Question : Five times of a positive integer is equal to 3 less than twice the square of that number. The number is:
Option 1: 3
Option 2: 13
Option 3: 23
Option 4: 33
Correct Answer: 3
Solution : Let the positive integer be $x$. $5x+3 = 2x^{2}$ ⇒ $2x^{2}- 5x-3=0$ ⇒ $2x^{2}- 6x+x-3=0$ ⇒ $2x(x-3)+1(x-3)=0$ ⇒ $(2x+1)(x-3)=0$ Since $x$ cannot be negative, ⇒ $(x-3)=0$ ⇒ $x=3$ Hence, the correct answer is 3.
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Question : There are three numbers A, B, and C such that twice of A is equal to thrice of B and four times of B is equal to five times of C. Then the ratio between A and C is:
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