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CAT · Practice Sheet 16

Sheet code: CAT-S16 · 20 questions

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

    Divide ₹2,090 between two people in the ratio 5:6. 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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  2. 2.
    Quantitative Aptitude

    A invests ₹10,000 and B invests ₹9,000 for the same period. If the total profit is ₹8,000, 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.
    Mathematics

    Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  4. 4.
    Quantitative Aptitude

    A can finish a job in 8 days and B in 6 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  5. 5.
    Quantitative Aptitude

    A vehicle covers 225 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  6. 6.
    Quantitative Aptitude

    The marked price of an item is ₹1,500. After a 5% 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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  7. 7.
    Quantitative Aptitude

    Find the simple interest on ₹28,000 at 5% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  8. 8.
    Mathematics

    Find the distance between the points (1, -8) and (-8, -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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  9. 9.
    Mathematics

    For the quadratic 1x² + 1x + 4 = 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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  10. 10.
    Quantitative Aptitude

    A invests ₹5,000 and B invests ₹9,000 for the same period. If the total profit is ₹22,000, 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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  11. 11.
    Quantitative Aptitude

    Find the simple interest on ₹33,000 at 8% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  12. 12.
    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 3.

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

    A invests ₹5,000 and B invests ₹9,000 for the same period. If the total profit is ₹28,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
    View formula →
  14. 14.
    Mathematics

    In an arithmetic progression with first term 19 and common difference 2, find term number 8.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  15. 15.
    Quantitative Aptitude

    Pipe A fills a tank in 3 hours and pipe B in 8 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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  16. 16.
    Quantitative Aptitude

    Divide ₹1,440 between two people in the ratio 2:6. 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}}
    View formula →
  17. 17.
    Quantitative Aptitude

    Find the average of these 8 numbers: 82, 68, 86, 61, 75, 45, 53, 76.

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

    Pipe A fills a tank in 10 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  19. 19.
    Quantitative Aptitude

    Find the simple interest on ₹25,000 at 12% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  20. 20.
    Quantitative Aptitude

    Find the compound interest on ₹14,000 at 10% per annum compounded annually for 2 years.

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