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11+ · Practice Sheet 23

Sheet code: ELEVEN-PLUS-S23 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    A invests £6,000 and B invests £8,000 for the same period. If the total profit is £18,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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  2. 2.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  3. 3.
    Mathematics

    Find the sum of the first 17 terms of an AP with first term 7 and common difference 4.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  4. 4.
    Quantitative Aptitude

    A vehicle covers 616 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  5. 5.
    Mathematics

    Find the sum of the first 4 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  6. 6.
    Quantitative Aptitude

    A can finish a job in 19 days and B in 5 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  7. 7.
    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
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  8. 8.
    Quantitative Aptitude

    Two varieties costing £27 and £94 per kg are mixed to give a mixture worth £53 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  9. 9.
    Quantitative Aptitude

    A value changes from 700 to 560. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  10. 10.
    Quantitative Aptitude

    Two varieties costing £21 and £98 per kg are mixed to give a mixture worth £63 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  11. 11.
    Quantitative Aptitude

    The marked price of an item is £500. After a 40% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  12. 12.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  13. 13.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  14. 14.
    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  15. 15.
    Quantitative Aptitude

    Divide £940 between two people in the ratio 2:3. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
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  16. 16.
    Quantitative Aptitude

    Find the HCF and LCM of 24 and 27.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  17. 17.
    Quantitative Aptitude

    Find the average of these 8 numbers: 33, 88, 74, 26, 42, 54, 83, 89.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  18. 18.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  19. 19.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  20. 20.
    Quantitative Aptitude

    A vehicle covers 270 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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