GRE Math Problem 52

A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long is the rug?
(A) 6
(B)
(C)
(D)
(E)


Solution for GRE Analytical Problem 4:
Let’s arrange data and write down requirements and restrictions

• One piece is purple and two pieces each are red, green, yellow, and blue.

We have the colours of P, R, R, G, G, Y, Y, B, B,

• The two red pieces are consecutive numbers.

Requirement 1: R-R

• The number 4 is green.

Requirement 2: 4G

• The two blue pieces are not consecutive numbers.

Restriction 1: NOT B-B

• Both the 1 and the 9 are yellow.

Requirement 3: 1Y
Requirement 4: 9Y

• The purple piece is not a number immediately greater than or less than either green piece.

Restriction 2: NOT G-P
Restriction 3: NOT P-G
And we can fill in the table using the requirements 2, 3, 4:

1	2	3	4	5	6	7	8	9
Y			G					Y

Then, using the Restrictions 2 and 3, we can say that neither 3, nor 5 can be Purple.

Question I. If one of the red pieces is the number 3, what number is the other red piece?

1	2	3	4	5	6	7	8	9
Y		R	G					Y

According to Requirement 1: R-R, number 2 must be Red.
Answer: (A) 2

Question II. If the number 5 is green, each of the following could be true EXCEPT

1	2	3	4	5	6	7	8	9
Y			G	G				Y

Answer: (B) The number 6 is purple. – This statement contradicts Restriction 2: NOT G-P

Question III. If the number 6 is green, which of the following could be true?

1	2	3	4	5	6	7	8	9
Y			G		G			Y

If 6G, we’ll have only two places for the Purple piece: 2 or 8 . If 2P, then we’ll have two consecutive slots for R-R, it is 7-8. Two remaining slots will be taken by the Blue pieces

1	2	3	4	5	6	7	8	9
Y	P	B	G	B	G	R	R	Y

If 8G, we’ll have only two places for the Purple piece. If 2P, then the two consecutive slots for R-R are 2-3. Two remaining slots will be taken by the Blue pieces

1	2	3	4	5	6	7	8	9
Y	R	R	G	B	G	B	P	Y

Now let’s look trough the answers
(A) The number 2 is blue. - impossible
(B) The number 3 is purple. - impossible
(C) The number 5 is red. - impossible
(D)The number 5 is purple. - impossible
(E) The number 7 is blue. – possible within the second arrangement
Answer: (C) The number 5 is red (Thanks to swath for correction).

Question IV. Which of the following, if true, would enable you to determine the color of every number?
Let’s first find the statement, which involves the color and location with more restrictions. Let’s test (E) The 7 is green.

1	2	3	4	5	6	7	8	9
Y			G			E		Y

Restriction 2: NOT G-P and Restriction 3: NOT P-G leave only one slot for P: 2P

1	2	3	4	5	6	7	8	9
Y	P		G			E		Y

Now we have only single pair of consecutive slots for R-R

1	2	3	4	5	6	7	8	9
Y	P		G	R	R	E		Y

And the remaining slots will be taken by B:

1	2	3	4	5	6	7	8	9
Y	P	B	G	R	R	E	B	Y

So, using statement  (E) we managed to determine the colors of all the pieces

Answer: (E) The 7 is green.
Answer:

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