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# At 11 AM, Abraham leaves from his home for a meeting that is scheduled

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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

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