GRE
Practice Test 29
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A right circular cylinder of base radius 4 and height ‘h’ is filled with milk upto (1⁄3)rd of its height. The entire milk is now transferred to a cone of the same height as that of the cylinder and cone gets completely filled with milk.
Base radius of right circular cone 4
  • Solution

    Volume of milk in cylinder = Volume of cone

    ∴ 1⁄3(πr2h) = 1⁄3πr2h ∴1⁄3π42h = 1⁄3πr2h

    ∴ 42 = r2 ∴ r = 4

Linda has to buy 10 pieces of bread.store a gives her 9% discount on the total cost of pieces of bread.store B gives $1 discount on the purchase of 4 pieces of bread .cost of bread per piece is $4.
Amount linda pays if she buys from store A Amount she pay if she buys from store B
  • Solution

    Col. A:

    Total price of 10 pieces of bread = 10 × 4 = $40.

    Discount is 9% on total price.

    She pays 40 - 3.6 = $36.4 for 10 pieces.

    Col. B:

    Discount offered is $1 on the purchase of 4 pieces.

    ∴ Cost of 4 pieces will be (4 x $4) - $1 = $15

    ∴ For 8 pieces, she pays $30. But for the remaining 2 pieces she has to pay $8.

    ∴ Total price she pays = $38

m + n + o + p = 23

m, n, 0 belong to set of natural numbers, p belongs to the set of whole numbers.

maximum possible value of m maximum possible value of p
  • Solution

    Col. A:

    Natural numbers begin with 1, while whole numbers begin with O.

    Form to be maximum, n, 0 and p each must take minimum values.

    Let n = 0 = 1 and p = O. In that case, m can take 21 as the maximum value.

    Col. B:

    Similarly, assigning minimum values to m, n, 0, we have m = n = 0 = 1.

    ∴ Maximum possible value of p = 23 - 3 = 20

    ∴ Col. A = 21, Col. B = 20

    Since problem does not mention that m, n, 0, p are different integers. They can have same value.'

value of p + q + r value of 2(m + n)
  • Solution

    Col. A:

    Since side r is the least p + q + r must be more than 3r.

    Col. B:

    2(m + n) = 2(0.75r + 0.75r) = 3r

P and Q are regular polygons
(5a + x + 27)° (8m + y)°
  • Solution

    P is a regular pentagon. ∴ Each interior angle measures 1080

    and each exterior angle measures 720

    ∴ Col. A: 5a + x + 27 = (5 × 72) + 108 + 27 = (360 + 135)°

    Similarly, Q is a regular octagon.

    ∴ Each interior angle measures 135° and each exterior angle measure 45°

    ∴ Col. B : 8m + y = 8 × 45 + 135 = (360 + 135)°

    ∴ Col. A = Col.. B

Linda makes a cocktail of Lemon juice, Apple juice and Pineapple juice. She adds Lemon juice thrice the quantity of Apple juice. She further adds Pineapple juice till it becomes 2⁄3 of the total cocktail content.
Ratio of Pineapple juice to Lemon juice in cocktail Column B
  • Solution

    Let there be 1 unit of Apple juice.

    ∴ There are 3 units of Lemon juice.

    ∴ Since Pineapple juice is 2⁄3 of the cocktail,

    Apple + Lemon juice will be 1⁄3 of the cocktail, which is 4 units, therefore Pineapple juice will be 8 units.

    ∴ Col.A = 8⁄3 Col.B = \(\frac{Lemon}{Apple}\)= 3⁄1 = 9⁄3

    ∴. Col. B > Co!. A

John’s expenditure and savings are in the ratio 5:3. His income increases by 15% and expenses by 12%.
% increase in savings 18%
  • Solution

    Let John's expenditure be $500 and savings be $300.

    ∴ His income = $800

    Income after increase = 800 × 1.15 = $920

    Expenditure after increase = 500 × 1.12 = $560

    ∴ New savings = 920 - 560 = $360

    ∴ Increase in savings = $(360 - 300) = $60

    ∴ % increase in savings = \(\frac{60}{300}\) × 100 = 20%

John and George entered into a partnership with capitals in the ratio 5:6. After 3 months John withdrew 1⁄5 of his capital and George withdrew 1⁄6 of his capital. Gain at the end of 12 months was $11400.
john share in the profit $5,400
  • Solution

    Let the capitals of John and George be 5x and 6x respectively.

    ∴ John's investment in the first 3 months = 5x × 3 = $15x

    Similarly, George's investment for the same 3 months = 6x × 3 $18x

    For the remaining 8 months, John's investment = \(\left ( 5x-\frac{5x}{5} \right )\)× 9 = $36x

    Georges investment = \(\left ( 6x-\frac{6x}{6} \right )\) × 9 = $45x

    ∴ Total investment of John and George for 12 months is $(15x + 36x) and $(18x + 45x) respectively.

    ∴ Ratio of investments is 51 : 63

    ∴ John's share = = \(\left ( \frac{51}{51+63} \right )\) × 2100

    = \(\frac{17}{38}\) × 11400 = $5100

Out of 60 articles, sold, 1/3 were sold at 20% profit and rest at 30% profit. If all the articles had been sold at 25%, profit, total profit would have been $100 less.
cost price of each article $100
  • Solution

    Method 1:

    Cost of 1 article is $1.

    20 articles sold at $24 (20% profit)

    40 articles sold at $52 (30% profit)

    ∴ Total 60 articles sold at $76.

    Method 2:

    If all articles are sold at 25% profit, selling price, would be $75.

    ∴ Difference is $1

    But actual difference is $100.

    ∴ Actual cost must be $100.

pq and qp are 2 digit numbers, p and q are distinct digits from 0 to 9. Difference of pq and qp is HCF of pq and qp.
value of p + q 6
  • Solution

    Difference between a 2 digit number and the number when its digit are reversed is always a multiple of 9.

    The difference is equal to the HCF only in case of number 54 (or 45).

    ∴ Value of p + q = 4 + 5 = 9

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