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GRE · Practice Sheet 43

Sheet code: GRE-S43 · 20 questions

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

    An item is bought for $900 and sold for $1,080. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  2. 2.
    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 7 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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  3. 3.
    Quantitative Aptitude

    An item is bought for $600 and sold for $660. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  4. 4.
    Quantitative Aptitude

    Find the compound interest on $8,000 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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  5. 5.
    Mathematics

    For the quadratic 1x² + 6x + 7 = 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

    A can finish a job in 4 days and B in 12 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  7. 7.
    Quantitative Aptitude

    Divide $1,267 between two people in the ratio 5:2. 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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  8. 8.
    Quantitative Aptitude

    The sum of the ages of two people is 38 years, and one is 14 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  9. 9.
    Mathematics

    If f(x) = 3x³ + 6x² + 9x, find f′(3).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  10. 10.
    Quantitative Aptitude

    An item is bought for $800 and sold for $920. Find the profit percentage.

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

    Find the distance between the points (-2, -3) and (6, 6).

    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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  12. 12.
    Mathematics

    Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  13. 13.
    Quantitative Aptitude

    The sum of the ages of two people is 94 years, and one is 18 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  14. 14.
    Mathematics

    Find the slope of the line through (-3, -3) and (-2, 2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  15. 15.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 3 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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  16. 16.
    Quantitative Aptitude

    A value changes from 200 to 160. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  17. 17.
    Quantitative Aptitude

    The sum of the ages of two people is 72 years, and one is 4 years older than the other. Find their ages.

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

    For the quadratic 4x² − 1x + 2 = 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}
    View formula →
  19. 19.
    Quantitative Aptitude

    Pipe A fills a tank in 13 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  20. 20.
    Mathematics

    If f(x) = 5x³ + 4x² + 2x, 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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