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GMAT · Practice Sheet 14

Sheet code: GMAT-S14 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    If f(x) = 4x³ + 1x² + 7x, 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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  2. 2.
    Mathematics

    Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  3. 3.
    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 4 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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  4. 4.
    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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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  5. 5.
    Quantitative Aptitude

    Find the compound interest on $4,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  6. 6.
    Quantitative Aptitude

    A invests $2,000 and B invests $7,000 for the same period. If the total profit is $22,000, 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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  7. 7.
    Quantitative Aptitude

    Find the simple interest on $46,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  8. 8.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  9. 9.
    Quantitative Aptitude

    An item is bought for $200 and sold for $240. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  10. 10.
    Quantitative Aptitude

    Two varieties costing $16 and $80 per kg are mixed to give a mixture worth $62 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

    A invests $4,000 and B invests $10,000 for the same period. If the total profit is $21,000, 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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  12. 12.
    Quantitative Aptitude

    A vehicle covers 264 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  13. 13.
    Quantitative Aptitude

    Find the average of these 6 numbers: 47, 36, 42, 75, 55, 38.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  14. 14.
    Mathematics

    Evaluate ∫ from 2 to 3 of 3x^1 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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  15. 15.
    Quantitative Aptitude

    A invests $8,000 and B invests $9,000 for the same period. If the total profit is $21,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
    View formula →
  16. 16.
    Quantitative Aptitude

    Pipe A fills a tank in 10 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 →
  17. 17.
    Quantitative Aptitude

    Divide $1,782 between two people in the ratio 6:5. 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.
    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  19. 19.
    Mathematics

    In an arithmetic progression with first term 1 and common difference 2, find term number 29.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  20. 20.
    Quantitative Aptitude

    Two varieties costing $40 and $88 per kg are mixed to give a mixture worth $82 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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