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GRE · Practice Sheet 18

Sheet code: GRE-S18 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  2. 2.
    Quantitative Aptitude

    Find the compound interest on $13,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  3. 3.
    Mathematics

    Find the distance between the points (-1, -8) and (8, -1).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  4. 4.
    Quantitative Aptitude

    Find the simple interest on $40,000 at 5% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  5. 5.
    Mathematics

    If f(x) = 1x³ + 3x² + 7x, find f′(2).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  6. 6.
    Quantitative Aptitude

    Divide $1,170 between two people in the ratio 5:4. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
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  7. 7.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  8. 8.
    Quantitative Aptitude

    An item is bought for $900 and sold for $1,350. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  9. 9.
    Quantitative Aptitude

    The marked price of an item is $1,300. After a 5% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  10. 10.
    Quantitative Aptitude

    An item is bought for $900 and sold for $1,260. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  11. 11.
    Mathematics

    Find the slope of the line through (-3, 8) and (0, 1).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  12. 12.
    Quantitative Aptitude

    A value changes from 400 to 460. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  13. 13.
    Mathematics

    For the quadratic 3x² + 4x − 9 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  14. 14.
    Quantitative Aptitude

    The marked price of an item is $800. After a 10% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  15. 15.
    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  16. 16.
    Mathematics

    Evaluate ∫ from 0 to 4 of 1x^3 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
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  17. 17.
    Mathematics

    Find term number 3 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  18. 18.
    Mathematics

    Find the slope of the line through (-3, -8) and (0, 3).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  19. 19.
    Mathematics

    For the quadratic 4x² + 0x − 9 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  20. 20.
    Quantitative Aptitude

    Find the average of these 10 numbers: 25, 73, 45, 28, 29, 47, 60, 30, 85, 88.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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