GMAT · Practice Sheet 41

1. 1.

   Quantitative Aptitude

   A vehicle covers 395 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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2. 2.

   Mathematics

   In an arithmetic progression with first term 3 and common difference 7, find term number 28.

   Formula:AP nth Term

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

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3. 3.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 15 and common difference 3.

   Formula:AP Sum of n Terms

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

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4. 4.

   Mathematics

   Evaluate log base 10 of 1,000.

   Formula:Logarithm Evaluation

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

   Formula:Combinations

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

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6. 6.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

   Formula:Probability (two dice)

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

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7. 7.

   Mathematics

   For the quadratic 2x² + 3x + 2 = 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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8. 8.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 6, find term number 24.

   Formula:AP nth Term

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

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10. 10.

    Quantitative Aptitude

    An item is bought for $700 and sold for $875. Find the profit percentage.

    Formula:Profit Percentage

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

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11. 11.

    Quantitative Aptitude

    Find the average of these 6 numbers: 63, 69, 73, 44, 51, 26.

    Formula:Arithmetic Mean

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

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12. 12.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

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13. 13.

    Mathematics

    Find the distance between the points (4, -5) and (-2, 1).

    Formula:Distance Between Two Points

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

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14. 14.

    Mathematics

    Find the slope of the line through (1, 5) and (4, -5).

    Formula:Slope of a Line

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations

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

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16. 16.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

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

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17. 17.

    Quantitative Aptitude

    A can finish a job in 16 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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18. 18.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

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

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19. 19.

    Mathematics

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

    Formula:Slope of a Line

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

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20. 20.

    Mathematics

    Find term number 6 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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