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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Solve the following questions and select the correct answer from the given five options.

1. When a women weighing 65 kg is replaced by another women, then the average weight of a group of 10 women is found to be increased by 1 kg. Find out the weight of the new woman that is added to the group.

1. 65 kg
2. 75 kg
3. 85 kg
4. 60 kg
5. None of the above

Explanation:

According to the data given in the question,

Total number of women in the group = 10 ……………i

The average weight of a group of 10 women increases by 1 kg when a women weighing 65 kg is replaced with a new woman.

∴ Total increase in the weight of a group of 10 women = 10 * 1 = 10 kg ………ii

Now, weight of the new woman added to the group = weight of the woman that is replaced + total increase in the weight of the entire group of 10 women

∴ Weight of the new woman added to the group = 65 + 10 = 75 kg ………….iii

Hence, the correct answer is option d.

2. In what proportion should we mix the wheat of Rs. 2.50 per kg with the wheat of Rs. 3.50 per kg such that the resultant mixture of wheat costs Rs. 3.00 per kg?

1. 1 : 1
2. 1 : 2
3. 2 : 1
4. 1 : 1.5
5. None of the above

Explanation:

We will solve this solve using the concept of allegation.

According to the data given in the question,

Rate of the first type of wheat = R1 = Rs. 2.50 = 250 paise ………….i

Rate of the second type of wheat = R2 = Rs. 3.50 = 350 paise …………..ii

The mean rate of the mixture of the two types of wheat = Rm = 250 +350 / 2 = 600 / 2 = 300 paise …………iii

The quantity of the first type of wheat = N1 = Rm – R1 = 300 – 250 = 50 paise …………….iv

The quantity of the second type of wheat = N2 = R2 – Rm = 350 – 300 = 50 paise …………….v

Now, N1 / N2 = 50 / 50 = 1 : 1

So the required ratio = 1 : 1

Hence, the correct answer is option a.

3. The working capacity of John is twice as that of Jim and hence, John can finish a piece of work in 15 days less than the number of days required by Jim to do the same piece of work. In how much time can they complete the same piece of work when both John and Jim work together?

1. 10 days
2. 20 days
3. 30 days
4. 40 days
5. None of the above

Explanation:

According to the data given in the question,

Let, Jim finishes the piece of work in 'x' days ………….i

∴ John can complete the work in (x – 30) days …………….ii

The working capacity of John is twice as that of Jim.

∴ Time taken by John is 1 / 2 of the time taken by Jim ………..iii

∴ From equations (i), (ii) and (iii), we can say that,

(x – 30) = x / 2 ………..iv
∴2 (x – 30) = x
∴ 2x – 60 = x
∴ x = 30 ………….v

∴ Time taken by Jim to complete the work = 30 days

Since, it is given that John can complete the piece of work in 15 days less than the days required by Jim.

Thus, we can say that the time taken by John = 30 – 15 = 15 days ……………..vi

Now, work done by John in 1 day = 1 / 15 ………………vii

Work done by Jim in 1 day = 1 / 30 ………………….viii

Work done by both John and Jim in 1 day = (1 / 15) + (1 / 30) = (3 / 30) = 1 / 10

∴ John and Jim together can finish the whole work in 1 / (1 / 10) = 10 days.

Hence, the correct answer is option a.

4. Certain numbers of boys are able to finish a work in 25 days. If the number of boys is increased by 10, then they can finish the same work in 10 days less. How many boys were employed originally to do the work?

1. 10
2. 20
3. 15
4. 40
5. None of the above

Explanation:

Let the original number of boys employed = 'x' …………..i

Then, according to the data given in the question,

Number of boys is increased by 10

∴ New number of boys = x + 10 …………ii

Time required by x boys to do the work = 25 days …………..iii

Time required by the new number of boys = 25 – 10 = 15 days ………….iv

Now, equating equations (i), (ii), (iii) as well as (iv), we get,

x : (x + 10) :: 15 : 25
∴ (x / x + 10) = 15 / 25
∴ 25x = 15 (x + 10)
∴ 25x = 15x + 150
∴ 25x – 15x = 150
∴ 10x = 150
∴ x = 15 ……………..v

Thus, there were 15 boys employed originally to do the work.

Hence, the correct answer is option c.

5. Two pipes A and B can fill a tank in 10 hours and 12 hours respectively when they are opened at the same time to fill the tank. But, because of one leakage at the bottom of the tank, it takes 30 more minutes to fill up the tank. In what time will the leakage empty the tank, if the tank is filled completely?

1. 10 hours
2. 12 hours
3. 30 hours
4. 60 hours
5. None of the above

Explanation:

According to the data given in the question,

Time taken by pipe A to fill the tank = 10 hours ………….i

Time taken by pipe B to fill the tank = 12 hours ………….ii

∴ Work done by both the pipes A and B in 1 hour = (1 / 10) + (1 / 12)

∴ Work done by both the pipes A and B in 1 hour = 22 / 120 ……………iii

∴ Time taken by both the pipes A and B to fill the tank completely in the absence of the leakage = 120 / 22 hours = 5 hours and 30 minutes ……………iv

Time taken to fill the tank with leakage = (5 hours 30 minutes) + (30 minutes) = 6 hours …………….v

∴ The amount of work done by the pipes A as well as B and the leak in 1 hour = 1 / 6 ……….vi

∴ Work done by the leak in 1 hour = (22 / 120) – ( 1 / 6) = 1 / 60

∴ Time required by the leakage to empty the tank = 1 / (1 / 60) = 60 hours.

Hence, the correct answer is option d.

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