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SAT · Practice Sheet 26

Sheet code: SAT-US-S26 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  3. 3.
    Mathematics

    Find term number 6 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  4. 4.
    Mathematics

    Find the sum of the first 18 terms of an AP with first term 19 and common difference 1.

    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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  5. 5.
    Quantitative Aptitude

    A vehicle covers 162 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  6. 6.
    Quantitative Aptitude

    A can finish a job in 4 days and B in 18 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  7. 7.
    Mathematics

    Find the sum of the first 18 terms of an AP with first term 19 and common difference 2.

    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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  8. 8.
    Quantitative Aptitude

    An item is bought for $700 and sold for $875. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  9. 9.
    Mathematics

    Find the slope of the line through (-8, -6) and (4, 0).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  10. 10.
    Quantitative Aptitude

    A value changes from 800 to 960. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  11. 11.
    Quantitative Aptitude

    Pipe A fills a tank in 15 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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  12. 12.
    Mathematics

    For the quadratic 5x² + 1x + 0 = 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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  13. 13.
    Quantitative Aptitude

    What is 60% of 180?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  14. 14.
    Quantitative Aptitude

    Find the average of these 6 numbers: 72, 52, 48, 42, 30, 33.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  15. 15.
    Quantitative Aptitude

    The marked price of an item is $600. After a 25% 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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  16. 16.
    Mathematics

    Find term number 6 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  17. 17.
    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  18. 18.
    Quantitative Aptitude

    Find the average of these 8 numbers: 39, 73, 58, 88, 54, 43, 73, 33.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  19. 19.
    Mathematics

    In an arithmetic progression with first term 17 and common difference 3, find term number 11.

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

    Pipe A fills a tank in 5 hours and pipe B in 11 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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