GRE
Practice Test 22
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% gain made when an article is sold for $84 is twice as much as when it is sold for $72.
Cost price of the article in $ 64
  • Solution

    Amount gained in $ when the article is sold for $84 is twice that gained when article is sold for $72.

    Let the cost price of the article be x.

    ∴ 72 - x = 84 - 72 ∴ x = 60

    Note that, when article is sold, for $72, the % gain is 20% and-when it is sold for $84, % gain is 40%.

Out of 100 families surveyed, 45 own radios, 75 have TVs, 25 have VCRs. Only 10 families have all the three equipments. Each VCR owner also has a TV and 25 families have radios only.
Number of households that have only TVs 35
  • Solution

    No VCR owner owns only a VCR or a Radio, s it can be said that all 100 families own atleast one among a TV or a Radio. This is shown by figure zero in the Venn diagram.

    ∴ If out of 100 families, 75 own TV and 45 own a Radio, then (75 + 45) - 100 = 20 own both TV and Radio. Out of these 20, 10 own all the three.

    Hence number of families having only TV and Radio = 10.

    ∴ Number of families owing only TV

    = 75 - 10 - 10 - 15 = 40.

Linda has the same number of sisters as she has brothers, but her brother Paul has twice as many sisters as brothers.
Number of children in the family 7
  • Solution

    Let g denote the number of girls and b denote the number of boys in the family. From the information given in the problem, it is clear that number of girls exceeds the number of boys by one.

    But excluding Linda, we have b = g - I

    Similarly, excluding Paul, including Linda 2(b - 1) = g + 1 - II

    ∴ 2b - 2 = g + 1 ∴ 2b - 2 = b + 1

    ∴ b = 3 ∴ g = 3 + 1= 4

    Number of children = 7

A few liters of spirit is mixed in greater quantity of glycerin in the ratio of the roots of the equation 9x2 -30x + 25 = 0
Spirit content In liters In mixture of 64 liters 28
  • Solution

    9x2 - 30x + 25 = 0 ∴ (3x - 5)2 = 0

    ∴ Out of every 8 D2~s of mixture, sprit must be 3 parts and glycerin 5 because spirit is mixed in greater quantity of glycerin.

    ∴ In 64 liters we have 3⁄8 × 64 = 24 litres of spirit and remaining 40 litres of glycerin.

Linda can give Jack a start of 25m in a race of 300m and Paul a start of 30m in 360m.
The start in m Paul can give Jack in a race of 600m 5m
  • Solution

    When Linda gives Jack a start of 25m in a 300m race, it implies .that when Jack completes 300m, Linda completes 275m.

    ∴ In 600m race, Linda gives Jack a start of 50rn. On similar lines, in a 600m race, Linda gives Paul a start of 600 - \(\left (\frac{600\times 330}{360} \right )\)

    = 600 - 550 = 50m

    ∴ Both Paul and Jack receive a start of 50m in 600m race.

    ∴ They cannot give each other any starts at all (i.e. start is zero m).

    ∴ Col. A = 0

Mona went to the market to buy fruits; she has to buy at least 30 each of apples, figs and oranges. Also the number of apples should be more than that of figs and number of figs should be more than that of the number of oranges. She buys a total of 100 fruits.
Maximum number of figs she can buy 34
  • Solution

    To buy the maximum number of figs, she has to first buy the least number of oranges i.e. 30 .. -.30 oranges, 34 figs and 36 apples is a combination which gives the maximum number of figs and a total of 100 fruits

A shopkeeper bought coffee powder of brand CI at $32 per kg. and mixed it with better quality brand C2 costing $45 per kg. He then sold the blend at $44 per kg. that gave him a profit of 10%.
Ratio in which C1 and C2 are mixed 3⁄4
  • Solution

    S. P. = $44, Profit = 10% ∴ CP. = $40

    ∴ The cost price of the blend is $40 per kg.

    By the principle of alligation

    ∴ C1 and C2 should be mixed in the ratio 5⁄8

    Col. B = 3⁄4 = 6⁄8 ∴ Col. B > Col. A

Linda bought a clock for $600. Later she sold it to Paul for $700. After 2 months she bought it back from Paul for $800 and sold it to John for $900.
Linda’s profit in the whole transaction Paul’s profit in the whole transaction +$50
  • Solution

    Linda's profit in the first transaction (i.e. with Paul): CP. = $600, S.P. = $700

    ∴ Profit = S.P.-CP. = $100

    Linda's profit in the second transaction (i.e. with John) : CP. = $800, S.P. = $900

    ∴ Profit = S.P. - CP. = $100

    ∴ Linda's total profit = 100 + 100 = $200 = Col. A

    Paul's profit in the whole transaction:

    CP. $700,S.P.$800

    ∴ Profit = S.P.-CP. = $100

    ∴ Col. B = 100 + 50 = $150

2 cars are traveling at speeds of 45 and 60 kmph respectively. The second car takes 41⁄2 hours less than first for journey.
Length of the journey in km 630 km
  • Solution

    Distance = Speed × Time

    Here distance remains constant.

    ∴ speed X time1 = speed2 × time2

    ∴ \(\frac{s_{1}}{s_{2}}=\frac{t_{2}}{t_{1}}\) ∴ \(\frac{45}{60}=\frac{t_{2}}{t_{1}}=\frac{3}{4}\)

    Ratio of time taken for journey is 4 : 3

    ∴ 4x - 3x = 4.5 ∴ x = 4.5 ∴ 3x = 13.5, 4x = 18

    ∴ Length of journey = 45 × 18 = 810 kms.

Value of x 60°
  • Solution

    The figure shows a polygon PQRSTUVWX with nine side.

    Measure of the internal angle of this polygon

    \(=\frac{(n-2)\times 180}{n}=\frac{(9-3)\times 180}{9}=\frac{7\times 180}{9}\)=140°

    Now consider ΔSDT as shown in figure

    ∠RST = ∠STU = 140°

    ∴ y = 40° ........Angles in linear pair

    ∴ x = 180 - (40 + 40) = 100° = Col. A

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