SAT · Practice Sheet 42

1. 1.

   Quantitative Aptitude

   The sum of the ages of two people is 74 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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2. 2.

   Mathematics

   Find the distance between the points (-1, -6) and (4, -3).

   Formula:Distance Between Two Points

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

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3. 3.

   Mathematics

   For the quadratic 3x² − 5x − 6 = 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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4. 4.

   Quantitative Aptitude

   Find the simple interest on AED 19,000 at 5% per annum for 3 year(s).

   Formula:Simple Interest

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

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5. 5.

   Quantitative Aptitude

   What is 25% of 540?

   Formula:Percentage of a Number

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

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6. 6.

   Quantitative Aptitude

   Two varieties costing AED 25 and AED 90 per kg are mixed to give a mixture worth AED 43 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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7. 7.

   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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8. 8.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)

   Formula:Combinations

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

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9. 9.

   Mathematics

   Find the slope of the line through (4, -8) and (0, -3).

   Formula:Slope of a Line

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

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10. 10.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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11. 11.

    Quantitative Aptitude

    Find the HCF and LCM of 6 and 12.

    Formula:LCM & HCF

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

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12. 12.

    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation

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

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13. 13.

    Quantitative Aptitude

    Two varieties costing AED 25 and AED 77 per kg are mixed to give a mixture worth AED 54 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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14. 14.

    Quantitative Aptitude

    Pipe A fills a tank in 8 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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15. 15.

    Mathematics

    Find term number 7 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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16. 16.

    Quantitative Aptitude

    Find the compound interest on AED 18,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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17. 17.

    Mathematics

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

    Formula:Slope of a Line

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

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18. 18.

    Quantitative Aptitude

    A invests AED 9,000 and B invests AED 3,000 for the same period. If the total profit is AED 27,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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19. 19.

    Quantitative Aptitude

    Find the average of these 6 numbers: 86, 59, 58, 56, 47, 34.

    Formula:Arithmetic Mean

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

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20. 20.

    Quantitative Aptitude

    Find the HCF and LCM of 12 and 19.

    Formula:LCM & HCF

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

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