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SAT · Practice Sheet 39

Sheet code: SAT-S39 · 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

    A can finish a job in 15 days and B in 20 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  3. 3.
    Quantitative Aptitude

    Find the HCF and LCM of 23 and 14.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  4. 4.
    Mathematics

    Find the distance between the points (3, -2) and (6, -5).

    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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  5. 5.
    Quantitative Aptitude

    Two varieties costing AED 30 and AED 69 per kg are mixed to give a mixture worth AED 53 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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  6. 6.
    Quantitative Aptitude

    An item is bought for AED 300 and sold for AED 420. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  7. 7.
    Quantitative Aptitude

    Divide AED 1,940 between two people in the ratio 6:4. 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.
    Mathematics

    Find term number 6 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  9. 9.
    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  10. 10.
    Quantitative Aptitude

    Find the compound interest on AED 11,000 at 20% 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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  11. 11.
    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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  12. 12.
    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 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.
    Mathematics

    Find the sum of the first 6 terms of an AP with first term 2 and common difference 4.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  14. 14.
    Quantitative Aptitude

    Find the compound interest on AED 9,000 at 20% 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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  15. 15.
    Quantitative Aptitude

    A invests AED 9,000 and B invests AED 8,000 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.
    Mathematics

    For the quadratic 3x² + 3x + 4 = 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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  17. 17.
    Mathematics

    In an arithmetic progression with first term 20 and common difference 3, find term number 26.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  18. 18.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  19. 19.
    Quantitative Aptitude

    A vehicle covers 300 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  20. 20.
    Quantitative Aptitude

    The sum of the ages of two people is 90 years, and one is 16 years older than the other. Find their ages.

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