Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
Is A>B ?
I. A2 + A = ¾ and B2 + 2B = 24
II. A2 – 3A = -9/4 and B2 – 3B = 4
Solution
Correct Answer: Option E
A2 + A = ¾ and B2 + 2B = 24
Solving both the quadratic equations to obtain the roots,
A2 + A = ¾
We can solve this equation using two methods. One is to use formula \(\frac{{ - b \pm \left( {\sqrt {{b^2} - 4ac} } \right)}}{{2a}}\)
or we can solve it by adding a certain number to both sides such that it makes the LHS a perfect square.
In this case, we add ¼ on both sides to make the LHS of the above equation a perfect square.
⇒ A2 + A+ ¼ = ¾ + ¼ ⇒A2 + A+ ¼ = 1
A2 + A + ¼ = (A + ½)2
⇒ (A + ½)2= 1
⇒ A + ½ = ± 1
⇒ A = +1/2 or -3/2
Similarly, for B2 + 2B = 24, we add 1 on both sides,
⇒ B2 + 2B+ 1 = 24 + 1 = 25
⇒ (B + 1)2 = 25
⇒ B + 1 = ± 5 ⇒B = 4 or – 6
The question cannot be answered by using only these two statements, since each of X and Y have two values.
Hence, statement I is insufficient to answer the question.
From statement II:
A2 – 3A = -9/4 and B2 – 3B = 4
We solve these equations in a method similar to the one explained previously.
We add 9/4 on both sides
⇒ A2 – 3A+ (9/4) = (-9/4) + (9/4)
⇒ A2 – 3A+ (9/4) = 0
⇒ (A – (3/2))2 = 0
⇒ A = 3/2
Similarly, B2 – 3B = 4
We add 9/4 on both sides
B2 – 3B+ (9/4) = 4 + (9/4)
⇒ B2 – 3B + (9/4) = 25/4
⇒ (B – (3/2))2 = 25/4
⇒ B – (3/2) = ± 5/2
⇒ B = 4 or –1
Although the value of A is known, the question cannot be answered since B has 2 values, one less than A and the other greater than A.
Combining the two statements we are not able to reach to a conclusion about values of A and B, and hence the relation between them cannot be determined.
The question can not be answered even if both the statements are combined.
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions