GMAT · Practice Sheet 16

1. 1.

   Mathematics

   Evaluate ∫ from 0 to 4 of 3x^2 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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2. 2.

   Mathematics

   Find the distance between the points (-5, -5) and (2, 7).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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3. 3.

   Quantitative Aptitude

   What is 30% of 220?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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4. 4.

   Quantitative Aptitude

   Pipe A fills a tank in 3 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 14 and common difference 8, find term number 28.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 14 and 27.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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7. 7.

   Mathematics

   If f(x) = 4x³ + 6x² + 8x, find f′(1).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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8. 8.

   Quantitative Aptitude

   Divide $1,750 between two people in the ratio 5:2. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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9. 9.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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10. 10.

    Quantitative Aptitude

    The sum of the ages of two people is 89 years, and one is 17 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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11. 11.

    Quantitative Aptitude

    Find the average of these 10 numbers: 50, 65, 47, 24, 61, 34, 50, 78, 84, 50.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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12. 12.

    Quantitative Aptitude

    What is 30% of 900?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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13. 13.

    Quantitative Aptitude

    The sum of the ages of two people is 63 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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14. 14.

    Quantitative Aptitude

    Divide $2,450 between two people in the ratio 7:7. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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15. 15.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)

    Formula:Combinations

    $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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16. 16.

    Quantitative Aptitude

    A invests $5,000 and B invests $2,000 for the same period. If the total profit is $5,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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17. 17.

    Quantitative Aptitude

    Find the simple interest on $11,000 at 12% per annum for 5 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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18. 18.

    Quantitative Aptitude

    An item is bought for $900 and sold for $990. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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19. 19.

    Quantitative Aptitude

    A invests $6,000 and B invests $8,000 for the same period. If the total profit is $26,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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20. 20.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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