Bunuel
Bunuel
Is a^2 > 3a – b^4?
(1) 3a – b^4 = -5
(2) a > 5 and b > 0
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Question Type: Yes/No This question asks whether a^2 > 3a – b^4.
Statement 1: 3a – b^4 = -5. This statement may not appear sufficient at first. You cannot manipulate it algebraically to mirror the question stem as might be the first impulse. However, the important thing is that “3a – b^4 equals a negative number.” Remember that a^2 cannot be less than zero, as a squared number cannot be negative. The answer, then, is “yes,” as you can absolutely conclude that a^2 will be greater than -5. The correct answer is either A or D.
Statement 2: a > 5 and b > 0. Again, this statement may not appear to be sufficient. It does not give specific values for a or b. However, if you “Just Do It” and plug in the numbers then you will see that it is sufficient. A good strategy for these “greater than” statements is to use the actual numbers given. Although the statement says a > 5 and b > 0 you can just use 5 and 0 in the inequality. The inequality becomes “25 > 15 – 0?” The answer is clearly “yes”: 25 > 15. And as you increase both “a” and “b” the result becomes a stronger “yes.” For example, if “a = 6 and b = 2” the inequality is “36 > 18 – 16?” Conceptually it looks like this, so long as a is greater than 3 then a^2 will be greater than 3a. Whatever number “b” is can only take away from the 3a it cannot add to it. In fact, Statement 2 gives more information than strictly necessary; “a > 3” would be sufficient.
The correct answer is D.I have a small doubt, in the 2nd option it is nowhere mentioned that a>b, or b>a, it just simply says a>5 and b>0, now lets consider two scenarios:
1. a= 6, b=1, then the value of the expression comes 36>18-1=17, hence we can say the inequality holds.
2. a= 6, b= 9, then the value of the expression comes 36>18-6561= -6543, the inequality does not hold.
considering both these scenarios how can we conclude that option 2 alone is sufficient to provide a definite answer?
please guide where I am getting it wrong.