GRE · Practice Sheet 29

1. 1.

   Quantitative Aptitude

   Pipe A fills a tank in 4 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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2. 2.

   Mathematics

   Find the sum of the first 16 terms of an AP with first term 15 and common difference 2.

   Formula:AP Sum of n Terms

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

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3. 3.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

   Formula:Combinations

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

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4. 4.

   Quantitative Aptitude

   Find the average of these 10 numbers: 48, 78, 60, 55, 68, 83, 38, 79, 82, 48.

   Formula:Arithmetic Mean

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

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5. 5.

   Mathematics

   Evaluate log base 5 of 125.

   Formula:Logarithm Evaluation

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

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6. 6.

   Quantitative Aptitude

   The sum of the ages of two people is 29 years, and one is 5 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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7. 7.

   Quantitative Aptitude

   Find the average of these 6 numbers: 81, 84, 22, 83, 34, 24.

   Formula:Arithmetic Mean

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

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8. 8.

   Mathematics

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

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   Evaluate ∫ from 1 to 5 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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10. 10.

    Quantitative Aptitude

    Find the HCF and LCM of 15 and 14.

    Formula:LCM & HCF

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

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11. 11.

    Mathematics

    Find term number 4 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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12. 12.

    Quantitative Aptitude

    Find the simple interest on $4,000 at 8% per annum for 2 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 (5, -7) and (2, -6).

    Formula:Slope of a Line

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

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14. 14.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 8 and common difference 5.

    Formula:AP Sum of n Terms

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

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15. 15.

    Quantitative Aptitude

    A can finish a job in 4 days and B in 17 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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16. 16.

    Mathematics

    If f(x) = 1x³ + 1x² + 8x, find f′(4).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Quantitative Aptitude

    An item is bought for $400 and sold for $520. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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18. 18.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 6, find term number 23.

    Formula:AP nth Term

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

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19. 19.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 18 and common difference 6, find term number 17.

    Formula:AP nth Term

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

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