GRE
Practice Test 30
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2 gallons of mixture of spirit and water contains 12% water. They are added to 3 gallons of mixture containing 7% of water. Then one gallon of water is added to the resultant mixture.
% of water in the resultant mixture 19.5%
  • Solution

    2 gallons of mixture contains 2 × 0.12 = 0.24 gallons of water.

    3 gallons of mixture contains 3 × 0.07 = 0.21 gallons of water.

    After adding another one gallon of water, we have 0.24 + 0.21 + 1.00 = 1.45 gallons of water in 6 gallons of mixture.

    ∴ Required % = \(\frac{1.45}{6}\) × 100 = 24.16%

When 2 trains are running in the same direction at 90 kms./hr. and 60 kms./hr. respectively, faster train crosses the man in slower train in 27 seconds.
Length of faster train 250 m.
  • Solution

    Since the trains are running in the same direction, relative speed of faster train = 90 - 60 = 30 kmph.

    30 kmph = 30 × \(\frac{5}{18}=\frac{25}{3}\) meters per second.

    Now when the train crosses the man in 27 seconds, it travels a distance equivalent to its own length in 27 seconds.

    ∴ 27 = \(\frac{L_{T}}{\frac{25}{3}}\) ∴ LT = 225 m.

    ∴ Length of the train is = 225 meters

P > 5, Q > 10, R > 15, S > 20 where P, Q, R, S are natural numbers less than 25.
P⁄Q R⁄S
  • Solution

    Since

    P can take value between 6 to 24,

    Q can take value between 11 to 24,

    R can take value between 16 to 24,

    S can take value between 21 to 24,

    We cannot determine the exact value for A as well as B

 

The ideal time in minutes between any two consecutive overlaps of the hands of a clock 644⁄7 min.
  • Solution

    In one hour, the two hands of a clock (viz.minute and hour hand) coincide once, are at right angles twice and are at 180° once.

    In one hour, the minute hand gains 55 minutes over the hour hand. Now, to coincide with the-hour hand, the minute hand has to gain 60 minutes over the hour hand. So this will occur after 60 × \(\frac{60}{55}\) = 65\(\frac{5}{11}\)
    minutes.

A watch strikes 9 strokes within 9 seconds.
Time required to strike 65 strokes 67 sec.
  • Solution

    When the watch strikes 9 strokes, there are 8 intervals of time in between. For the watch to strike 65 strokes, there are 64 intervals of time in between.

    For 8 intervals time required is 9 seconds.

    ∴ For 64 intervals time required 72 seconds.

If a sum x is kept as Simple Interest for 2 years, the interest generated is $320. But if the same sum is kept at compound interest at same rate for 2 years, the interest is $352.
Rate of interest 16%
  • Solution

    The difference between the interests at the end of 2nd year is $32. This is the simple interest on the interest of 1st year $160 for 1 year.

    ∴ 32 = \(\frac{160 \times 1 \times R}{100}\) ∴ R = 20% ∴ Col. A = 20%

 

32√3 (3√3)2
  • Solution

    Col. A = 32√3 = (32)√3= 33.464

    Col. B = (3√3)2 = 27 = 33

    ∴ Value of Col. A is greater.

An enclosed figure has a perimeter of 44 inches.
Maximum area that the figure can enclose 121 sq. inches
  • Solution

    For a given perimeter, circle has the maximum area.

    44 = 2πR ∴ R = 7 (inches)

    ∴ Area = nR2 = 154(inches)2

Given that PST is a right angle triangle and PQRS is a parallelogram.

2 X area of triangle PTS Area of PQRS
  • Solution

    Area of parallelogram = base × height

    ∴ Area of PQRS = PQ × PT

    Col. A = 2 × area of ΔPTS = 2 × 1⁄2 × TS × PT = TS x PT

    ∴ Col. A = TS × PT Col. B = PQ × PT

    With the relationship between TS and PQ not known. TS is not necessary equal to PQ unless it is specifically mentioned in the problem.

A man walked at 2 meters per second towards a train approaching him at 20 meters per second. The distance of the man from train is 22 meters. After getting into the train, further walks 22 meters to take his seat.
Time required by man to get into the train Time required by man to walk to take his seat in the train
  • Solution

    The man and the train are moving towards each other.

    ∴ Relative speed = 2 + 20 = 22 m/s

    ∴ Time taken by man to meet the train

    =\(\frac{Distance}{Relative\, Speed}=\frac{22}{22}\)= 1 second.

    Col. A = 1 second

    Walking speed of man is 2 meters per second.

    ∴ To walk 22 meters, he will take 11 seconds.

    Col. B = 11 seconds.

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