GRE · Practice Sheet 13

1. 1.

   Quantitative Aptitude

   Find the simple interest on $25,000 at 8% per annum for 2 year(s).

   Formula:Simple Interest

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

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2. 2.

   Quantitative Aptitude

   A value changes from 400 to 440. Find the percentage increase.

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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3. 3.

   Mathematics

   Find the distance between the points (1, 4) and (-3, 2).

   Formula:Distance Between Two Points

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

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4. 4.

   Mathematics

   Find term number 4 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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5. 5.

   Mathematics

   Find the distance between the points (4, 1) and (0, 4).

   Formula:Distance Between Two Points

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

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6. 6.

   Mathematics

   Find the slope of the line through (7, 6) and (8, 6).

   Formula:Slope of a Line

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

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7. 7.

   Quantitative Aptitude

   Two varieties costing $10 and $87 per kg are mixed to give a mixture worth $51 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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8. 8.

   Mathematics

   For the quadratic 5x² − 5x − 7 = 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.

   Quantitative Aptitude

   The marked price of an item is $700. After a 15% discount, find the selling price.

   Formula:Discount & Selling Price

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

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10. 10.

    Mathematics

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

    Formula:GP Sum of n Terms

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

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11. 11.

    Mathematics

    Find the sum of the first 9 terms of an AP with first term 10 and common difference 7.

    Formula:AP Sum of n Terms

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

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12. 12.

    Mathematics

    If f(x) = 1x³ + 1x² + 5x, find f′(2).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Quantitative Aptitude

    A can finish a job in 13 days and B in 17 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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14. 14.

    Quantitative Aptitude

    Find the HCF and LCM of 33 and 23.

    Formula:LCM & HCF

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

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15. 15.

    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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16. 16.

    Quantitative Aptitude

    Pipe A fills a tank in 6 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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17. 17.

    Quantitative Aptitude

    Find the HCF and LCM of 29 and 33.

    Formula:LCM & HCF

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

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18. 18.

    Quantitative Aptitude

    What is 75% of 1,020?

    Formula:Percentage of a Number

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

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19. 19.

    Quantitative Aptitude

    Find the simple interest on $49,000 at 5% per annum for 2 year(s).

    Formula:Simple Interest

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

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20. 20.

    Quantitative Aptitude

    An item is bought for $300 and sold for $375. Find the profit percentage.

    Formula:Profit Percentage

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

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