Sufficient & Necessary Questions - - Question 10

Because of the recent transformation of the market, Quore, Inc., must increase productivity 10 percent over the cours...

SawyerJeppson April 2, 2021

Answer B verse answer E

Because of the recent transformation of the market, Quore, Inc., must increase productivity 10 percent over the course of the next two years, or it will certainly go bankrupt. In fact, however, Quore's production structure is such that if a 10 percent productivity increase is possible, then a 20 percent increase is attainable. If the statements above are true, which one of the following must on the basis of them also be true? B: Quore will not go bankrupt if it achieves a productivity increase of 20 percent over the next two years. 20%increase --> ~B [B---> ~20% increase] E:If a 20 percent productivity increase is unattainable for Quore, then it must go bankrupt. ~20%increase ---> B [~B----> 20%increase] Hi I am confused on the difference between answer B and answer E? For answer B: Wouldn't having a 20% increase mean a 10% increase has already been met, which would keep it from going bankrupt? But the question asks for the answer that must be true, so what scenario or in what way does answer B not stand true in all cases? I understand answer E, but I don't understand why answer B does not work either.

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Victoria April 2, 2021

Hi @SawyerJeppson,

Happy to help!

Answer choice (B) is incorrect because it reverses the logic.

We know that if Quore does not increase productivity 10%, then they will go bankrupt.

Not IP10% --> B
Not B --> IP10%

We also know that, if Quore can increase their productivity by 10%, then they can also increase their productivity by 20%.

IP10% --> IP20%
Not IP20% --> Not IP10%

We can then use the transitive property to conclude:

Not IP20% --> B
Not B --> IP20%

Answer choice (B) simply reverses this, claiming that, if IP20%, then not B.

As we must always reverse and negate, answer choice (B) is incorrect.

Hope this helps! Please let us know if you have any further questions.

SawyerJeppson April 2, 2021

Thank you!

SawyerJeppson April 22, 2021

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