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08 Jan 2020, 02:33
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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:
28% (03:11) correct
72%
(03:30)
wrong
based on 67
sessions
History
Date
Time
Result
Not Attempted Yet
Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southeast of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to
(A) 6:15 am
(B) 6:30 am
(C) 6:45 am
(D) 7:00 am
(E) 7:15 am
Are You Up For the Challenge: 700 Level Questions
(A) 6:15 am
(B) 6:30 am
(C) 6:45 am
(D) 7:00 am
(E) 7:15 am
Are You Up For the Challenge: 700 Level Questions
08 Jan 2020, 08:06
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C should be in the Southwest Of A
BCA is a (60-90-30) triangle. hence, BC= 500/2=250 Km and AC= 500*\((\frac{\sqrt{3}}{2})\)
Time taken by train to reach C= 250/50= 5hr
Train will arrive C at 1 PM
hence, Rahim must arrive C latest by 12:45 PM
Time taken by Rahim to reach C= \(\frac{250\sqrt{3}}{70} \)= 6.18 hrs =~ 6 hrs 12 mins
The latest time by which Rahim must leave A and still catch the train= 1245 - 612 =~ 0633 hrs or 6:33 AM
B
BCA is a (60-90-30) triangle. hence, BC= 500/2=250 Km and AC= 500*\((\frac{\sqrt{3}}{2})\)
Time taken by train to reach C= 250/50= 5hr
Train will arrive C at 1 PM
hence, Rahim must arrive C latest by 12:45 PM
Time taken by Rahim to reach C= \(\frac{250\sqrt{3}}{70} \)= 6.18 hrs =~ 6 hrs 12 mins
The latest time by which Rahim must leave A and still catch the train= 1245 - 612 =~ 0633 hrs or 6:33 AM
B
Bunuel
29 Jan 2020, 08:13
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Bunuel
C is located at:
{A}N…
W{C}E
…S{B}
Angles: CAB=30, ABC=60, ACB=90
Distance: AB=500 is opposite angle ACB=90
Specials: 30:60:90=x:x√3:2x=250:250√3:500
AB=500, AC=250√3, CB=250
Train at B departs 08:00 and arrives 250/50=5hrs at 13:00
Rahim's takes 250√3/70=~250*7/4/70=6:15hrs from A to C
Rahim's latest: 13:00-15min-6:15hrs=13-6.5=6.5=06:30hrs
Ans (B)
