GRE
Practice Test 8
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At the beginning of a class, a classroom has 5 empty chairs and all students are seated. No student leaves the classroom and additional students equal to 25% of number of students already seated, enter the class late and fill the empty chairs. What is the total number of chairs in classroom?

  • Solution

    25% of x = 5

    ∴ x = 20

    Originally there were 20 + 5 = 25 chairs.

The figure above represents a wooden block 4cm on edge. All the faces are painted yellow. If block is cut along the lines as shown, we get 64 smaller blocks of volume l cm>. Of these small blocks, how many will have no painted faces?

  • Solution

    4 × 4 = 16 blocks will be at the centre.

    Out of which 4 on the top and 4 at the bottom to be painted yellow on 1 side. But 4 + 4 = 8 block at the core do not have any face exposed would be the ones with no face painted.

Water runs into a pool at rate of 1 kl. every 7 seconds and simultaneously runs out at the rate of 1 kl. Every 13 seconds. The pool is filling at a rate of 1 kl every

  • Solution

    Water entering and leaving the pools in 1 second is 1/7 and 1/13 kl. respectively.

    ∴ In one second 1⁄7 - \(\frac{7}{13}\) = \(\frac{6}{91}\) kl. of water gets filled in tank.

    ∴ 1 Kilo litre gets filled in \(\frac{91}{6}\) = 151⁄6 seconds.

What is the least integer which when added to both terms of ratio 4 : 7 will make a ratio greater than 7:10

  • Solution

    Let x be the least integer

    \(\frac{4+x}{7+x}\) > \(\frac{4+x}{7+x}\)

    ∴ 40 + 10x > 49 + 7x

    ∴ 3x > 9 ∴ x > 3 ∴ x = 4

In a party, the boss took 1/8 of the cake and he had 4 times as much as others had. The total no. of people at the party is

  • Solution

    Let there be 32 pieces of this cake (8 × 4). The boss takes 1/8 of the cake.

    ∴ He consumes 4 pieces. The remaining 28 pieces are shared by 28 members, 1 piece per member.

    ∴ Total no. of people = 28 + boss = 29

The rent of a guest house was $5 per day for first 3 days, $10 per day for next 5 days and $30 per day for other days. The registration fee in the beginning is $5. If John has to pay $130 for how many days he availed this facility?

  • Solution

    5 + (5 × 3)+ (10 × 5)+ (x × 30) = 130

    ∴ 5 + 15 + 50 + 30x = 130

    ∴ 30x = 60 x = 2

    Ans: The facility is availed for 3 + 5 + 2 = 10 days.

From a group of boys and girls if 3 girls leave, then the numbers of girls are twice that of boys. Thereafter, 11 boys leave and then the number of girls is four times that of boys. The number of girls in the beginning was

  • Solution

    Let there be 'b' boys and 'g' girls initially.

    ∴ According to first condition 2b = g - 3

    ∴ g = 2b + 3 (I)

    According to second condition

    4(b - 11) = g - 3 ∴ 4b - 44 = g - 3

    ∴ g = 4b - 41 (II)

    ∴ 2b + 3 = 4b + 41 ∴ 2b = 44 ∴ b = 22, g = 47

1/4 of Bill’s monthly SALARY is equal to 1/6 of Jack’s monthly salary. If both together earn $9600 every month, difference between their salary is

  • Solution

    Let Bill's salary be $24. 1/4 of Bill's salary is $6 which is 1/6 of Jack's salary.

    ∴ Jack's salary is $36.

    ∴ Together they earn $60. Actual total is $9600. ∴ Bill's salary is \(\frac{24}{60}\) × 9600 = 3840

    Jack's salary is $5760

    ∴ Difference = $5760 - $3840 = $1920.

    Whenever you have more than one fraction, multiply denominators and start with that number.

In the figure above, rectangle CDEF with perimeter 32 has the maximum area. Find area of ΔABF.

  • Solution

    A rectangle has maximum area when it becomes a square. ∴ CF = 8 = FB

    Also ΔFBA is a 30°, 60°, 90° triangle with triplet of 1, √3 and 2.

    BA = 8√3

    ∴ Area of ΔFBA = \(\frac{8\times 8\sqrt{3}}{2}\)

    = 32√3 sq. units.

One bottle contains some brandy and another contains an equal quantity of water. To prepare a solution, 20 grams of brandy is poured from the 1st bottle into the second bottle which contains water. Then 2/3 of this new solution is poured from 2nd bottle into first, If fluid in first bottle is 4 times than in second, what quantity of water was taken initially?

  • Solution

                                       Brandy           Water

    Original                  x                      x

    1st operation       x-20               x + 20

    (x - 20)      + 1⁄3(x + 20)

    2⁄3(x + 20)

    ∴ (x -20)+2⁄3(X + 20) = 4[1⁄3(X+20)]

    ∴ x - 20 + \(\frac{2x}{3}+\frac{40}{3}=\frac{4x}{3}+\frac{80}{3}\)

    3x - 60 + 2x + 40 = 4x + 80

    ∴ x = 100

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