GMAT · Practice Sheet 25

1. 1.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 3 and common ratio 3.

   Formula:GP Sum of n Terms

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

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2. 2.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 15 and common difference 5.

   Formula:AP Sum of n Terms

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

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3. 3.

   Quantitative Aptitude

   A can finish a job in 13 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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4. 4.

   Quantitative Aptitude

   The marked price of an item is $700. After a 50% discount, find the selling price.

   Formula:Discount & Selling Price

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

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5. 5.

   Quantitative Aptitude

   What is 50% of 980?

   Formula:Percentage of a Number

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

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6. 6.

   Mathematics

   Find term number 5 of a geometric progression with first term 6 and common ratio 3.

   Formula:GP nth Term

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

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7. 7.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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8. 8.

   Mathematics

   Find the distance between the points (7, -3) and (1, -8).

   Formula:Distance Between Two Points

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

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9. 9.

   Quantitative Aptitude

   The marked price of an item is $1,500. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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10. 10.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 1, find term number 24.

    Formula:AP nth Term

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

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11. 11.

    Quantitative Aptitude

    A vehicle covers 414 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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12. 12.

    Quantitative Aptitude

    Find the simple interest on $7,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest

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

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13. 13.

    Mathematics

    Find the slope of the line through (-3, -8) and (-2, -8).

    Formula:Slope of a Line

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

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14. 14.

    Quantitative Aptitude

    Find the average of these 6 numbers: 26, 64, 58, 84, 61, 52.

    Formula:Arithmetic Mean

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

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15. 15.

    Quantitative Aptitude

    Find the compound interest on $19,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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16. 16.

    Mathematics

    If f(x) = 2x³ + 4x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Quantitative Aptitude

    A can finish a job in 17 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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18. 18.

    Mathematics

    If f(x) = 4x³ + 2x² + 1x, 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

    The sum of the ages of two people is 46 years, and one is 4 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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20. 20.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations

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

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