GRE
Practice Test 17
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Ratio of number of boys to girls in tennis club is 5:2. The ratio of number of boys to girls in basketball club is 11 :4.
Number of boys in tennis club Number of boys in basketball club
  • Solution

    Ratios do not furnish any information about actual numbers.

A large jar is full of marbles. When a single marble is drawn at random from jar, the probability that it is red is 3⁄7.
Ratio of number of Red to non-red Marbles in jar 1⁄2
  • Solution

    Out of every 7 marbles, 3 are red, 4.are non red.

    So the ratio is 3 : 4 which is greater than 1 : 2.

Ratio of red to blue marbles in ajar was 4:7. The same number of red and blue marbles were added to jar.
Ratio of red to Blue marbles now 4 : 7
  • Solution

    Side B is 4⁄7 = .57

    When we add one marble each to side A the ratio will be always more than .57

In 1980, John was 8 times as old as Paul and Linda was 3 times as old as Paul. John is 20 years older than Linda.
paul’s age in 1988 12
  • Solution

    Let Paul's age in 1980 be x.

    ∴ John's age = 8x Linda's age = 3x

    ∴ 8x - 3x = 20 ∴ x = 4

    ∴ Paul's age in 1980 = 4 years

    ∴ Paul's age in 1988 = 12 years.

In the figure above, all line segments meet to form right angles.

Perimeter of figure 52
  • Solution

    x + x + 1 + x + 2 + x + 3 = 14

    Y + Y + Y + Y = 12

    Perimeter = 2(12 + 14) = 2 × 26 = 52

0, P, Q are centres of three circles, all lie on diameter AB.

Area of entire shaded region 4 times the area of unshaded region
  • Solution

    Col. A -

    Let radius of smallest circle be r.

    ∴ Radius of middle circle and largest circle is 2r and 4r respectively.

    Col. A -

    π(4r2) - π(2r)2 + πr2 = 16πr2 - 4πr2 + πr2 = 13πr2

    Col. B-

    4(area of unshaded region) = 4 × [ π(2r)2 - πr2] = 12πr2

Three circles have same centre. Radii of circles are 3, 4, 5.

Area of region R Area of region P
  • Solution

    Col. A = πr2 = π32 = 9π

    Col. B = 25π - 16π = 9π

 

The average of measures of 3 angles of a triangle whose largest angle measures 79° The average of measures of 3 angles of the triangle whose smallest angle measure 43°
  • Solution

    Sum of angles of any triangle = 180°

    ∴ Average = 60°

0 < m < n < 1
\(\sqrt{m+n}\) \(\sqrt{m}+\sqrt{n}\)
  • Solution

    Squaring both sides

    Col. A = m + n

    Col. B = m + n + 2\(\sqrt{mn}\)

    Since 2\(\sqrt{mn}\) = positive

There are 143 people lined up outside a theatre. Jack is 25th person from front and Jill is 39th from the last.
Number of people between jack & jill 79
  • Solution

    Jack's ranking from front = 25. Jill's ranking from last = 39.

    = 143 - 25 - 39 = 79

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