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CAT · Practice Sheet 34

Sheet code: CAT-S34 · 20 questions

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

    A value changes from 700 to 875. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  2. 2.
    Quantitative Aptitude

    A invests ₹8,000 and B invests ₹9,000 for the same period. If the total profit is ₹35,000, 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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  3. 3.
    Quantitative Aptitude

    Pipe A fills a tank in 14 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  4. 4.
    Quantitative Aptitude

    Two varieties costing ₹13 and ₹96 per kg are mixed to give a mixture worth ₹85 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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  5. 5.
    Mathematics

    Find term number 4 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  6. 6.
    Mathematics

    For the quadratic 5x² + 8x + 9 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  7. 7.
    Quantitative Aptitude

    A can finish a job in 18 days and B in 12 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  8. 8.
    Quantitative Aptitude

    A invests ₹7,000 and B invests ₹10,000 for the same period. If the total profit is ₹21,000, 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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  9. 9.
    Mathematics

    Find the sum of the first 5 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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  10. 10.
    Quantitative Aptitude

    Find the simple interest on ₹38,000 at 6% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  11. 11.
    Quantitative Aptitude

    Pipe A fills a tank in 4 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  12. 12.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  13. 13.
    Mathematics

    In an arithmetic progression with first term 20 and common difference 1, find term number 15.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  14. 14.
    Quantitative Aptitude

    The marked price of an item is ₹1,000. After a 30% 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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  15. 15.
    Mathematics

    In an arithmetic progression with first term 10 and common difference 8, find term number 25.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  16. 16.
    Mathematics

    For the quadratic 3x² − 8x + 2 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  17. 17.
    Quantitative Aptitude

    What is 30% of 260?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  18. 18.
    Quantitative Aptitude

    A value changes from 600 to 570. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  19. 19.
    Quantitative Aptitude

    An item is bought for ₹600 and sold for ₹780. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  20. 20.
    Quantitative Aptitude

    A invests ₹9,000 and B invests ₹4,000 for the same period. If the total profit is ₹20,000, 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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