GRE
Practice Test 9
Previous Solution Next

In a day, 18 Men and 10 boys can do as much work as 10 men and 22 boys. How much should a man be paid a day if boy is paid $5 per day?

  • Solution

    18M + 10B = 10M + 22B

    ∴ 8M = 12B ∴ M = 1.5B

    ∴ Money earned by man is 1.5 times that of boy, i.e. $7.5.

Linda has finshed ploughing 2⁄3 of her rectangular garden that is 10ft wide. When she finishes ploughing another 60 sq.ft. of garden, she will complete 3⁄4 of her job. What is length of garden?

  • Solution

    Let x be the area of garden.

    ∴ \(\frac{2x}{3}+60=\frac{3x}{4}\)

    60 = \(\frac{3x}{4}-\frac{2x}{3}=\frac{x}{12}\) ∴ x = 720

    If width is 10 ft., Length would be 72 ft.

a > 4, b > -2, then

  • Solution

    Consider (a)

    Let a = 10, b = -1

    ∴ ab = -10 and -10 < - 8 So (a) is false. Consider (b) 4 < - 4 which is false Consider (c) Leta=5,b=-1 ∴ a - b = 6, not necessarily> 6

    Consider (d)

    Let a = 5, b = -1

    ∴ a + b = 4 always greater than 2

Two cars compete for 10 hours on a path. One car runs at 40 mph and runs for whole time. The other runs 10% quicker, but loses 10% of allotted time due to breakdown. Who is winner and by how much?

  • Solution

    Distance covered by 1st car = 40 mph. X 10 hrs. = 400 miles.

    Distance covered by 2nd car = 44 mph. X 9 hrs. = 396 miles.

    ∴ 1st car wins by 4 miles.

Pipes can fill a reservoir in 15,20,30 and 60 hours respectively. First was opened at 6 a.m., second at 7 a.m. and third at 8 a.m. and fourth at 9 a.m. When will reservoir be filled?

  • Solution

    Let time bet hours after 6 a.m.

    ∴ \(\frac{t}{15}+\frac{(t-1)}{20}+\frac{t-2}{30}+\frac{t-3}{60}=1\)

    ∴ 4t + 3(t -1) + 2(t - 2)+ t - 3 = 60 ∴ t = 7 hours

    ∴ It is filled at 1 p.m

Three vertices of a triangle are (0, 1), (0, -7) and (6, p) P denotes an integer, which of the following could be area of triangle (in sq. units)

  • Solution

    Irrespective of the value of P,

    Area = 1⁄2 × 8 × 6 = 24 sq. units

Paul and Maria start a business Paul invests $600 more than Maria and Paul invests his money for 4 months and Maria invests her money for 5 months. Paul’s share in profit is $48 more than that of Maria.

Total profit is $528. Find capital contributed by Paul.

  • Solution

    Let Maria's profit be P and Paul's profit be P + 48

    ∴ P + P + 48 = 528 ∴ P = 240

    ∴ Paul's profit = 288$, Maria's profit = $240

    \(\frac{Paul's\, Capital\times 4}{Maria's\, Capital\times 5}=\frac{288}{240}\)

    ∴\(\frac{Paul's\, Capital}{Maria's\, Capital}=\frac{3}{2}\)

    ∴ 3x - 2x = 600 ∴ 3x = 1800

BD = 8, AB = 6, ED = 5

EF = EC, then AF = ?

  • Solution

    According to Pythagoras theorem

    (AB)2 + (BD)2 = (AD)2

    ∴ (6) + (8) = ((AD)2

    ∴ (AD)2 = 100 ∴ AD = 10

    AD = AE + ED ∴ AE = 10 - 5 = 5

    Also EF = EC = \(\frac{AB}{2}\) = 3

    Again by Pythagoras theorem

    (AF)2= (AE)2 - (FE)2 = 25 - 9

When an integer ‘n’ is divided by 36, remainder is 1. Which of the following could also be an integer?

  • Solution

    Note that 4,3,9,6 are factors of 36. So n is not a multiple of 4,3,9,6 as well.

The net income of XYZ Corporation in 2000 was approximately what % of net income of ABC Corporation in 2005?

  • Solution

    The income of XYZ corporation in 2005 was $1.74 billion, This is 13% decrease from 2000.

    ∴ $1.74 billion corresponds to 87% of income in 2000.

    ∴ Income in 2000 =\(\frac{1.74\, billion}{0.87}\)= 2 billion

    ∴ Required%= \(\frac{2}{5.8}\) × 100 = 35%

Attempted

0

Correct

0

Wrong

0

Complete
Problem solving
Attempted
Wrong
Correct