GMAT · Practice Sheet 18

1. 1.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 18 and common difference 2.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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2. 2.

   Mathematics

   Find the distance between the points (8, 3) and (-6, 5).

   Formula:Distance Between Two Points

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

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3. 3.

   Mathematics

   Evaluate log base 5 of 3,125.

   Formula:Logarithm Evaluation

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

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4. 4.

   Mathematics

   Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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5. 5.

   Quantitative Aptitude

   A can finish a job in 10 days and B in 5 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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6. 6.

   Mathematics

   Evaluate log base 3 of 9.

   Formula:Logarithm Evaluation

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 8, find term number 8.

   Formula:AP nth Term

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

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8. 8.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 14 and common difference 2.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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9. 9.

   Quantitative Aptitude

   The marked price of an item is $800. After a 50% discount, find the selling price.

   Formula:Discount & Selling Price

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

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10. 10.

    Mathematics

    Evaluate ∫ from 1 to 3 of 3x^3 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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11. 11.

    Quantitative Aptitude

    Find the average of these 6 numbers: 89, 43, 50, 89, 21, 80.

    Formula:Arithmetic Mean

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

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12. 12.

    Mathematics

    Find the slope of the line through (-4, -6) and (5, 5).

    Formula:Slope of a Line

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

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13. 13.

    Quantitative Aptitude

    Two varieties costing $14 and $80 per kg are mixed to give a mixture worth $23 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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14. 14.

    Mathematics

    For the quadratic 4x² − 8x + 4 = 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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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 7 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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16. 16.

    Quantitative Aptitude

    What is 75% of 220?

    Formula:Percentage of a Number

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 2, find term number 8.

    Formula:AP nth Term

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

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18. 18.

    Mathematics

    For the quadratic 3x² − 2x − 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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19. 19.

    Mathematics

    Find the distance between the points (2, 3) and (0, -8).

    Formula:Distance Between Two Points

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

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20. 20.

    Mathematics

    Find the sum of the first 9 terms of an AP with first term 17 and common difference 10.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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