GRE
Practice Test 12
Previous Solution Next

 

Surface area of a Rectangular parallelepiped of volume 64 cm3 and dimensions 1,b. h (all different integers) Surface area of a cube having volume 64 cm3
  • Solution

    Col. A-

    Surface area = 2(ℓb+ ℓh + bh)

    For all distinct integral values of t , b, h such as (1, 2, 32) (1, 4, 16) (2,4,8) the surface area is more than 96 cm3.

    Col. B-

    Volume is 643. ∴ Side = 4 cm.

    Surface area = 6 × (4)2 = 96 cm2

Average weight of 3 people is 70 kg and the heaviest weighs 82 kg.
weight of lightest person 40 kg.
  • Solution

    Total weight of 3 people = 210 kgs.

    ∴ Total weight of remaining 2 people = (210 - 82) = 128 kgs. The second heaviest person will be maximum 81 kg.

    ∴ The lightest one has to weight at least 47 kgs. to make the total 210 kgs

The price of a property was reduced by (2⁄5)th to $7,200.
Percentage increase required in the reduced price so as to reach a price that is 1.5 times the original price . 125%
  • Solution

    (3⁄5)th of original price = $7,200

    ∴ Original price = 12,000

    1.5 times original = 18,000

    ∴ Increase required from $7,200 is $10,800.

    ∴ % increase =\(\frac{10800\times 100}{7200}\)= 150%

The perimeter of a rhombus is 52 cm. One of the diagonals measures 10 cm in length.
Length of other diagonal 16√2
  • Solution

    Perimeter = 52 cm. ∴ Side = 3 cm.

    Diagonals of a rhombus are ⊥ bisectors of each other.

    ∴ Other diagonal is 24.

    Col. B 16√2 = 16 × 1.414 which will be less than 24.

 

Area of an equilateral triangle with side 4 cm. Area of an square diagonal of length 4 cm.
  • Solution

    Col. A = \(\frac{\sqrt{3}}{4}\times (4)^{2}\) × (4)2 = 4√3

    Col. B = \(\frac{(4)^{2}}{2}\)= 8

The figure below shows an equiangular octagon.

Area of rectangle ADEH 4
  • Solution

    Col. A-

    Each angle of octagon is 135°

    ∴ ΔABJ is a right angle isosceles Δ. Since hypotenuse is √2 sides BJ and AJ are 1 each.

    ∴ Area of rectangle ADEH = 3

ΔABC lies in XY plane and points A and C have (x, y) co-ordinates (0, 0) and (13, 0). Area of ΔABC = 39 sq. units.
x co-orclinate of B y co-ordinate of B
  • Solution

    Area = 1⁄2 × (13) × (y co-ordinate) = 39

    ∴ y co-ordinate = 6

    However x co-ordinate can take any position without altering the area.

There was a total of ‘C Computers in a certain store. After (3/4)th of these were removed from store and (4/5)th of those removed were delivered back to store, the total number of computers in the store were 170.
C 240
  • Solution

    Col. AC-

    \(\frac{3C}{4}+\left ( \frac{3}{4}\times \frac{4}{5} \right )C=170\)

    ∴ 20C - 15C + 12C = 3400

    ∴ 17C = 3400 ∴. C = 200

After 3 females leave a party, there are thrice as many males as females. Thereafter 8 males leave the party, there are twice as many males as females.
Total no. of people left at Part! after 8 males leave 24
  • Solution

    Let 'm' males and 'f females be originally present.

    Condition 1 m = 3(f - 3) ∴ m = 3f - 9

    Condition 2 m - 8 = 2(f - 3) ∴ m = 2f + 2

    3f - 9 = 2f + 2 ∴ f = 11 ∴ m = 24

    ∴ First 3 females and then 8 males leave the party.

    ∴ No. of people left in the party (24 + 11) - (3 + 8) = 24

In a certain three digit number divisible by 5, the sum of unit’s digit and hundred’s digit is half that of
the digit in tens place.
Digital in hundred’s place 5
  • Solution

    The 3 digit number must necessarily end in 0, because if it ends in 5, then according to given condition the number at ten's digit would be 2 digit number which is not possible. The maximum value for digit in ten's place will be 8, for which the maximum digit in hundred's place is 4. e.g., 120,240,360,480.

Attempted

0

Correct

0

Wrong

0

Complete
Quantitative Comparison
Attempted
Wrong
Correct