Exercise 30

A child withdraws a certain amount from his piggy bank every day. On the first day he withdrew $243, and on the last day $32. It is known that the amounts withdrawn form a geometric progression and that the total sum of the withdrawals was $665. Then, the number of withdrawals made was: 5 6 […]

Exercise 29

A father splits his land among his three sons. To the eldest son he assigns one third of the land, plus 80 hectares. To the second, a fourth, plus 20 hectares, and to the third, a fourth. The shares of the land that correspond to each son, in hectares, are: 280, 160 and 140 200, […]

Exercise 28

A father says to his son, “Now your age is a third of mine, but 10 years ago it was only a fifth.” In 5 years the son will be: 18 years old 25 years old 21 years old 29 years old 20 years old Try to solve it before checking the answer. Answer 25 […]

Exercise 27

Jhon used to spend $30 a month on baldness treatment. He stopped treatment 10 months ago and has been completely bald for the last 7 months. If he used to cut his hair twice a month and spent $20 per cut, the savings he has made are: $440 $460 $280 $580 $490 Try to solve […]

Exercise 26

If ( a = frac{1}{2} ), ( b = frac{-1}{4} ), ( c = frac{-1}{3} ) and ( d = frac{1}{9} ), then the expression ( cfrac{a}{b} – cfrac{c}{d} ) equals: ( 5) (0) (1) (-5) (-1) Try to solve it before checking the answer. Answer 1 Step by Step Solution Indeed: [ begin{aligned} frac{a}{b} […]

Exercise 25

The tenth term of a 10-term geometric progression is 10, and the ratio is 0.1. Then the third term is: ( 10^8 ) ( 10^9 ) ( 10^{10} ) ( 10^{11} ) ( 10^3 ) Try to solve it before checking the answer. Answer ( 10^8 ) Step by Step Solution From Geometric Progressions we […]

Exercise 24

The solution set of the inequation ( left| cfrac{2x + 1}{3} right| < 5 ) is the following: The solution set of the inequation: [ left| cfrac{2x + 1}{3} right| < 5, ] is the following: ( ( -infty, , 7 ) ) ( ( -8, +infty ) ) ( ( -infty, -8 ) ) […]

Exercise 23

In the square (square ABCD ), (E) and (F) are midpoints. The ratio between the area of the trapezoid (AFCD) and the area of the triangle ( triangle FEC ) is: ( 0.75 ) ( 1.33 ) ( 0.125 ) ( 6 ) ( 4 ) Try to solve it before checking the answer. Answer […]

Exercise 22

The dot product of the vectors ( vec{V} ) and ( vec{W} ) is: ( -2 ) ( 1 ) ( 0 ) ( 2 ) ( -1 ) Try to solve it before checking the answer. Answer ( -2 ) Step by Step Solution Indeed: [ vec{V} = (1, , 1) quad text{ and […]

Exercise 21

In the illustration, (D) is the midpoint of ( overline{AC} ), (E) is the midpoint of ( overline{BC} )   and   (F) is the midpoint of ( overline{EC} ). Then the pair of similar triangles is: (triangle DEF )   and   (triangle ABE ) (triangle DFC )   and   (triangle AED ) […]