GRE Math Problem 17

A business firm reduces the number of hours its employees work from 40 hours per week to 36 hours per week while continuing to pay the same amount of money. If an employee earned x dollars per hour before the reduction in hours, how much does he earn per hour under the new system?



A

B

C

D

E 9x

Solution for Analytical Problem 3:

Let’s fix the conditions:

The West Field must be planted with either barley or beans:

W: Ba OR Be

At least one field must be planted with corn.

Co: N OR E OR S

If, in the previous year, a field was planted with beans, then it must be planted with beans again.

Be –> Be

If, in the previous year, a field was planted with either wheat or alfalfa, then it must be planted with oats.

Wh –> Oa

Al –> Oa

To answer Question I we should first use condition 1 to cross out answer A (oats of the field for beans or barney). Then, we can see, that answers B and C have no place for corn. Then, in answer E one filed is planned for Alfalfa, which is not mentioned among four crops for this yesr. So, the answer is D.

Answer: D oats, barley, corn, beans.

To solve Question II, let’s draw a table:

	N	E	S	W
Year 1		Wh	Be
Year 2

We can determine the crops for Year 2 in E and S:

	N	E	S	W
Year 1		Wh	Be
Year 2		Oa	Be

The only place for corn left in the Year 2 is the North field, so, answer B must be true.

Answer: B The North Field is planted with corn.

Among the answers Question III we must look for one, which violates conditions for Western field. And we can see that if the Western field had been planted with alfalfa, then we’d have to plant neither barney, nor beans, but only wheat there the following year.

Answer: A alfalfa.

We’ll need a table again to arrange data from Question IV:

	N	E	S	W
Year 1	Oa	Oa	Oa	Co
Year 2

So, the crop in the Western must be changed. Besides, the crop in one of the other fields must be changed to corn. That’s why no less that two fields must be planted with crops that are different from those planted there for the previous year.

Answer: C two.

In Question V we should remember about the field for corn. The following year three fields will be planted with beans and the forth one – with corn. But the fourth one can’t be the Western field, because the Western field will be planted with beans or barney. The fourth field can’t be planted neither with wheat or beans, because it will be planted either with oats, or with beans the following year. So, we can see, that the fourth field was planted with oats.

Answer: C the fourth field was planted with oats.

Question VI can be solved with the help of the table:

	N	E	S	W
Year 1	Oa	Be	Al
Year 2

Using the initial conditions. We can determine the crops for Year 2:

	N	E	S	W
Year 1	Oa	Be	Al
Year 2	Co	Be	Oa	Ba OR Be

Answer: A Corn is planted in the North Field.

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