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Re: At 11 AM, Abraham leaves from his home for a meeting that is scheduled [#permalink]
At 11 AM, Abraham leaves from his home for a meeting that is scheduled for 1 PM. If the venue of the meeting is not less than 100 kilometers away and Abraham drives at a speed not less than 60 kilometers per hour, will he be late for the meeting?

Rephrase the question: Is d/s<= 2

(1) The venue of the meeting is less than 120 kilometers away

Test the threshold

Let d=100 & S=60..........100/60= 1 2/3 hr < 2

Let d=120 & S=60..........120/60=2 hrs

This means that if we increase the distance to be not less than 60, then the time required will be always less than 2 hrs. So he will catch up his meeting,

Sufficient

(2) He does not drive at a speed greater than 80 kilometers per hour

Let d=160 & S=80.........160/80=2 hrs .........arrive on time

Let d= 320 & S=80.........320/80=4 hrs ........arrive late

Insufficient


Answer: A
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Re: At 11 AM, Abraham leaves from his home for a meeting that is scheduled [#permalink]
Expert Reply
Hey,

PFB the official solution.

Steps 1 & 2: Understand Question and Draw Inferences

    • Let Distance between home and meeting venue = D kilometers
      o \(D_{min} = 100 km\)
    • Let Speed of driving be S kilometers per hour
      o \(S_{min} = 60 kmph\)
    • Let time taken = T hours

To Find:

Is \(T > 2 hours\)?

    • \(Time = \frac{Distance}{Speed}\)

      o \(T_{min} = \frac{D_{min}}{S_{max}}\)

      o \(T_{max} =\frac{D_{max}}{S_{min}}\)

If:
    o \(T_{min} > 2\) hours, then the answer is NO

    o If \(T_{max} < 2\) hours, then the answer is YES.

    o If \(T_{min} < 2 < T_{max}\), then a definite answer cannot be determined

Step 3: Analyze Statement 1 independently

Statement 1 says that

\(D_{max} < 120\) km

So, \(T_{max} < \frac{120}{60}\) hours

That is, \(T_{max} < 2\)hours

Sufficient to answer the question (he will reach the venue in time)

Step 4: Analyze Statement 2 independently

Statement 2 says that

\(S_{max} = 80\) kmph

This means, \(T_{min} = \frac{100}{80} =\frac{5}{4}\) hours

So,\(T_{min} = 1\) hour \(15\) minutes

But we don’t know about the maximum time he’ll take.

So, not sufficient.

Answer: A


Thanks,
Saquib
Quant Expert
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Re: At 11 AM, Abraham leaves from his home for a meeting that is scheduled [#permalink]
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