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Some problems I can't solve
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beat_gmat_09
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1) Distance is same both ways, speeds are constant, therefore we can calculate the average speed using the formula -N:Dure wrote:??
2S1*S2/S1+S2
Lexy's average speed = 2*5*15/5+15 = 7.5
Ben's speed = 7.5/2
Time spent = Distance / speed = 5+5 / 7.5/2 = 10*2/7.5 = 20*2/15 hrs.
In minutes = (20*2/15)*60 = 160 minutes. Option D.
2) angle CAB = 45, angle COB = 2 * angle CAB = 2*45 = 90.
Area of sector covered by COB = 90/360(pie*r^2) = 1/4(pie)*2^2 = pie ......... (1)
Shaded region = area of sector covered by sector + area of triangle COA.
area of triangle can be calculated as = 1/2*(b*h) ; base and height are both 2.
THerefore are of triangle = (1/2)*2*2 = 2...........................................................(2)
Area of shaded region = (1)+(2) = pie + 2. Option B.
3) x^2-y^2 = 12; x^2-y^2 = (x-y)(x+y) = 12; x+y=3; using x+y; (3)(x-y)=12. Therefore x-y = 4.
Option D.
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Dani@MasterGMAT
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good solutions methods.beat_gmat_09 wrote:1) Distance is same both ways, speeds are constant, therefore we can calculate the average speed using the formula -N:Dure wrote:??
2S1*S2/S1+S2
Lexy's average speed = 2*5*15/5+15 = 7.5
Ben's speed = 7.5/2
Time spent = Distance / speed = 5+5 / 7.5/2 = 10*2/7.5 = 20*2/15 hrs.
In minutes = (20*2/15)*60 = 160 minutes. Option D.
2) angle CAB = 45, angle COB = 2 * angle CAB = 2*45 = 90.
Area of sector covered by COB = 90/360(pie*r^2) = 1/4(pie)*2^2 = pie ......... (1)
Shaded region = area of sector covered by sector + area of triangle COA.
area of triangle can be calculated as = 1/2*(b*h) ; base and height are both 2.
THerefore are of triangle = (1/2)*2*2 = 2...........................................................(2)
Area of shaded region = (1)+(2) = pie + 2. Option B.
3) x^2-y^2 = 12; x^2-y^2 = (x-y)(x+y) = 12; x+y=3; using x+y; (3)(x-y)=12. Therefore x-y = 4.
Option D.
In Q1, If Ben walks at half the speed, he takes twice as long to cover the same distance. find Lexy's time and multiply times two: Lexy takes one hour to do 5 miles, then 1/3 of an hour to do 5 miles at 15 mph - total time of 4/3. So Ben's time is twice that, or 8/3 = 2 hours and 2/3 = 120+40 minutes = 160.
