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

YOU TITLE HERE

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?

  1. 70
  2. 120
  3. 60
  4. 130
  5. 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?

  1. 12 years
  2. 6 years
  3. 3 years
  4. 9 years
  5. 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?

  1. 12
  2. 9
  3. 3
  4. 7.5
  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 a/d not equal to b/e
In the question given above, a = 3, b = 4, d = k and e = 12.
Therefore, k not equal to 9 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?

  1. $111
  2. $52.5
  3. $210
  4. $58.5
  5. $6

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