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SAT · Practice Sheet 19

Sheet code: SAT-US-S19 · 20 questions

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

    A invests $5,000 and B invests $9,000 for the same period. If the total profit is $34,000, 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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  2. 2.
    Quantitative Aptitude

    Find the HCF and LCM of 17 and 17.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  3. 3.
    Mathematics

    Find the slope of the line through (6, -4) and (0, 5).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  4. 4.
    Mathematics

    If f(x) = 4x³ + 1x² + 2x, find f′(4).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  5. 5.
    Quantitative Aptitude

    An item is bought for $300 and sold for $375. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  6. 6.
    Mathematics

    Find the slope of the line through (-2, -6) and (5, -5).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  7. 7.
    Quantitative Aptitude

    Two varieties costing $13 and $64 per kg are mixed to give a mixture worth $19 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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  8. 8.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  9. 9.
    Mathematics

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

    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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  10. 10.
    Quantitative Aptitude

    The marked price of an item is $300. 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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  11. 11.
    Quantitative Aptitude

    Find the compound interest on $7,000 at 10% 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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  12. 12.
    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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  13. 13.
    Mathematics

    If f(x) = 3x³ + 1x² + 1x, 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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  14. 14.
    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  15. 15.
    Quantitative Aptitude

    The marked price of an item is $900. After a 5% 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.
    Quantitative Aptitude

    The sum of the ages of two people is 39 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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  17. 17.
    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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  18. 18.
    Quantitative Aptitude

    Pipe A fills a tank in 7 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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  19. 19.
    Quantitative Aptitude

    A invests $8,000 and B invests $9,000 for the same period. If the total profit is $7,000, 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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  20. 20.
    Mathematics

    Find the sum of the first 17 terms of an AP with first term 14 and common difference 10.

    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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