GRE · Practice Sheet 3

1. 1.

   Quantitative Aptitude

   Find the compound interest on $2,000 at 10% per annum compounded annually for 3 years.

   Formula:Compound Interest

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

   View formula →
2. 2.

   Quantitative Aptitude

   A invests $9,000 and B invests $2,000 for the same period. If the total profit is $21,000, find A's share.

   Formula:Partnership (profit share)

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

   View formula →
3. 3.

   Quantitative Aptitude

   The sum of the ages of two people is 42 years, and one is 20 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

   View formula →
4. 4.

   Mathematics

   For the quadratic 4x² − 2x + 8 = 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 →
5. 5.

   Quantitative Aptitude

   Two varieties costing $11 and $78 per kg are mixed to give a mixture worth $22 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

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

   View formula →
6. 6.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

   Formula:Combinations

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

   View formula →
7. 7.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 3 and common difference 9.

   Formula:AP Sum of n Terms

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

   View formula →
8. 8.

   Mathematics

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

   Formula:Binomial Coefficient

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

   View formula →
9. 9.

   Mathematics

   Evaluate ∫ from 2 to 3 of 2x^3 dx.

   Formula:Definite Integral of a Power

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

   View formula →
10. 10.

    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

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

    View formula →
11. 11.

    Quantitative Aptitude

    What is 75% of 740?

    Formula:Percentage of a Number

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

    View formula →
12. 12.

    Quantitative Aptitude

    Pipe A fills a tank in 8 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

    View formula →
13. 13.

    Quantitative Aptitude

    The sum of the ages of two people is 29 years, and one is 3 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

    View formula →
14. 14.

    Quantitative Aptitude

    A can finish a job in 18 days and B in 4 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

    View formula →
15. 15.

    Quantitative Aptitude

    A invests $10,000 and B invests $4,000 for the same period. If the total profit is $35,000, find A's share.

    Formula:Partnership (profit share)

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

    View formula →
16. 16.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)

    Formula:Permutations

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

    View formula →
17. 17.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

    View formula →
18. 18.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

    Formula:Permutations

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

    View formula →
19. 19.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

    Formula:Combinations

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

    View formula →
20. 20.

    Quantitative Aptitude

    Pipe A fills a tank in 3 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

    View formula →

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