SAT · Practice Sheet 28

1. 1.

   Quantitative Aptitude

   The sum of the ages of two people is 34 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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2. 2.

   Quantitative Aptitude

   Find the average of these 10 numbers: 35, 89, 50, 76, 45, 44, 65, 71, 73, 20.

   Formula:Arithmetic Mean

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

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3. 3.

   Quantitative Aptitude

   What is 40% of 1,060?

   Formula:Percentage of a Number

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

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4. 4.

   Quantitative Aptitude

   Find the HCF and LCM of 9 and 23.

   Formula:LCM & HCF

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

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5. 5.

   Mathematics

   If f(x) = 1x³ + 5x² + 2x, find f′(3).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Mathematics

   Evaluate ∫ from 1 to 3 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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7. 7.

   Quantitative Aptitude

   A vehicle covers 504 km in 6 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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8. 8.

   Mathematics

   In an arithmetic progression with first term 6 and common difference 4, find term number 27.

   Formula:AP nth Term

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 25 and 12.

   Formula:LCM & HCF

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

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10. 10.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

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11. 11.

    Quantitative Aptitude

    Find the HCF and LCM of 17 and 35.

    Formula:LCM & HCF

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

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12. 12.

    Mathematics

    For the quadratic 2x² + 6x + 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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13. 13.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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14. 14.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations

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

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15. 15.

    Quantitative Aptitude

    An item is bought for $800 and sold for $920. Find the profit percentage.

    Formula:Profit Percentage

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

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16. 16.

    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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17. 17.

    Quantitative Aptitude

    Pipe A fills a tank in 11 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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18. 18.

    Quantitative Aptitude

    The sum of the ages of two people is 28 years, and one is 4 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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19. 19.

    Quantitative Aptitude

    Find the HCF and LCM of 9 and 19.

    Formula:LCM & HCF

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

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20. 20.

    Quantitative Aptitude

    Find the simple interest on $11,000 at 10% per annum for 2 year(s).

    Formula:Simple Interest

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

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