GMAT · Practice Sheet 1

1. 1.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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2. 2.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

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

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3. 3.

   Quantitative Aptitude

   A invests $6,000 and B invests $8,000 for the same period. If the total profit is $22,000, find A's share.

   Formula:Partnership (profit share)

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

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4. 4.

   Quantitative Aptitude

   A vehicle covers 720 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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5. 5.

   Quantitative Aptitude

   Divide $1,090 between two people in the ratio 7:3. 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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6. 6.

   Mathematics

   Find term number 5 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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7. 7.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)

   Formula:Combinations

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

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8. 8.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

   Formula:Permutations

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

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9. 9.

   Quantitative Aptitude

   Find the simple interest on $5,000 at 4% per annum for 1 year(s).

   Formula:Simple Interest

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

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10. 10.

    Quantitative Aptitude

    An item is bought for $500 and sold for $700. Find the profit percentage.

    Formula:Profit Percentage

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

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11. 11.

    Mathematics

    Find the slope of the line through (5, 8) and (-4, -5).

    Formula:Slope of a Line

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

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12. 12.

    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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13. 13.

    Quantitative Aptitude

    Find the HCF and LCM of 29 and 30.

    Formula:LCM & HCF

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

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14. 14.

    Mathematics

    For the quadratic 2x² + 8x − 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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15. 15.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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16. 16.

    Quantitative Aptitude

    A vehicle covers 588 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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17. 17.

    Mathematics

    Find the slope of the line through (-1, -1) and (-2, 6).

    Formula:Slope of a Line

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

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18. 18.

    Mathematics

    If f(x) = 1x³ + 6x² + 8x, find f′(5).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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20. 20.

    Quantitative Aptitude

    Divide $1,225 between two people in the ratio 3:2. 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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