Quiz In Quantitative Aptitude

Directions (Q. 1-5) : In each of the questions below, two equations are provided. On the basis of these you have to
find out the relation between p and q. Give answer
(1) If P = Q
(2) If P > Q
(3) If P < Q
(4) If P ≥ Q
(5) If P ≤ Q

1. P² – P – 12 = 0;      Q² – 3Q – 28 = 0(5)
2. 2P² – 11P + 5 = 0;  3Q² – 13Q + 4 = 0(2)
3. P² + 7P + 12 = 0;    Q² + 2Q – 3 = 0(5)
4. 3P + Q = 1;               8P + 12Q = 5(1)
5. P² + 5P – 14 = 0;    Q² + 6Q – 7 = 0(4)

Directions (Q. 6-10) : In each of the questions below, two equations are provided. On the basis of these you have to
find out the relation between p and q.

Give answer
(1) If P = Q
(2) If P > Q
(3) If P < Q
(4) If P ≥ Q
(5) If P ≤ Q

6. P² – 5P + 6 = 0;        Q² +Q – 6 = 0(4)
7. 2P² + 12P + 16 = 0;  2Q² + 14 Q + 24 = 0(4)
8. 2P² + 48 = 20P;        2Q² + 18 = 12Q(2)
9. Q² + Q = 2;                 P² + 7P + 10 = 0(5)
10. P² + 36 = 12P;           4Q² + 144 = 48Q(1)

EXPLANATIONS

11. P² – P – 12 = 0 By solving P = –4 and 3

Q² – 3Q – 28 = 0 By solving Q = –4 and 7
∴ P ≤ Q.

12. 2P² – 11P + 5 = 0 By solving P = 1/2 and 5
3Q² – 13Q + 4 = 0 By solving Q =1/3 and 4
∴ P > Q.

13.P²+ 7P + 12 = 0
⇒ (P + 3) (P + 4) = 0 ⇒ P = –3, –4
Q² + 2Q – 3 = 0
⇒ (Q – 1) (Q + 3) = 0 ⇒ Q = 1, –3
∴ P ≤ Q.

14. 3P + Q = 1 8P + 12Q = 5
By solving P =1/4 and Q =1/4
∴ P = Q.

15. P² + 5P – 14 = 0
⇒ (P – 2) (P + 7) = 0 ⇒ P = 2, –7
Q² + 6Q – 7 = 0
⇒ (Q – 1) (Q + 7) = 0 ⇒ Q = 1, –7
∴ P ≥ Q.

16. P² – 5P + 6 = 0
By solving we get P values as 2 and 3
Q² +Q – 6 = 0
By solving we get Q values as 2 and –3
∴ P ≥ Q.

17. 2P² + 12P + 16 = 0
By solving we get P values as –4 and –2.
2Q² + 14 Q + 24 = 0
By solving we get Q values as –3 and –4
∴ P ≥ Q.

18. 2P² + 48 = 20P
By solving we get P values as 4 and 6
2Q² + 18 = 12Q
By solving we get Q values as 3 and 3
∴ P > Q.

19.Q²  + Q = 2
By solving we get P values as 1 and –2
P² + 7P + 10 = 0
By solving we get Q values as –2 and –5
∴ P ≤ Q.

20. P²+ 36 = 12P
By solving we get P values as 6 and –6
4Q² + 144 = 48Q
By solving we get Q values as 6 and –6
∴ P = Q.