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SAT · Practice Sheet 23

Sheet code: SAT-S23 · 20 questions

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

    A can finish a job in 17 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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  2. 2.
    Mathematics

    Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  3. 3.
    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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  4. 4.
    Quantitative Aptitude

    The sum of the ages of two people is 33 years, and one is 11 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  5. 5.
    Quantitative Aptitude

    Find the HCF and LCM of 40 and 16.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  6. 6.
    Quantitative Aptitude

    What is 15% of 1,040?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  7. 7.
    Mathematics

    Evaluate log base 2 of 16.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  8. 8.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  9. 9.
    Quantitative Aptitude

    A invests AED 7,000 and B invests AED 8,000 for the same period. If the total profit is AED 19,000, 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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  10. 10.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  11. 11.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  12. 12.
    Quantitative Aptitude

    Find the simple interest on AED 32,000 at 8% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  13. 13.
    Quantitative Aptitude

    Two varieties costing AED 14 and AED 100 per kg are mixed to give a mixture worth AED 68 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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  14. 14.
    Quantitative Aptitude

    The sum of the ages of two people is 80 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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  15. 15.
    Quantitative Aptitude

    A invests AED 7,000 and B invests AED 4,000 for the same period. If the total profit is AED 13,000, 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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  16. 16.
    Quantitative Aptitude

    Two varieties costing AED 16 and AED 86 per kg are mixed to give a mixture worth AED 66 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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  17. 17.
    Quantitative Aptitude

    A invests AED 4,000 and B invests AED 6,000 for the same period. If the total profit is AED 14,000, 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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  18. 18.
    Mathematics

    If f(x) = 5x³ + 6x² + 6x, 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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  19. 19.
    Mathematics

    Evaluate ∫ from 2 to 4 of 5x^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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  20. 20.
    Mathematics

    Find term number 6 of a geometric progression with first term 5 and common ratio 2.

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