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SAT · Practice Sheet 47

Sheet code: SAT-S47 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  2. 2.
    Quantitative Aptitude

    The marked price of an item is AED 1,500. After a 30% 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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  3. 3.
    Mathematics

    Find the sum of the first 6 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  4. 4.
    Quantitative Aptitude

    Divide AED 2,367 between two people in the ratio 7:2. 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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  5. 5.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 19 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  6. 6.
    Quantitative Aptitude

    A invests AED 9,000 and B invests AED 2,000 for the same period. If the total profit is AED 35,000, 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

    A vehicle covers 385 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  8. 8.
    Quantitative Aptitude

    Pipe A fills a tank in 6 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}
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  9. 9.
    Mathematics

    For the quadratic 4x² + 0x + 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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  10. 10.
    Quantitative Aptitude

    Find the average of these 10 numbers: 58, 78, 22, 33, 84, 27, 50, 81, 62, 82.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  11. 11.
    Mathematics

    Evaluate ∫ from 2 to 3 of 4x^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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  12. 12.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  13. 13.
    Mathematics

    Find the distance between the points (7, 7) and (-2, 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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  14. 14.
    Quantitative Aptitude

    Divide AED 840 between two people in the ratio 2:4. 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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  15. 15.
    Quantitative Aptitude

    Find the simple interest on AED 24,000 at 6% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  16. 16.
    Quantitative Aptitude

    What is 15% of 100?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  17. 17.
    Quantitative Aptitude

    A value changes from 600 to 540. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  18. 18.
    Mathematics

    Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  19. 19.
    Quantitative Aptitude

    A can finish a job in 6 days and B in 17 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  20. 20.
    Quantitative Aptitude

    Find the compound interest on AED 18,000 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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