SAT · Practice Sheet 22

1. 1.

   Quantitative Aptitude

   The sum of the ages of two people is 31 years, and one is 9 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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2. 2.

   Quantitative Aptitude

   What is 60% of 540?

   Formula:Percentage of a Number

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

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3. 3.

   Quantitative Aptitude

   Find the average of these 5 numbers: 61, 80, 20, 44, 81.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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4. 4.

   Mathematics

   Evaluate log base 2 of 32.

   Formula:Logarithm Evaluation

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

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5. 5.

   Mathematics

   For the quadratic 2x² + 4x + 1 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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6. 6.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

   Formula:Permutations

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

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7. 7.

   Mathematics

   Find term number 5 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

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8. 8.

   Mathematics

   Find the slope of the line through (3, 3) and (-3, -7).

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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10. 10.

    Quantitative Aptitude

    The marked price of an item is $1,200. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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11. 11.

    Quantitative Aptitude

    Pipe A fills a tank in 7 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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12. 12.

    Mathematics

    Find the distance between the points (1, 5) and (-3, 3).

    Formula:Distance Between Two Points

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

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13. 13.

    Quantitative Aptitude

    The marked price of an item is $600. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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14. 14.

    Quantitative Aptitude

    A can finish a job in 4 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

    Formula:Permutations

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

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16. 16.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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17. 17.

    Mathematics

    Find term number 3 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

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

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18. 18.

    Quantitative Aptitude

    The sum of the ages of two people is 78 years, and one is 14 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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19. 19.

    Mathematics

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

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    Find the distance between the points (5, -4) and (-5, 4).

    Formula:Distance Between Two Points

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

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