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15 Apr 2015, 04:49
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
36% (03:05) correct
64%
(03:32)
wrong
based on 133
sessions
History
Date
Time
Result
Not Attempted Yet
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, what is the difference in the distance traveled by the two?
(A) 20
(B) 40
(C) 80
(D) 120
(E) 140
Kudos for a correct solution.
(A) 20
(B) 40
(C) 80
(D) 120
(E) 140
Kudos for a correct solution.
20 Apr 2015, 06:06
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Bunuel
VERITAS PREP OFFICIAL SOLUTION
The first thing we do in these “direction” questions is draw the diagram. But there is a problem here: how do we decide the orientation of the rectangle? It could be either of these two.
Attachment:
Ques5.jpg [ 9.54 KiB | Viewed 4197 times ]
1. Length is the longest side of the rectangle.
2. Width is from side to side and length is whatever width isn’t (i.e. the side from up to down in a rectangle) (this definition is less embraced than the first one)
If the side from up to down is the longest side, then there is no conflict.
Keeping this in mind, when drawing the figure, given that length is the longer of the two, one could make the rectangle on the left and there will be no conflict. But the question maker may not want to take for granted that you know this.
So he/she leaves a clue – the question mentions that ‘Jacob walks 180 ft down the west side of the field’. There needs to be at least 180 ft on the west side of the field for him to travel that much. So the orientation on the left makes sense. This is something the question maker would have put to try to give you a hint of the orientation. Now that we know what our diagram should look like, we can proceed to solve this question.
Attachment:
Ques4.jpg [ 10.63 KiB | Viewed 4179 times ]
QR = 160, RS = 300
So QR:RS = 8:15
Remember 8-15-17 pythagorean triplet? (the third triplet after 3-4-5 and 5-12-13)
Since the two sides are in the ratio 8:15, the hypotenuse must be 17. The common multiplier is 20 so QS should be 17*20 = 340
Therefore, Peter traveled 340 feet.
TP = 120, PS = 160
TP:PS = 3:4
Does it remind you of 3-4-5 triplet?
120 is 3*40 and 160 is 4*40 so TS will be 5*40 = 200
So Jacob traveled a total distance of 180 + 200 = 380 feet.
Difference between the distance traveled = 380 – 340 = 40 feet
Note: The following triplets come in handy: (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) and (9, 40, 41)
General Discussion
15 Apr 2015, 08:51
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Bunuel
Distance by Peter=Diagonal of the rectangle of 300*160 ft
\(\sqrt{90000+25600}\)
\(\sqrt{115600}\)
=340
Distance by Jacob = 180 + Diagonal of rectangle of 300*20 ft
=180 + \(\sqrt{90000+400}\)
=180+approx 300
=480 approx
Difference between the distance of Peter and Jacob = 480-340
=140
Answer: E
