GRE · Practice Sheet 47

1. 1.

   Mathematics

   Find the sum of the first 24 terms of an AP with first term 19 and common difference 6.

   Formula:AP Sum of n Terms

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

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2. 2.

   Quantitative Aptitude

   What is 30% of 1,040?

   Formula:Percentage of a Number

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

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3. 3.

   Mathematics

   Find term number 7 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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4. 4.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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5. 5.

   Mathematics

   Evaluate log base 10 of 100,000.

   Formula:Logarithm Evaluation

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

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6. 6.

   Quantitative Aptitude

   A can finish a job in 8 days and B in 18 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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7. 7.

   Mathematics

   Find the sum of the first 4 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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8. 8.

   Mathematics

   If f(x) = 2x³ + 3x² + 1x, find f′(4).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 2, find term number 10.

   Formula:AP nth Term

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

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10. 10.

    Quantitative Aptitude

    Find the HCF and LCM of 25 and 9.

    Formula:LCM & HCF

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

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11. 11.

    Mathematics

    Evaluate ∫ from 0 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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12. 12.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

    Formula:Combinations

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

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13. 13.

    Quantitative Aptitude

    A invests $7,000 and B invests $2,000 for the same period. If the total profit is $24,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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14. 14.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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15. 15.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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16. 16.

    Quantitative Aptitude

    Two varieties costing $28 and $71 per kg are mixed to give a mixture worth $43 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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17. 17.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

    Formula:Combinations

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

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18. 18.

    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 3 of 2x^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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20. 20.

    Quantitative Aptitude

    What is 10% of 580?

    Formula:Percentage of a Number

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

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