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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Choose the most correct answer from the given five options for each of the following problem solving question.

1. Tina can do a piece or work in 15 days, whereas Mina can do the same piece of work in 20 days. If they work together for 7 days and then Tina goes away for a leave. Then, in how many days will Mina alone complete the remaining piece of work?

1. 3.66 days
2. 2 days
3. 1 day
4. 10 days
5. None of the above

Explanation:

According to the data given in the question,

Number of days required by Tina to complete the work = 15 days …………i

Number of days required by Mina to complete the work = 20 days …………ii

Now, work done by Tina in 1 day = 1 / 15 ……….iii

And, work done by Mina in 1 day = 1 / 20 ………………iv

∴ Work done by both Tina and Mina in 1 day = (1 / 15) + (1 / 20) = 7 / 60 ……v

∴ Work done by both Tina and Mina in 7 days = 7 (7 / 60) = 49 / 60 ……vi

Now, remaining amount of work = 1 – 49 / 60

∴ Remaining amount of work = 60 – 49 / 60 = 11 / 60 ……………vii

Since, according to the data in statement (iv), 1 / 20 of the work is done by Mina in 1 day.

∴ 11 / 60 of the work will be done Mina in (20) * (11 / 60) = 11 / 3 = 3.66 days

Hence, Mina will complete the remaining work in 3.66 days.

Hence, the correct answer is option a.

2. A can complete a piece of work in 12 days, whereas B and C can complete the same piece of work in 15 days and 18 days respectively. A, B and C start working together. But, A leaves the work after 3 days and B leaves the job incomplete just before 2 days before the completion of the work. For how many days did the work last?

1. 7 days
2. 7.7727 days
3. 8 days
4. 8.7727 days
5. None of the above

Explanation:

According to the data given in the question,

Days required by A to do the work = 12 days ……….i

Days required by B to do the work = 15 days ……….ii

Days required by C to do the work = 18 days ……….iii

Hence, from data i, ii and iii, we can say that,

A, B and C work together for 3 days ……………iv

C works alone for 3 days …………….v

Work done by A, B and c in 3 days = 3 * (1 / 12 + 1 / 15 + 1 / 18) = 37 / 60

∴ A, B as well as C complete 37 / 60 of the total work in 3 days ……………vi

Now, work done by C alone in 3 days = 3 * (1 / 18) = 1 / 6 …………..vii

Remaining work to be done = 1 – (37 / 60 + 1 / 6) = 13 / 60 ……………viii

∴ Work done by both B and C in 1 day = (1 / 15 + 1 / 18) = 11 / 90

Thus, 11 / 90 of the total work is completed by both B and C in 1 day ………………ix

∴ Time required by both B and C to complete 13 / 60 of the total work = (90 / 11) * (13 / 60) = 39 / 22 days = 1.7727 days ……………..x

∴ Total time taken by all three of A, B and C to complete the work = 3 + 3 + 1.7727 = 7.7727 days

Hence, the correct answer is option b.

3. Pipe A can fill the bucket in 10 minutes while pipe B can fill the same bucket in 15 minutes respectively. First both pipes are opened together to fill the bucket. But, after 2.5 minutes the pipe A is turned off. In how much time will the bucket can be filled?

1. 5 minutes
2. 6 minutes
3. 8.125 minutes
4. 7.125 minutes
5. None of the above

Explanation:

According to the data given in the question,

Time taken by pipe A to fill the bucket = 10 minutes …………….i

Time taken by pipe B to fill the bucket = 15 minutes …………….ii

∴ Part of the bucket filled by A in 1 minute = 1 / 10 …………iii

And, part of the bucket filled by B in 1 minute = 1 / 15 ………..iv

∴ Part of the bucket filled by both A and B in 2.5 minutes = 2.5 * (1 / 10 + 1 / 15)

∴ Part of the bucket filled by both A and B in 2.5 minutes = 2.5 / 4 …………..v

Now, part of the bucket left to be filled = 1 – (2.5 / 4) = (4 – 2.5 / 4) = 1.5 / 4 ……vi

As, 1 / 15 part of the bucket is filled by pipe B in 1 minute

∴ 1.5 / 4 part of the bucket will be filled by pipe B in 15 * (1.5 / 4) = 5.625 minutes.

∴ Total time required to fill the bucket completely = 2.5 + 5.625 = 8.125 minutes

Hence, the correct answer is option c.

4. Tom and Jerry can complete a piece of work in 12 days when they work together. When only Tom works, he can finish the work in 20 days. How long will Jerry take to complete the work?

1. 10 days
2. 20 days
3. 25 days
4. 30 days
5. None of the above

Explanation:

According to the data given in the question,

Time taken by both Tom and Jerry to do a piece of work = 12 days ………i

Time taken by tom alone to do the work = 20 days …………..ii

∴ Work done by both Tom and Jerry in 1 day = 1 / 12 ……….iii

And, similarly, work done by Tom alone in 1 day = 1 / 20 ………..iv

∴ Work done by Jerry alone in a day = (1 / 12) – (1 / 20) = 1 / 30 …………v

∴ Time taken by Jerry to finish the work alone = 30 days.

Hence, the correct answer is option d.

5. X and Y together can do a piece of work in 18 days. When Y and Z work together, they can do the work in 24 days. But, when X and Z work together, they can do the same piece of work in 30 days. In how much time will the three of X Y as well as z will complete the same work?

1. 3.8297 days
2. 3 days
3. 4 days
4. 5 days
5. None of the above

Explanation:

According to the data given in the question,

Time taken by both X and Y to do a piece of work = 18 days ………i

∴ Work done by both X and Y in 1 day = 1 / x + 1 / y = 1 / 18 …………..ii

Time taken by both Y and Z to do a piece of work = 24 days ………iii

∴ Work done by both, Y and Z in 1 day = 1 / y + 1 / z = 1 / 24 …………..iv

Time taken by both X and Z to do a piece of work = 30 days ………v

∴ Work done by both X and Z in 1 day = 1 / x + 1 / z = 1 / 30 …………..vi

Now, let, X, Y and z complete the work in x, y and z days respectively …………..vii

Thus, work done by X, Y and Z in 1 day = 1 / x, 1 / y, 1 / z respectively ……………viii

Now, adding equations ii, iv and vi we get,

2(1 / x + 1 / y + 1 / z) = 1 / 18 + 1 / 24 + 1 / 30

∴ (1 / x + 1 / y + 1 / z) = 2(1 / 18 + 1 / 24 + 1 / 30)

∴ (1 / x + 1 / y + 1 / z) = 423 / 1620

∴ X, Y and Z can complete the work together in 1620 / 423 days = 3.8297 days.

Hence, the correct answer is option a.

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