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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