GRE · Practice Sheet 32

1. 1.

   Quantitative Aptitude

   A vehicle covers 245 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

   Find the distance between the points (7, -3) and (-3, 8).

   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

   Pipe A fills a tank in 14 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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4. 4.

   Quantitative Aptitude

   What is 25% of 220?

   Formula:Percentage of a Number

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

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5. 5.

   Quantitative Aptitude

   Find the HCF and LCM of 20 and 20.

   Formula:LCM & HCF

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

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6. 6.

   Quantitative Aptitude

   What is 75% of 820?

   Formula:Percentage of a Number

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

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7. 7.

   Mathematics

   For the quadratic 4x² + 6x − 8 = 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 sum of the first 15 terms of an AP with first term 10 and common difference 1.

   Formula:AP Sum of n Terms

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

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9. 9.

   Quantitative Aptitude

   What is 50% of 440?

   Formula:Percentage of a Number

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

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10. 10.

    Mathematics

    Find the distance between the points (-7, 8) and (4, 3).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Find the slope of the line through (1, 7) and (-2, -5).

    Formula:Slope of a Line

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

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12. 12.

    Quantitative Aptitude

    A can finish a job in 5 days and B in 10 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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13. 13.

    Quantitative Aptitude

    Find the average of these 10 numbers: 65, 88, 63, 40, 61, 77, 30, 77, 62, 64.

    Formula:Arithmetic Mean

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

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14. 14.

    Quantitative Aptitude

    Divide $1,960 between two people in the ratio 4:3. 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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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 4 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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16. 16.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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18. 18.

    Mathematics

    If f(x) = 1x³ + 6x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Quantitative Aptitude

    A vehicle covers 164 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

    Formula:Permutations

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

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