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GRE · Practice Sheet 7

Sheet code: GRE-S07 · 20 questions

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

    In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  2. 2.
    Mathematics

    In an arithmetic progression with first term 6 and common difference 5, find term number 5.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  3. 3.
    Quantitative Aptitude

    Find the simple interest on $21,000 at 10% per annum for 2 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  4. 4.
    Mathematics

    If f(x) = 5x³ + 4x² + 4x, find f′(5).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  5. 5.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 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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  6. 6.
    Mathematics

    Find term number 5 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  7. 7.
    Mathematics

    In an arithmetic progression with first term 17 and common difference 3, find term number 24.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  8. 8.
    Quantitative Aptitude

    The marked price of an item is $2,000. 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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  9. 9.
    Mathematics

    Find term number 5 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  10. 10.
    Quantitative Aptitude

    Two varieties costing $33 and $81 per kg are mixed to give a mixture worth $54 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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  11. 11.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  12. 12.
    Mathematics

    Find the distance between the points (-5, 2) 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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  13. 13.
    Mathematics

    For the quadratic 4x² − 2x + 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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  14. 14.
    Mathematics

    In an arithmetic progression with first term 1 and common difference 6, find term number 23.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  15. 15.
    Quantitative Aptitude

    An item is bought for $700 and sold for $770. 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

    Pipe A fills a tank in 11 hours and pipe B in 12 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

    Divide $1,067 between two people in the ratio 5:6. 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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  18. 18.
    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
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  19. 19.
    Quantitative Aptitude

    The marked price of an item is $2,000. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  20. 20.
    Mathematics

    Find the sum of the first 7 terms of a GP with first term 5 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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