CAT · Practice Sheet 4

1. 1.

   Quantitative Aptitude

   Two varieties costing ₹21 and ₹71 per kg are mixed to give a mixture worth ₹48 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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2. 2.

   Mathematics

   Find term number 4 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

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3. 3.

   Quantitative Aptitude

   Find the compound interest on ₹9,000 at 20% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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4. 4.

   Mathematics

   Find term number 4 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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5. 5.

   Quantitative Aptitude

   Divide ₹441 between two people in the ratio 4:3. 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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6. 6.

   Quantitative Aptitude

   A can finish a job in 10 days and B in 15 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 8, find term number 13.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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8. 8.

   Quantitative Aptitude

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

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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9. 9.

   Mathematics

   In an arithmetic progression with first term 9 and common difference 10, find term number 18.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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10. 10.

    Mathematics

    Find term number 6 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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11. 11.

    Quantitative Aptitude

    The marked price of an item is ₹1,500. After a 15% discount, find the selling price.

    Formula:Discount & Selling Price

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

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12. 12.

    Mathematics

    Find term number 7 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term

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

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13. 13.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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14. 14.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

    Formula:Combinations

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

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16. 16.

    Mathematics

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

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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17. 17.

    Quantitative Aptitude

    Two varieties costing ₹39 and ₹84 per kg are mixed to give a mixture worth ₹73 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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18. 18.

    Quantitative Aptitude

    Divide ₹1,482 between two people in the ratio 6:7. 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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19. 19.

    Mathematics

    For the quadratic 3x² − 4x − 5 = 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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20. 20.

    Mathematics

    Find term number 7 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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