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GRE · Practice Sheet 14

Sheet code: GRE-S14 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find term number 7 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  2. 2.
    Mathematics

    Find the distance between the points (6, 6) and (-1, -5).

    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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  3. 3.
    Mathematics

    Find the slope of the line through (5, -4) and (-8, 1).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  4. 4.
    Quantitative Aptitude

    A can finish a job in 19 days and B in 18 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  5. 5.
    Mathematics

    For the quadratic 1x² − 1x − 6 = 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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  6. 6.
    Quantitative Aptitude

    An item is bought for $800 and sold for $1,200. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  7. 7.
    Quantitative Aptitude

    What is 15% of 860?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  8. 8.
    Mathematics

    For the quadratic 1x² + 3x + 8 = 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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  9. 9.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  10. 10.
    Mathematics

    In an arithmetic progression with first term 7 and common difference 10, find term number 23.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  11. 11.
    Mathematics

    Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  12. 12.
    Quantitative Aptitude

    What is 40% of 1,120?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  13. 13.
    Quantitative Aptitude

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

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  14. 14.
    Quantitative Aptitude

    A vehicle covers 178 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  15. 15.
    Quantitative Aptitude

    An item is bought for $800 and sold for $1,120. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  16. 16.
    Quantitative Aptitude

    Find the simple interest on $32,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  17. 17.
    Quantitative Aptitude

    A can finish a job in 5 days and B in 17 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  18. 18.
    Quantitative Aptitude

    The marked price of an item is $800. After a 40% 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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  19. 19.
    Mathematics

    For the quadratic 5x² − 8x + 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.
    Mathematics

    Evaluate ∫ from 1 to 3 of 4x^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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