GMAT · Practice Sheet 48

1. 1.

   Quantitative Aptitude

   A vehicle covers 630 km in 7 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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2. 2.

   Mathematics

   Evaluate ∫ from 0 to 4 of 5x^1 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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3. 3.

   Quantitative Aptitude

   Divide $1,504 between two people in the ratio 4:4. 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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4. 4.

   Mathematics

   For the quadratic 1x² + 0x − 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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5. 5.

   Mathematics

   Find term number 5 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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6. 6.

   Quantitative Aptitude

   Two varieties costing $24 and $94 per kg are mixed to give a mixture worth $56 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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7. 7.

   Mathematics

   For the quadratic 2x² − 4x − 7 = 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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8. 8.

   Quantitative Aptitude

   The marked price of an item is $300. After a 10% discount, find the selling price.

   Formula:Discount & Selling Price

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

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9. 9.

   Mathematics

   Evaluate ∫ from 2 to 3 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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10. 10.

    Mathematics

    Find the distance between the points (-1, -3) and (3, 6).

    Formula:Distance Between Two Points

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

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11. 11.

    Quantitative Aptitude

    A vehicle covers 312 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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12. 12.

    Quantitative Aptitude

    Divide $704 between two people in the ratio 7:4. 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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13. 13.

    Quantitative Aptitude

    The marked price of an item is $1,300. After a 50% discount, find the selling price.

    Formula:Discount & Selling Price

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

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14. 14.

    Mathematics

    Evaluate ∫ from 2 to 5 of 2x^1 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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15. 15.

    Quantitative Aptitude

    Find the average of these 10 numbers: 75, 83, 88, 59, 88, 38, 33, 32, 78, 38.

    Formula:Arithmetic Mean

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

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16. 16.

    Mathematics

    Find the slope of the line through (4, -3) and (1, 0).

    Formula:Slope of a Line

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

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17. 17.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)

    Formula:Permutations

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

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18. 18.

    Mathematics

    Find the slope of the line through (-6, -6) and (7, -1).

    Formula:Slope of a Line

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

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19. 19.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations

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

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20. 20.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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