GMAT · Practice Sheet 17

1. 1.

   Quantitative Aptitude

   Find the HCF and LCM of 17 and 22.

   Formula:LCM & HCF

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

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2. 2.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

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

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3. 3.

   Quantitative Aptitude

   Find the compound interest on $18,000 at 20% per annum compounded annually for 2 years.

   Formula:Compound Interest

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

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4. 4.

   Quantitative Aptitude

   An item is bought for $700 and sold for $840. Find the profit percentage.

   Formula:Profit Percentage

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

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5. 5.

   Mathematics

   Find the slope of the line through (-5, -7) and (3, 6).

   Formula:Slope of a Line

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

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6. 6.

   Quantitative Aptitude

   Find the average of these 8 numbers: 33, 67, 70, 71, 74, 54, 37, 30.

   Formula:Arithmetic Mean

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

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7. 7.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

   Formula:Permutations

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

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8. 8.

   Mathematics

   Evaluate log base 3 of 81.

   Formula:Logarithm Evaluation

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

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9. 9.

   Quantitative Aptitude

   Find the simple interest on $37,000 at 12% per annum for 1 year(s).

   Formula:Simple Interest

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

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10. 10.

    Mathematics

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

    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 binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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12. 12.

    Quantitative Aptitude

    Two varieties costing $26 and $88 per kg are mixed to give a mixture worth $75 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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13. 13.

    Quantitative Aptitude

    Find the simple interest on $44,000 at 10% per annum for 3 year(s).

    Formula:Simple Interest

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

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14. 14.

    Mathematics

    Find term number 7 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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15. 15.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 1 and common ratio 2.

    Formula:GP Sum of n Terms

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

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16. 16.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 7, find term number 22.

    Formula:AP nth Term

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

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17. 17.

    Quantitative Aptitude

    The sum of the ages of two people is 68 years, and one is 20 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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18. 18.

    Mathematics

    Find term number 3 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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19. 19.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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20. 20.

    Quantitative Aptitude

    Find the HCF and LCM of 23 and 12.

    Formula:LCM & HCF

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

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