The product of two consecutive even numbers exceeds twice their sum be more than 20. Which of the following is the range of values that the smaller of the numbers can take ?

x > 4

x < - 6

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- 6 < x < 4

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x > 6

x < - 4

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- 4 < x < 6

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Solution

The correct option is B $x > 6$ or $x < - 4$
Let the smaller of the numbers be x. The greater number = x+2
$x (x + 2) > [2 (x + x + 2)] + 20$
$x^{2} + 2 x > 4 x + 4 + 20$
$x^{2} - 2 x - 24 > 0$
$(x - 6) (x + 4) > 0$
The smaller is positive as the greater is negative.
That is $x > 6$ or $x < - 4$ .
Hence, option C is correct.

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The product of two consecutive even numbers exceeds twice their sum be more than 20. Which of the following is the range of values that the smaller of the numbers can take ?

The correct option is B x>6 or x<−4Let the smaller of the numbers be x. The greater number = x+2x(x+2)>[2(x+x+2)]+20x2+2x>4x+4+20x2−2x−24>0(x−6)(x+4)>0The smaller is positive as the greater is negative.That is x>6 or x<−4.Hence, option C is correct.