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GRE · Practice Sheet 15

Sheet code: GRE-S15 · 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

    What is 75% of 260?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  3. 3.
    Quantitative Aptitude

    A vehicle covers 666 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  4. 4.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  5. 5.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  6. 6.
    Quantitative Aptitude

    A value changes from 300 to 420. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  7. 7.
    Quantitative Aptitude

    The marked price of an item is $1,400. 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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  8. 8.
    Quantitative Aptitude

    Two varieties costing $28 and $83 per kg are mixed to give a mixture worth $40 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  9. 9.
    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  10. 10.
    Quantitative Aptitude

    Find the simple interest on $27,000 at 12% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  11. 11.
    Quantitative Aptitude

    The sum of the ages of two people is 78 years, and one is 4 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  12. 12.
    Quantitative Aptitude

    What is 75% of 1,060?

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

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  14. 14.
    Quantitative Aptitude

    A invests $8,000 and B invests $8,000 for the same period. If the total profit is $25,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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  15. 15.
    Mathematics

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

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  16. 16.
    Quantitative Aptitude

    Pipe A fills a tank in 12 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  17. 17.
    Quantitative Aptitude

    The sum of the ages of two people is 83 years, and one is 15 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  18. 18.
    Mathematics

    For the quadratic 3x² − 3x + 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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  19. 19.
    Mathematics

    Find the slope of the line through (1, 7) and (-8, -7).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  20. 20.
    Mathematics

    Find the sum of the first 7 terms of a GP with first term 6 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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