GRE
Practice Test 13
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The total cost of renting a boat was originally to be shared by 5 people. If number of people is increased by 1, the cost per person will be $10 less.

Total cost of renting the boat $ 250
  • Solution

    5x = 6(x -10) .∴ x = 60

    ∴ Cost = 5x = $300

 

Angle between hour hand and minute hand at 1.10 p.m 30°
  • Solution

    Since the hour hand also moves downwards 10 minutes, actual distance between hour hand and minute hand is less than 5 minutes i.e. than 30°.

    Distance at 1.05 p.m. between two hands is

    (theoretical difference in time × 6° ) - (time × 1⁄2°)

    (5 × 6°) - (10 × 1⁄2°) = 30° - 5° = 25°

In the diagram below ACD & BCE are straight lines.

∠ A – ∠ D ∠ E – ∠ B
  • Solution

    Col. 1 ∠A + ∠B + ∠C = 180°

    Col. 2 ∠E + ∠C + ∠D = 180°

    ∴ ∠A + ∠B = ∠D + ∠E

    ∴ ∠A - ∠D = ∠E - ∠B

Letters are put into N envelops so that each envelop contains at least 1 letter, but no two envelopes contain same number of letters.

maximum possible envelopes that certain a total of 39 letters 9
  • Solution

    Let 8 envelopes contain 1,2,3,4,5,6,7, letters respectively.

    We are left with three letters which can be put any of the 6th, 7th or 8th

    ∴ Total envelopes = 8

x lies between 4 and 16 (both inclusive) and y between 24 and 48 (both inclusive).

Maximum possible value for x⁄y \(\frac{16}{48}\)
  • Solution

    Col. A \(\frac{16}{24}\) = 2⁄3

    Col. B = 1⁄3

 

Ratio of surface area of cube of edge 2 cm to that of edge 3 cm. Ratio of volume of cylinder with radius 4 cm to that of radius 6 cm. and having equal height
  • Solution

    Col. A \(\frac{6 \times (2)^{2}}{6 \times (3)2^{2}}=\frac{4}{9}\)

    Col. B \(\frac{\pi (4)^{2}h}{\pi (6)^{2}h}=\frac{4}{9}\)

r, s, t are radii of 3 circular regions that have areas R,S,T respectively. R = 3S, S = 2T.
r 2.5t
  • Solution

    R = 3S = 6T ∴ πr2 = 6m2

    ∴ r = √6 t.........Col. A

    Col. B - 2.5t = \(\sqrt{6.25}\) t

Area of circular region with centre P is 100 π

Length BD 20
  • Solution

    ABCD need not be a square ∴ BD need not be the diameter.

    ∴ Length of BD cannot be exactly determined.

 

No. of arrangements that can be made of the letters of the word EDUCATION with the vowels never being separated. 1.44 × 105
  • Solution

    The word has 5 vowels and 4 consonants.

    ∴ No. of arrangements = 5! x 5! (5!) for 4 consonants and the block of vowels and again 51 for 5 vowels)

    = (120)2 = 14400 = 1.44 × 104

The present ages of 3 people are consecutive even numbers. 8 years hence their average age will be twice their average age now.
the present age of the oldest person 8 years
  • Solution

    If the average after 8 years is twice their average age now, average age today must be 8. So that average after 8 years will be 16.

    ∴ Present ages are 6,8,10

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