GMAT · Practice Sheet 4

1. 1.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

   Formula:Combinations

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

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2. 2.

   Mathematics

   Evaluate log base 3 of 243.

   Formula:Logarithm Evaluation

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

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3. 3.

   Mathematics

   Find the sum of the first 11 terms of an AP with first term 5 and common difference 6.

   Formula:AP Sum of n Terms

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

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 4 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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5. 5.

   Quantitative Aptitude

   A invests $2,000 and B invests $3,000 for the same period. If the total profit is $29,000, find A's share.

   Formula:Partnership (profit share)

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

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6. 6.

   Quantitative Aptitude

   Divide $1,120 between two people in the ratio 3:4. 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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7. 7.

   Quantitative Aptitude

   Find the average of these 8 numbers: 21, 33, 85, 75, 79, 50, 21, 59.

   Formula:Arithmetic Mean

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

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8. 8.

   Quantitative Aptitude

   Find the HCF and LCM of 31 and 13.

   Formula:LCM & HCF

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

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9. 9.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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10. 10.

    Mathematics

    If f(x) = 2x³ + 2x² + 6x, find f′(1).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 8 and common difference 7, find term number 20.

    Formula:AP nth Term

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

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12. 12.

    Quantitative Aptitude

    What is 20% of 80?

    Formula:Percentage of a Number

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

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13. 13.

    Mathematics

    Find term number 5 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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14. 14.

    Quantitative Aptitude

    What is 40% of 780?

    Formula:Percentage of a Number

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

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15. 15.

    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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16. 16.

    Mathematics

    If f(x) = 1x³ + 5x² + 3x, find f′(3).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Mathematics

    Find the sum of the first 3 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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18. 18.

    Quantitative Aptitude

    A can finish a job in 4 days and B in 9 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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19. 19.

    Quantitative Aptitude

    Two varieties costing $32 and $94 per kg are mixed to give a mixture worth $45 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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20. 20.

    Mathematics

    Find the sum of the first 7 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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