Practice ECAT questions with answers and explanations.
Choose an option to check your answer.
Multiply both sides by 4.
Thus, x = 7 × 4 = 28.
Choose an option to check your answer.
Adding the equations gives 2x = 14, so x = 7.
Substituting into x + y = 10 gives y = 3.
Choose an option to check your answer.
Substitute x = 2 to obtain 4 + 3y = 13.
Then 3y = 9, so y = 3.
Choose an option to check your answer.
In the same time, the faster runner covers 1,000 m while the slower covers 900 m.
Their speed ratio is therefore 1,000:900 = 10:9.
Choose an option to check your answer.
The expression is a difference of squares: x² - 3².
Thus, it factors as (x - 3)(x + 3).
Choose an option to check your answer.
Time is inversely proportional to speed.
The decrease is 1 - 50/60 = 1/6 = 16 2/3%.
Choose an option to check your answer.
The required numbers multiply to 6 and add to 5.
Those numbers are 2 and 3.
Choose an option to check your answer.
Let total distance be 3d; time is d/30 + 2d/60 = d/15.
Average speed is 3d ÷ (d/15) = 45 km/h.
Choose an option to check your answer.
The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
Choose an option to check your answer.
Travel time is 210 ÷ 70 = 3 hours.
Three hours after 8:00 a.m. is 11:00 a.m.
Choose an option to check your answer.
The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
Choose an option to check your answer.
Their closing speed is 20 + 25 = 45 km/h.
Time = 90 ÷ 45 = 2 hours.
