Word Problems

# Word Problems

Every GMAT exam includes a number of word problem questions. Topics include:

• Percentages
• Motion
• Work rate
• Ratio
• Equations

Here is an example of a word problem question from the quantitative section of the GMAT:

Rachel’s house is 85 kilometers north of Kelly’s house. If Rachel left her house at 17:00 and drove south at a speed of 40 kilometers per hour, and Kelly left her house at 18:30 and drove north at a speed of 20 kilometers per hour, at what time will Rachel and Kelly meet?

• 17:20
• 18:50
• 18:55
• 19:00
• 19:20

Solution:

Since Rachel and Kelly began their journeys at different times, it's best to divide the question into two parts:
Between 17:00 and 18:30, Rachel drove south alone at a speed of 40 km/h. That means that during that hour and a half she drove a distance of 60 km (1.5 multiplied by 40).
Between 18:30 until an unknown time, Rachel and Kelly drove towards each other with a starting distance between them of 25 km (85-60=25). Since we are talking about motion in opposite directions, we will use the formula D= (V1+ V2)T, where D is the distance, T is the time and V1 and V2 are their speeds.
We'll substitute the formula with numbers and we'll get:

T (40+20) =25
T=25/60

That is to say that at their combined speed of 60 km/h, it will take them 25 minutes to drive 25km together. We'll add 25 minutes to the time 18:30 and we'll get 18:55.

Therefore, the answer is 18:55 (C)

Here is another example of a word problem in the quantitative section of the GMAT:

At the Gur-A-Zahar local post office, the post office receives a new package every 3 minutes, and the mail man delivers packages at a rate of 12 packages an hour. If on Monday morning the mail man started working at 08:00, and there were no packages left from the previous days, at what time will there be exactly 100 undelivered packages in the Gur-A-Zahar local post office?

• 11:20
• 14:40
• 15:50
• 18:30
• 20:30

Solution:

The post office gets a new package every 3 minutes, i.e. 20 packages an hour. If the mail man delivers 12 packages an hour there are 8 undelivered packages left over after each hour. If we divide 100 by 8 we get 12.5. That means it will take 12.5 hours for 100 packages to accumulate at the post office. If we add 12.5 hours to 8:00 we arrive at 20:30.

Therefore the answer is 20:30 (E)

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