# (Paper) GMAT Math Problem Solving & DS Practice Questions Paper

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**Algebra**

**1. A poultry farm has only chickens and pigs. When the manager of the
poultry counted the heads of the stock in the farm, the number totaled up to
200. However, when the number of legs was counted, the number totaled up to
540. How many chickens were there in the farm? **

- 70
- 120
- 60
- 130
- 80

**The correct choice is (4) and the correct answer is 130.**

**Explanatory Answer:**

Let there by 'x' chickens and 'y' pigs.

Therefore, x + y = 200 --- (1)

Each chicken has 2 legs and each pig has 4 legs

Therefore, 2x + 4y = 540 --- (2)

Solving equations (1) and (2), we get x = 130 and y = 70.

There were 130 chickens and 70 pigs in the farm.

**2. Three years back, a father was 24 years older than his son. At
present the father is 5 times as old as the son. How old will the son be
three years from now?**

- 12 years
- 6 years
- 3 years
- 9 years
- 27 years

**The correct choice is (4) and the correct answer
is 9 years.****Explanatory Answer:**Let the age of the son 3 years back be x years

Therefore, the age of the father 3 years back was x + 24

At present the age of the son is x + 3 and the father is 5 times as old as the son.

i.e., x + 24 + 3 = 5(x + 3)

i.e., x + 27 = 5x + 15

or 4x = 12 or x = 3.

Therefore, the son was 3 years old 3 years back and he will be 9 years old three years from now.

**3. For what values of 'k' will the pair of equations 3x + 4y = 12 and
kx + 12y = 30 not have a unique solution?**

- 12
- 9
- 3
- 7.5
- 2.5

**The correct choice is (2) and the correct answer
is 9.****Explanatory Answer:**

A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a
unique solution if the two lines represented by the equations ax + by + c =
0 and dx + ey + g = 0 intersect at a point.

That is, if they are not parallel lines. i.e., the two lines should have
different slopes.

ax + by + c = 0 and dx + ey + g = 0 will not represent two parallel lines if
their slopes are different.

i.e., when

In the question given above, a = 3, b = 4, d = k and e = 12.

Therefore,
or 'k' should not be equal 9 for the pair of equations to have a unique
solution.

In other words, when k = 9, the system of equation will not have any solution as the two lines represented by the equations will be parallel lines.

**4. The basic one-way air fare for a child aged between 3 and 10 years
costs half the regular fare for an adult plus a reservation charge that is
the same on the child's ticket as on the adult's ticket. One reserved ticket
for an adult costs $216 and the cost of a reserved ticket for an adult and a
child (aged between 3 and 10) costs $327. What is the basic fare for the
journey for an adult?**

- $111
- $52.5
- $210
- $58.5
- $6

**The correct choice is (3) and the correct answer
is $210.**