Productivity

[neeti2711]

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?

(A) It is only Quore's production structure that makes it possible fro Quore to survive the transformation of the market.
(B) Quore will not go bankrupt if it achieves a productivity increase of 20 percent over the next two years.
(C) If the market had not been transformed, Quore would have required no productivity increase in order to avoid bankruptcy.
(D) Because of the transformation of the market Quore will achieve a productivity increase of 10 percent over the next two years.
(E) If a 20 percent productivity increase is unattainable for Quore, then it must go bankrupt.

OA: E

I selected B and got it wrong. I thought ways of eliminating B and concluded that since the argument says that productivity must increase 10 percent - so this is the minimum increase that has to happen to avoid bankruptcy. Below 10 percent will make the company bankrupt. But above 10 percent will not necessarily ensure non-bankruptcy. I hope this line of reasoning is correct.

But I am not sure how E is correct?

[GMATGuruNY]

The following information is more relevant to the LSAT than to the GMAT.

If A, then B:
If John is in Times Square, then John is in New York.
Since Times Square is located in New York, the statement above is true.

If B, then A:
If John is in New York, then John is in Times Square.
The statement above is NOT necessarily true, since it is possible to be in New York but not in Times Square.
Implication:
Given If A, then B, we CANNOT conclude If B, then A.

If not A, then not B:
If John is not in Times Square, then John is not in New York.
The statement above is NOT necessarily true. since it is possible not to be in Times Square but still be in New York.
Implication:
Given If A, then B, we CANNOT conclude If not A, then not B.

If not B, then not A:
If John is not in New York, then John is not in Times Square.
The statement above must be true, since New York is where Times Square is located.

Implication:
Given If A, then B, we CAN conclude If not B, then not A.
The statement in blue is known as the CONTRAPOSITIVE.
We CANNOT conclude If B, then A or If not A, then not B.

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?

(A) It is only Quore's production structure that makes it possible fro Quore to survive the transformation of the market.
(B) Quore will not go bankrupt if it achieves a productivity increase of 20 percent over the next two years.
(C) If the market had not been transformed, Quore would have required no productivity increase in order to avoid bankruptcy.
(D) Because of the transformation of the market Quore will achieve a productivity increase of 10 percent over the next two years.
(E) If a 20 percent productivity increase is unattainable for Quore, then it must go bankrupt.

The passage above, rephrased as a series of if-then statements:
If Quore does not improve productivity by 10%, then it will go bankrupt.
If Quore can improve productivity by 10%, then it can improve productivity by 20%.

Contrapositive of the blue statement:
If Quore cannot improve productivity by 20%, then it cannot improve productivity by 10%.

If we combine the green statement with the red statement, we get:
If Quora cannot improve productivity by 20%, then it cannot improve productivity by 10%.
If Quore does not improve productivity by 10%, then it will go bankrupt.
The two statements combined imply the following:
If Quore cannot improve productivity by 20%, then it will go bankrupt.

The correct answer is E.

I selected B and got it wrong. I thought ways of eliminating B and concluded that since the argument says that productivity must increase 10 percent - so this is the minimum increase that has to happen to avoid bankruptcy. Below 10 percent will make the company bankrupt. But above 10 percent will not necessarily ensure non-bankruptcy. I hope this line of reasoning is correct.

If A, then B:
If Quore does not improve productivity by 10%, then it will go bankrupt.
If not A, then not B:
If Quore improves productivity by 10%, then it will not go bankrupt.
As noted above, we cannot conclude that the statement in orange -- if not A, then not B -- is true.

B, rephrased:
If Quore achieves a productivity increase...then it will not go bankrupt.
Since the statement in orange does not have to be true, we cannot conclude that an increase in productivity will prevent bankruptcy.
Eliminate B.

[neeti2711]

Great explanation! Thank you!