GMAT · Practice Sheet 19

1. 1.

   Quantitative Aptitude

   Pipe A fills a tank in 5 hours and pipe B in 6 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.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

   Formula:Permutations

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

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3. 3.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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4. 4.

   Quantitative Aptitude

   What is 25% of 960?

   Formula:Percentage of a Number

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

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5. 5.

   Mathematics

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

   Formula:AP nth Term

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

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6. 6.

   Quantitative Aptitude

   The sum of the ages of two people is 41 years, and one is 15 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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7. 7.

   Mathematics

   Find the distance between the points (7, 8) and (-1, -4).

   Formula:Distance Between Two Points

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

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8. 8.

   Mathematics

   Find the sum of the first 23 terms of an AP with first term 6 and common difference 6.

   Formula:AP Sum of n Terms

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

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9. 9.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 4 and common ratio 2.

   Formula:GP Sum of n Terms

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

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10. 10.

    Quantitative Aptitude

    What is 10% of 860?

    Formula:Percentage of a Number

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

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11. 11.

    Mathematics

    Find the slope of the line through (8, 2) and (-5, 1).

    Formula:Slope of a Line

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

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12. 12.

    Quantitative Aptitude

    A invests $5,000 and B invests $6,000 for the same period. If the total profit is $14,000, find A's share.

    Formula:Partnership (profit share)

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

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13. 13.

    Quantitative Aptitude

    Pipe A fills a tank in 10 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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14. 14.

    Mathematics

    If f(x) = 1x³ + 5x² + 9x, find f′(2).

    Formula:Derivative of a Polynomial

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

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15. 15.

    Quantitative Aptitude

    Two varieties costing $33 and $73 per kg are mixed to give a mixture worth $67 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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16. 16.

    Mathematics

    Find term number 7 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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17. 17.

    Mathematics

    Evaluate ∫ from 1 to 4 of 2x^1 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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18. 18.

    Quantitative Aptitude

    The marked price of an item is $1,900. After a 50% discount, find the selling price.

    Formula:Discount & Selling Price

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

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19. 19.

    Quantitative Aptitude

    What is 15% of 720?

    Formula:Percentage of a Number

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

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20. 20.

    Quantitative Aptitude

    An item is bought for $700 and sold for $980. Find the profit percentage.

    Formula:Profit Percentage

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

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