Once you are well aware of the GMAT Syllabus and the exam pattern, the next thing you need to know is what types of question usually GMAT throws at you. Here are few practice questions on word problems which will provide you a glimpse of GMAT Words Problems’ question pattern.

## Profit

**Question:** Ram sells one radio at a profit of 20% for a cost of Rs. 840 and another radio at a loss of 4% at the price of Rs. 960. Calculate his total percentage of profit or loss:

\(A) \; Loss \; of \; 5\frac{15}{17}\%\)\(B) \; Gain \; of \; 5\frac{15}{17}\%\)

\(B) \; Gain \; of \; 5\frac{15}{17}\%\)\(C) \; Gain \; of \; 6\frac{2}{3}\%\)

\(C) \; Gain \; of \; 6\frac{2}{3}\%\)\(D) \; None\)

\(D) \; None\)

**Solution: **

The cost price of first radio \(= Rs. \left ( \frac{100}{120} \times 840\right ) = Rs. 700\)

The cost price of second radio \(= Rs. \left ( \frac{100}{90} \times 960\right ) = Rs. 1000\)

So, overall cost price of both radio \(= Rs. 700 + Rs. 1000 = Rs. 1700\)

The total selling price of both the radio \(= Rs. (840 + 960) = Rs. 1800\)

since selling price is more than the cost price, so,

\(= Gain = \left ( \frac{100}{1700} \times 100\right ) \% = 5\frac{15}{17} \%\)

## Sets and Venn Diagrams

**Question:** A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 studies Chemistry and 26 Biology. 10 study both Physics and Chemistry, 9 study Biology and Chemistry, while 8 study both Physics and Biology. Equal numbers study all three subjects as those who learn none of the three. How many study all the three subjects?

- 2
- 3
- 5
- 7
- 8

**Solution:** Let us first draw the Venn diagram for this question:

From the diagram, 3 students study all the three subjects, Therefore the correct option is (B).

## Time Speed (Rate) Problems

**Question: **Jack and Jill set out together on bicycle travelling at 15 and 12 miles per hour, respectively. After 40 minutes, Jack stops to fix a flat tire. If it takes Jack an hour to fix the flat tire and Jill continues to ride during this time, how many hours will it take Jack to catch up to Jill assuming he resumes his ride at 15 miles per hour?

(Consider Jack’s deceleration/ acceleration before/ after the flat tire to be negligible)

- 3
- 3.33
- 3.5
- 4
- 4.5

**Solution:**

Distance travelled by Jack in 40 mins \(= \frac{40}{60} \times 15 = 10 \; miles\)

Distance travelled by Jill in 40 mins \(= \frac{40}{60} \times 12 = 8 \; miles\)

When Jack stops to fix the flat tire, Jill is still travelling.

Distance covered by Jill in 1 Hour = 12 miles

Total distance covered by Jill in 1 hour 40 minutes = 20 miles

Distance between Jack and Jill after 1 hour and 40 mins = (20 – 10) miles = 10 miles

Since, Jack and Jill are travelling in the same direction, their relative velocity = 15 – 12 = 3 miles/hour.

Time taken by Jack to catch up with Jill \(= \frac{10}{4} = 3.33 \; hours\)

## Work Problems

**Question:** Tom working alone can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?

- 1/9
- 1/6
- 1/3
- 7/18
- 4/9

**Solution:** Let’s work with smart numbers here!

Let the total work be 24 units. Then using Rate we have

Tom’s rate of work = 4 units per hour [Tom paints the room in 6 hour, working alone]

Peter’s rate of work = 8 units per hour [Peter paints the room in 3 hour, working alone]

John’s rate of work = 12 units per hour [John paints the room in 2 hour, working alone]

First hour, Tom working alone, amount of work done = 4 units

Second hour, Tom and Peter working together, amount of work done = 4+ 8 = 12

Total work done in 2 hours = 16

Amount of work left = 24 – 16 = 8

Tom, Peter and John work together to complete the remaining work.

Their combined rate of work = 4 + 8 + 12 = 24 units per hour.

Time taken to complete the remaining work = \( \frac{8}{24} = \frac{1}{3} \; hour\)

Therefore, amount of work done by Peter in third hour = \( \frac{8}{3} \)

Total amount of work done by Peter = \( 8 + \frac{8}{3} = \frac{32}{3} \)

Fraction of total work done by Peter = \( \frac{\frac {32}{3}}{24} = \frac{4}{9} \)

Hence, the correct answer is (C).

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