SAT · Practice Sheet 49

1. 1.

   Quantitative Aptitude

   A can finish a job in 4 days and B in 5 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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2. 2.

   Mathematics

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

   Formula:GP nth Term

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

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3. 3.

   Quantitative Aptitude

   An item is bought for AED 900 and sold for AED 990. Find the profit percentage.

   Formula:Profit Percentage

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

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 5 of 5x^2 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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5. 5.

   Quantitative Aptitude

   A vehicle covers 230 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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6. 6.

   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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7. 7.

   Mathematics

   In an arithmetic progression with first term 12 and common difference 7, find term number 13.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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8. 8.

   Quantitative Aptitude

   The sum of the ages of two people is 63 years, and one is 3 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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9. 9.

   Mathematics

   For the quadratic 2x² + 7x − 3 = 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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10. 10.

    Mathematics

    Find the slope of the line through (-8, -5) and (-4, -7).

    Formula:Slope of a Line

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

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11. 11.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    Evaluate ∫ from 0 to 5 of 4x^1 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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13. 13.

    Quantitative Aptitude

    What is 50% of 740?

    Formula:Percentage of a Number

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

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14. 14.

    Mathematics

    For the quadratic 4x² − 3x + 0 = 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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15. 15.

    Mathematics

    Find the slope of the line through (3, 6) and (-8, 5).

    Formula:Slope of a Line

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

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16. 16.

    Mathematics

    Find the sum of the first 7 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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17. 17.

    Quantitative Aptitude

    Find the average of these 6 numbers: 34, 52, 32, 34, 40, 49.

    Formula:Arithmetic Mean

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

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18. 18.

    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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19. 19.

    Quantitative Aptitude

    What is 20% of 280?

    Formula:Percentage of a Number

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations

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

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