GRE
Practice Test 6
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A survey of n people found that 60% preferred brand A. An additional x people were surveyed -who all preferred brand A. 70% of all people surveyed preferred brand A. Find x in terms of

  • Solution

    \(\frac{3n}{5}+x=\frac{7x}{10}+\frac{7n}{10}\: \: ∴\frac{n}{10}=\frac{3x}{10}\) ∴ x = n⁄3

How many gallons of milk that has 2% butterfat must be mixed with milk that has 3.5% butterfat to get 10 gallons that is 3% butterfat?

  • Solution

    We can solve this problem by Allegation method.

    Ratio of mixture

    ∴ 1:2 ∴ 31⁄3:62⁄3

The negative of the sum of 2 consecutive odd nos. is less than -45, which of the following may be one of the numbers?

  • Solution

    The sum of the two consecutive odd numbers should be 46 or more. Therefore these numbers will be 23 and 25.

In a survey conducted with 95 people on readership of two newspapers A and B, it was noted that 30 people read both, 20 people read only A, 5 read only B and balance 40 read neither. What is ratio of total number of people who read A to the total number of people who read B?

  • Solution

    Total number of people who read A = People who read only A + people who read both A and B

    = 20 + 30 = 50

    Similarly, total number of people who read

    B = 30 + 5 = 35

    ∴ Ratio = 50 : 35 = 10 : 7

If a and b are lengths of legs of right triangle whose hypotenuse is 10 and whose area is 20, what is the value of (a + b)2?

  • Solution

    a2 + b2 = 100 ..... Pythagoras theorem

    Area = \(\frac{ab}{2}\) = 20 ∴ab = 40

    Now (a+ b)2 = a2 + 2ab + b2 = 100 + 2 × 40 = 180

The figure below consists of 4 semicircles in a large semicircle. If the small semicircles have radii of 1, 2, 3 and 4, what is the perimeter of shaded region?

  • Solution

    Perimeter of shaded region

    = perimeter of all 5 semicircles

    = π + 2π + 3π + 4π + 10π = 20π

If sum of all positive even integers less than 1000 is A, what is sum of all positive odd integers less than 1000?

  • Solution

    Sum of even integers beginning with 2 = n(n+ 1)

    Sum of odd integers begirming with 1 = n2

    There are 499 even and 500 odd integers less than 1000.

    ∴ Sum of even numbers = 499 x 500 = 249500

    ∴ Sum of odd numbers = 5002 = 250000

    ∴ If sum of even numbers is A, then sum of odd numbers is A + 500

In the figure above, each circle is tangent to other two circles and to sides of rectangle. If diameter of each circle is 20, what is area of rectangle?

  • Solution

    AB = CD = 2 × diameter = 40

    To find AD : (AD) = LO+ OO3 + O3M

    ℓ(AD) = 10 + ht of equilateral triangle

    OO1O2 + 10 = 20 + 10-√3

    ∴ Area of rectangle = 40(20 + 10-√3) = 800 + 400√3

A garment supplier stores 800 coats in a warehouse of which 15% are full length coats. If 500 of shorter length coats are removed from warehouse what % of remaining coats are full length

  • Solution

    No. of full length coats = 15% of 800 = 120

    After removing 500 coats, there are only 300 coats lefts.

    ∴ Require percentage = \(\frac{120}{300}\) = 40%

What is the arithmetic mean 425, 452, 4 and 475.

  • Solution

    A.M.=\(\frac{4^{25}+4^{52}+4^{67}+4^{75}}{4}=4^{24}+4^{51}+4^{66}+4^{74}\)

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