GMAT · Practice Sheet 27

1. 1.

   Quantitative Aptitude

   Find the average of these 8 numbers: 23, 82, 57, 29, 87, 88, 83, 66.

   Formula:Arithmetic Mean

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

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2. 2.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 15 and common difference 1.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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3. 3.

   Quantitative Aptitude

   Find the compound interest on $4,000 at 10% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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4. 4.

   Mathematics

   If f(x) = 1x³ + 2x² + 2x, find f′(1).

   Formula:Derivative of a Polynomial

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

   Formula:Permutations

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

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6. 6.

   Quantitative Aptitude

   A invests $8,000 and B invests $2,000 for the same period. If the total profit is $13,000, find A's share.

   Formula:Partnership (profit share)

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

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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   For the quadratic 2x² − 2x − 1 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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9. 9.

   Mathematics

   If f(x) = 4x³ + 4x² + 6x, find f′(3).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Quantitative Aptitude

    Find the average of these 8 numbers: 89, 23, 23, 31, 37, 58, 53, 23.

    Formula:Arithmetic Mean

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

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11. 11.

    Mathematics

    Find the distance between the points (3, -8) and (-5, -6).

    Formula:Distance Between Two Points

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

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12. 12.

    Quantitative Aptitude

    A invests $4,000 and B invests $5,000 for the same period. If the total profit is $30,000, find A's share.

    Formula:Partnership (profit share)

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

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13. 13.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

    Formula:Permutations

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

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14. 14.

    Mathematics

    Find the sum of the first 9 terms of an AP with first term 3 and common difference 5.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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15. 15.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

    Formula:Combinations

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

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16. 16.

    Mathematics

    Find the slope of the line through (3, -5) and (-7, 2).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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17. 17.

    Quantitative Aptitude

    Find the average of these 8 numbers: 48, 28, 24, 86, 72, 39, 33, 30.

    Formula:Arithmetic Mean

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

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18. 18.

    Quantitative Aptitude

    The marked price of an item is $300. After a 40% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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19. 19.

    Mathematics

    Find the slope of the line through (6, -3) and (-4, -7).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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20. 20.

    Quantitative Aptitude

    A can finish a job in 14 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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