Concept: Compound inequalities
Question: 5! + 3 < a < 5! + 8
a) 3 < a < 8
b) 0 < a < 5
c) 3 < a- 5! < 8
Compound Inequalities problem
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- GenEdMBA
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The answer is c. You simply subtract 5! from each of the 3 different expressions.
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This can also be solved by actually computing 5! (5 * 4 * 3 * 2 * 1, or 120).GenEdMBA wrote:Concept: Compound inequalities
Question: 5! + 3 < a < 5! + 8
a) 3 < a < 8
b) 0 < a < 5
c) 3 < a- 5! < 8
Then you have
120 + 3 < a < 120 + 8
or
123 < a < 128
From this you can tell that the first two inequalities won't work, while the last one is just
3 < a - 120 < 8
which is the same thing as the red inequality above, with 120 subtracted from all three parts.
- GenEdMBA
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Answer: 3 < a-5! < 8
Don't make the mistake of subtracting 5! From only first and last term and choosing option (a) as answer. Subtract 5! From all 3 terms, so
5!+3<a<5!+8
Subtracting 5! From all 3 terms
3!< a- 5! < 8
Mantra: For compound inequalities (inequalities with more than one inequality sign) , perform operations on all terms together, not on first and last term alone.
Don't make the mistake of subtracting 5! From only first and last term and choosing option (a) as answer. Subtract 5! From all 3 terms, so
5!+3<a<5!+8
Subtracting 5! From all 3 terms
3!< a- 5! < 8
Mantra: For compound inequalities (inequalities with more than one inequality sign) , perform operations on all terms together, not on first and last term alone.
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