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04 Oct 2018, 01:57
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B
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Difficulty:
15%
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Question Stats:
84% (01:59) correct
16%
(02:14)
wrong
based on 216
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Jack traveled from Town X to Town Y in 3 hours, and her speed was between 30 miles per hour and 45 miles per hour. Brian also traveled from Town X to Town Y along the same route in 2 hours, and his speed was between 35 miles per hour and 55 miles per hour. Which of the following could be the distance, in miles, from Town X to Town Y?
(A) 8
(B) 105
(C) 115
(D) 120
(E) 135
(A) 8
(B) 105
(C) 115
(D) 120
(E) 135
04 Oct 2018, 03:00
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If we take jack’s speed to be 30 or 45 we get distance = 3 * 30 = 90 miles
Or 3*45 = 135 miles
His speed is between 30 and 45 so the distance must be between these two values.
For brian if we do the same case 35 or 55
35 * 2 = 70
55 * 2 = 110
Brian’s distance is 70 < x < 110
Jack’s distance is 90 < y < 135
The only distance that overlaps between the two is 105
Answer choice B.
Posted from my mobile device
Or 3*45 = 135 miles
His speed is between 30 and 45 so the distance must be between these two values.
For brian if we do the same case 35 or 55
35 * 2 = 70
55 * 2 = 110
Brian’s distance is 70 < x < 110
Jack’s distance is 90 < y < 135
The only distance that overlaps between the two is 105
Answer choice B.
Posted from my mobile device
05 Oct 2018, 18:38
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Bunuel
I tried with the backsolving approach.
Of the answer choices given,let's assume that 115 could be a possible distance. So as per the question stem,Jack's speed would be 115/3 = 38.33mph which falls into the bracket given in the question. But Brian's speed would be 115/2 = 57.5mph which exceeds the given bracket. Going anything above 115 would make no sense as the speeds for the two of them would be too high. So we go to try with answer choice B,i.e.105. With 105,Jack's speed would be 35mph and Brian's speed would be 52.5mph,both of which satisfy the bracket. Hence,B is the correct choice.
