Subject
Quantitative Aptitude
Topic
Data Sufficiency
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
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
ক)
Statement I alone is sufficient to answer the question.খ)
Statement II alone is sufficient to answer the question.গ)
Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.ঘ)
Either Statement I or Statement II alone is sufficient to answer the question.ঙ)
Neither Statement I nor Statement II is sufficient to answer the question.Explanation
A 2 + A = ¾ and B 2 + 2B = 24 Solving both the quadratic equations to obtain the roots, A 2 + A = ¾ We can solve this equation using two methods. One is to use formula 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. ⇒ A 2 + A+ ¼ = ¾ + ¼ ⇒A 2 + A+ ¼ = 1 A 2 + A + ¼ = (A + ½) 2 ⇒ (A + ½) 2 = 1 ⇒ A + ½ = ± 1 ⇒ A = +1/2 or -3/2 Similarly, for B 2 + 2B = 24, we add 1 on both sides, ⇒ B 2 + 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: A 2 – 3A = -9/4 and B 2 – 3B = 4 We solve these equations in a method similar to the one explained previously. We add 9/4 on both sides ⇒ A 2 – 3A+ (9/4) = (-9/4) + (9/4) ⇒ A 2 – 3A+ (9/4) = 0 ⇒ (A – (3/2)) 2 = 0 ⇒ A = 3/2 Similarly, B 2 – 3B = 4 We add 9/4 on both sides B 2 – 3B+ (9/4) = 4 + (9/4) ⇒ B 2 – 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.Related questions
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