GMAT · Practice Sheet 6

1. 1.

   Quantitative Aptitude

   Two varieties costing $18 and $96 per kg are mixed to give a mixture worth $55 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

   For the quadratic 2x² − 1x − 3 = 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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3. 3.

   Quantitative Aptitude

   The marked price of an item is $1,500. After a 5% discount, find the selling price.

   Formula:Discount & Selling Price

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

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4. 4.

   Quantitative Aptitude

   A vehicle covers 612 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 16 and common difference 4, find term number 15.

   Formula:AP nth Term

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

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6. 6.

   Mathematics

   Evaluate ∫ from 1 to 4 of 2x^2 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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7. 7.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

   Formula:Combinations

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

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8. 8.

   Quantitative Aptitude

   Find the simple interest on $18,000 at 12% per annum for 3 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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9. 9.

   Quantitative Aptitude

   What is 15% of 260?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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10. 10.

    Mathematics

    Find the slope of the line through (8, -7) and (4, 5).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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11. 11.

    Quantitative Aptitude

    A can finish a job in 8 days and B in 11 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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12. 12.

    Quantitative Aptitude

    A value changes from 300 to 420. Find the percentage increase.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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13. 13.

    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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14. 14.

    Quantitative Aptitude

    Find the HCF and LCM of 23 and 26.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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15. 15.

    Quantitative Aptitude

    A invests $2,000 and B invests $10,000 for the same period. If the total profit is $7,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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16. 16.

    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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17. 17.

    Quantitative Aptitude

    The sum of the ages of two people is 44 years, and one is 18 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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18. 18.

    Mathematics

    In an arithmetic progression with first term 19 and common difference 4, find term number 15.

    Formula:AP nth Term

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

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19. 19.

    Quantitative Aptitude

    Find the HCF and LCM of 21 and 8.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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20. 20.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

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

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