11+ · Practice Sheet 22

1. 1.

   Quantitative Aptitude

   The sum of the ages of two people is 67 years, and one is 13 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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2. 2.

   Mathematics

   For the quadratic 2x² − 5x − 9 = 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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3. 3.

   Quantitative Aptitude

   Find the average of these 8 numbers: 35, 69, 74, 45, 25, 26, 89, 57.

   Formula:Arithmetic Mean

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

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4. 4.

   Quantitative Aptitude

   The marked price of an item is £1,900. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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5. 5.

   Quantitative Aptitude

   What is 40% of 140?

   Formula:Percentage of a Number

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

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 17 and 10.

   Formula:LCM & HCF

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

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7. 7.

   Quantitative Aptitude

   Divide £660 between two people in the ratio 6:5. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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8. 8.

   Quantitative Aptitude

   A invests £9,000 and B invests £8,000 for the same period. If the total profit is £37,000, find A's share.

   Formula:Partnership (profit share)

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

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9. 9.

   Quantitative Aptitude

   Find the average of these 10 numbers: 90, 82, 42, 50, 33, 88, 44, 75, 73, 40.

   Formula:Arithmetic Mean

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

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10. 10.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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11. 11.

    Quantitative Aptitude

    Two varieties costing £32 and £88 per kg are mixed to give a mixture worth £70 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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12. 12.

    Quantitative Aptitude

    Find the average of these 5 numbers: 27, 26, 20, 78, 48.

    Formula:Arithmetic Mean

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

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13. 13.

    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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14. 14.

    Mathematics

    Find term number 5 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Quantitative Aptitude

    Two varieties costing £12 and £83 per kg are mixed to give a mixture worth £24 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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16. 16.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

    Formula:Combinations

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

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17. 17.

    Quantitative Aptitude

    The marked price of an item is £1,200. After a 50% discount, find the selling price.

    Formula:Discount & Selling Price

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

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18. 18.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 3 and common difference 2.

    Formula:AP Sum of n Terms

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

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19. 19.

    Quantitative Aptitude

    Find the HCF and LCM of 33 and 21.

    Formula:LCM & HCF

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

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20. 20.

    Quantitative Aptitude

    The sum of the ages of two people is 54 years, and one is 18 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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