I- p2-p-56II- q 2-17 q -72-0A- If p is greater than qB- If p is equal to qC- If p is either equal to or greater than qD- If p is smaller than qE- If p is either equal to or smaller than q

The correct option is D If p is smaller than qEquation I p^2+p 56=0 ⇒ p^2+8p 7p 56=0 ⇒ p(p+8) 7(p+q)=0 ⇒ (p+8)(p 7)=0 ⇒ p=7 or 8 Equation II q^2 17q+72=0 q^2 ...

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Quantitative Aptitude

Quadratic Equations

I. p2+p=56II....

Question

I. $p^{2} + p = 56$
II. $q^{2} - 17 q + 72 = 0$

If p is greater than q

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If p is smaller than q

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If p is equal to q

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If p is either equal to or greater than q

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If p is either equal to or smaller than q

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Solution

The correct option is B If p is smaller than q
Equation I
$p^{2} + p - 56 = 0$
$\Rightarrow p^{2} + 8 p - 7 p - 56 = 0$
$\Rightarrow p (p + 8) - 7 (p + q) = 0$
$\Rightarrow (p + 8) (p - 7) = 0$
$\Rightarrow p = 7$ or $- 8$

Equation II
$q^{2} - 17 q + 72 = 0$
$q^{2} - 8 q - 9 q + 72 = 0$
$\Rightarrow q (q - 8) - 9 (q - 8) = 0$
$\Rightarrow (q - 8) (q - 9) = 0$
$\Rightarrow q = 8$ or $9$
Hence, $p < q$

Suggest Corrections

I. p2+p=56 II. q2−17q+72=0

The correct option is B If p is smaller than qEquation I p2+p−56=0 ⇒p2+8p−7p−56=0 ⇒p(p+8)−7(p+q)=0 ⇒(p+8)(p−7)=0 ⇒p=7 or −8 Equation II q2−17q+72=0 q2−8q−9q+72=0 ⇒q(q−8)−9(q−8)=0 ⇒(q−8)(q−9)=0 ⇒q=8 or 9 Hence, p<q

I. $p^{2} + p = 56$
II. $q^{2} - 17 q + 72 = 0$