SAT · Practice Sheet 33

1. 1.

   Quantitative Aptitude

   A invests $4,000 and B invests $4,000 for the same period. If the total profit is $17,000, find A's share.

   Formula:Partnership (profit share)

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

   View formula →
2. 2.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

   Formula:Permutations

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

   View formula →
3. 3.

   Quantitative Aptitude

   The sum of the ages of two people is 49 years, and one is 5 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

   View formula →
4. 4.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

   Formula:Probability (two dice)

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

   View formula →
5. 5.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 4 and common ratio 3.

   Formula:GP Sum of n Terms

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

   View formula →
6. 6.

   Quantitative Aptitude

   The sum of the ages of two people is 44 years, and one is 20 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

   View formula →
7. 7.

   Mathematics

   Find the distance between the points (-2, 8) and (-3, 6).

   Formula:Distance Between Two Points

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

   View formula →
8. 8.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

   Formula:Combinations

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

   View formula →
9. 9.

   Mathematics

   In an arithmetic progression with first term 3 and common difference 5, find term number 26.

   Formula:AP nth Term

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

   View formula →
10. 10.

    Quantitative Aptitude

    The marked price of an item is $1,100. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
11. 11.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

    View formula →
12. 12.

    Quantitative Aptitude

    A can finish a job in 20 days and B in 15 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

    View formula →
13. 13.

    Mathematics

    Find the slope of the line through (-4, 8) and (2, -4).

    Formula:Slope of a Line

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

    View formula →
14. 14.

    Quantitative Aptitude

    Find the simple interest on $19,000 at 6% per annum for 1 year(s).

    Formula:Simple Interest

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

    View formula →
15. 15.

    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient

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

    View formula →
16. 16.

    Quantitative Aptitude

    The marked price of an item is $1,900. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
17. 17.

    Quantitative Aptitude

    Find the average of these 10 numbers: 48, 36, 41, 72, 70, 66, 20, 48, 61, 67.

    Formula:Arithmetic Mean

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

    View formula →
18. 18.

    Mathematics

    Evaluate ∫ from 0 to 3 of 5x^2 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

    View formula →
19. 19.

    Mathematics

    For the quadratic 5x² − 8x + 4 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

    View formula →
20. 20.

    Quantitative Aptitude

    Two varieties costing $14 and $73 per kg are mixed to give a mixture worth $64 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.