Quantitative Aptitude Ques 833
Question: Directions: In each question below one or more equation (s) is / are provided. On the basis of these you have to find out relation between p, q and give answer. [SBI (PO) 2000]
I. $ 6q^{2}+\frac{1}{2}=\frac{7}{2}q $
II. $ 12p^{2}+2=10p $
Options:
A) If $ p=q $
B) If $ p>q $
C) If $ p<q $
D) If $ p\ge q $
Show Answer
Answer:
Correct Answer: D
Solution:
- I. $ 6q^{2}+\frac{1}{2}=\frac{7}{2}q $
$ \Rightarrow $ $ \frac{12q^{2}+1}{2}=\frac{7}{2}q $
$ \Rightarrow $ $ 12q^{2}+1=7q $
$ \Rightarrow $ $ 12q^{2}-7q+1=0 $
$ \Rightarrow $ $ 12q^{2}-3q-4q+1=0 $
$ \Rightarrow $ $ 3q(4q-1)-(4q-1)=0 $
$ \Rightarrow $ $ (4q-1)(3q-1)=0 $
$ \Rightarrow $ $ q=\frac{1}{3}, $ $ \frac{1}{4} $
II. $ 12p^{2}+2-10p=0 $
$ \Rightarrow $ $ 12p^{2}-10p+2=0 $
$ \Rightarrow $ $ 12p^{2}-6p-4p+2=0 $
$ \Rightarrow $ $ 6p(2p-1)(2p-1)=0 $
$ \Rightarrow $ $ (6p-2)(2p-1)=0 $
$ \Rightarrow $ $ p=\frac{1}{2}, $ $ \frac{1}{3} $
$ \therefore $ $ p\ge q $
BETA
