the only range of values for a that works with all three inequalities.
19 Aug 2020, 14:30
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IanStewart
Great explanation! Thanks
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
