SAT · Practice Sheet 42

1. 1.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 1 and common ratio 3.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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2. 2.

   Quantitative Aptitude

   What is 10% of 420?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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3. 3.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

   Formula:Combinations

   $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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4. 4.

   Mathematics

   Find the slope of the line through (-8, 0) and (-1, 2).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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5. 5.

   Quantitative Aptitude

   An item is bought for $500 and sold for $625. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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6. 6.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 20 and common difference 5.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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7. 7.

   Quantitative Aptitude

   A can finish a job in 10 days and B in 12 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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8. 8.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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9. 9.

   Quantitative Aptitude

   Pipe A fills a tank in 11 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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10. 10.

    Quantitative Aptitude

    Find the simple interest on $33,000 at 6% per annum for 6 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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11. 11.

    Mathematics

    Find the distance between the points (-3, -2) and (3, -7).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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12. 12.

    Quantitative Aptitude

    A value changes from 200 to 100. Find the percentage decrease.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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13. 13.

    Quantitative Aptitude

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

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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14. 14.

    Quantitative Aptitude

    An item is bought for $200 and sold for $220. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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15. 15.

    Mathematics

    If f(x) = 4x³ + 1x² + 3x, find f′(5).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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16. 16.

    Quantitative Aptitude

    The sum of the ages of two people is 94 years, and one is 16 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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17. 17.

    Quantitative Aptitude

    Find the compound interest on $15,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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18. 18.

    Mathematics

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

    Formula:GP Sum of n Terms

    $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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19. 19.

    Mathematics

    If f(x) = 5x³ + 3x² + 4x, find f′(4).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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20. 20.

    Quantitative Aptitude

    Find the HCF and LCM of 39 and 9.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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