Question : Twenty-one times a positive number is less than its square. The value of the positive number is:
Option 1: 25
Option 2: 26
Option 3: 42
Option 4: 41
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Correct Answer: 25
Solution : Let the number be x, According to the question x 2 – 21x = 100 ⇒ x 2 – 21x – 100 = 0 ⇒ x 2 – 25x + 4x – 100 = 0 ⇒ x (x – 25) + 4 (x – 25) = 0 ⇒ (x – 25) (x + 4) = 0 Taking, ⇒ (x – 25) = 0 ⇒ x = 25 Short Trick: With the help of options, the number is 25, then ⇒ 252 – 21 × 25 = 100 ⇒ 625 – 525 = 100 ⇒ 100 = 100 (satisfied)
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