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CAT · Practice Sheet 25

Sheet code: CAT-S25 · 20 questions

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

    What is 30% of 240?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  2. 2.
    Mathematics

    In an arithmetic progression with first term 13 and common difference 8, find term number 5.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  3. 3.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  4. 4.
    Quantitative Aptitude

    Two varieties costing ₹28 and ₹78 per kg are mixed to give a mixture worth ₹62 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.
    Quantitative Aptitude

    Find the compound interest on ₹19,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  6. 6.
    Quantitative Aptitude

    A invests ₹2,000 and B invests ₹2,000 for the same period. If the total profit is ₹23,000, 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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  7. 7.
    Mathematics

    Find the distance between the points (3, 8) and (2, -6).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  8. 8.
    Quantitative Aptitude

    A invests ₹6,000 and B invests ₹8,000 for the same period. If the total profit is ₹7,000, 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.
    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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  10. 10.
    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  11. 11.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  12. 12.
    Quantitative Aptitude

    An item is bought for ₹800 and sold for ₹960. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  13. 13.
    Quantitative Aptitude

    Divide ₹1,521 between two people in the ratio 6:3. 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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  14. 14.
    Quantitative Aptitude

    Two varieties costing ₹25 and ₹93 per kg are mixed to give a mixture worth ₹49 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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  15. 15.
    Quantitative Aptitude

    An item is bought for ₹800 and sold for ₹1,000. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  16. 16.
    Quantitative Aptitude

    A can finish a job in 13 days and B in 10 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  17. 17.
    Mathematics

    For the quadratic 3x² − 8x − 7 = 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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  18. 18.
    Quantitative Aptitude

    Two varieties costing ₹22 and ₹95 per kg are mixed to give a mixture worth ₹31 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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  19. 19.
    Quantitative Aptitude

    A invests ₹2,000 and B invests ₹3,000 for the same period. If the total profit is ₹27,000, 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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  20. 20.
    Mathematics

    Find term number 5 of a geometric progression with first term 3 and common ratio 3.

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