GMAT · Practice Sheet 22

1. 1.

   Quantitative Aptitude

   Divide $1,727 between two people in the ratio 6:5. 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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2. 2.

   Quantitative Aptitude

   The sum of the ages of two people is 34 years, and one is 14 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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3. 3.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 2 and common ratio 2.

   Formula:GP Sum of n Terms

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

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4. 4.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 3, find term number 12.

   Formula:AP nth Term

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

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5. 5.

   Quantitative Aptitude

   Two varieties costing $18 and $67 per kg are mixed to give a mixture worth $50 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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6. 6.

   Quantitative Aptitude

   Find the average of these 10 numbers: 51, 23, 90, 69, 58, 83, 42, 36, 39, 24.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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7. 7.

   Mathematics

   Evaluate log base 2 of 32.

   Formula:Logarithm Evaluation

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

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8. 8.

   Mathematics

   For the quadratic 3x² + 9x − 6 = 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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9. 9.

   Quantitative Aptitude

   Find the average of these 10 numbers: 21, 26, 27, 49, 46, 81, 60, 23, 20, 60.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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10. 10.

    Mathematics

    Find the slope of the line through (1, -4) and (-4, 2).

    Formula:Slope of a Line

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 8, find term number 17.

    Formula:AP nth Term

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

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12. 12.

    Quantitative Aptitude

    The sum of the ages of two people is 94 years, and one is 16 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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13. 13.

    Quantitative Aptitude

    The marked price of an item is $1,100. After a 15% discount, find the selling price.

    Formula:Discount & Selling Price

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

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14. 14.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations

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

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15. 15.

    Quantitative Aptitude

    What is 40% of 240?

    Formula:Percentage of a Number

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

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16. 16.

    Quantitative Aptitude

    A can finish a job in 20 days and B in 7 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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17. 17.

    Quantitative Aptitude

    Find the HCF and LCM of 34 and 13.

    Formula:LCM & HCF

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

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18. 18.

    Mathematics

    If f(x) = 3x³ + 1x² + 6x, find f′(5).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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19. 19.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 4.)

    Formula:Combinations

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

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