GRE · Practice Sheet 30

1. 1.

   Mathematics

   Evaluate ∫ from 2 to 3 of 4x^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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2. 2.

   Quantitative Aptitude

   Pipe A fills a tank in 14 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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3. 3.

   Quantitative Aptitude

   The marked price of an item is $800. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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4. 4.

   Mathematics

   Find term number 6 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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5. 5.

   Quantitative Aptitude

   Two varieties costing $11 and $82 per kg are mixed to give a mixture worth $29 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.

   Mathematics

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

   Formula:GP nth Term

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

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7. 7.

   Quantitative Aptitude

   Find the HCF and LCM of 23 and 13.

   Formula:LCM & HCF

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

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8. 8.

   Quantitative Aptitude

   Find the compound interest on $12,000 at 10% per annum compounded annually for 2 years.

   Formula:Compound Interest

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

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9. 9.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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10. 10.

    Mathematics

    Find the distance between the points (5, 7) and (4, 5).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 4 and common difference 9.

    Formula:AP Sum of n Terms

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

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12. 12.

    Quantitative Aptitude

    The marked price of an item is $1,700. After a 10% discount, find the selling price.

    Formula:Discount & Selling Price

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

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13. 13.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 19 and common difference 1.

    Formula:AP Sum of n Terms

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

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14. 14.

    Quantitative Aptitude

    What is 75% of 820?

    Formula:Percentage of a Number

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

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15. 15.

    Quantitative Aptitude

    The sum of the ages of two people is 56 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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16. 16.

    Mathematics

    If f(x) = 1x³ + 4x² + 7x, 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

    Find the average of these 6 numbers: 25, 65, 25, 29, 85, 22.

    Formula:Arithmetic Mean

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

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18. 18.

    Quantitative Aptitude

    What is 30% of 180?

    Formula:Percentage of a Number

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

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19. 19.

    Mathematics

    Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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20. 20.

    Quantitative Aptitude

    Find the compound interest on $9,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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