A function f is defined by f(x,y) = x^2 - y. Is the value of

Question

A function f is defined by f(x,y) = x^2 - y. Is the value of f(3,b) less than the value of f(a,3)?

(1) a < b 
(2) a + 4 < 0

Bunuel · Accepted Answer

A function f is defined by f(x,y) = x^2 - y. Is the value of f(3,b) less than the value of f(a,3)?

Since \(f(x,y) = x^2 - y\), then \(f(3,b)=9-b\) and \(f(a,3)=a^2-3\). The question asks whether \(9-b<a^2-3\) --> is \(a^2+b>12\)?

(1) a < b. If \(a=1\) and \(b=2\), then the answer is NO but \(a=3\) and \(b=4\), then the answer is YES. Not sufficient.

(2) a + 4 < 0 --> \(a<-4\). If \(a=-5\) and \(b=0\), then the answer is YES but \(a=-5\) and \(b=-15\), then the answer is NO. Not sufficient.

(1)+(2) From (1) we have that \(a<b\). Add \(a^2\) to both parts: \(a^2+a<a^2+b\). Now, since \(a<-4\), then \(a^2+a>12\) (if a=-4 then a^2+a=12 and if we decrease a, then we increase a^2+a). Thus we have that \(12<a^2+a<a^2+b\). Sufficient.

Answer: C.

PerfectScores · Answer

The question is asking is 9 - b less than a(a) - 3

Is 9 - b < a(a) - 3?
Is 12 < a(a) + b

Statement I is insufficient:
a = 2, b = 3 and a = 4, b = 15 will give us a Yes and a No

Statement II is insufficient:
a< -4, a = -5, b = 1 and a = -5 and b = -16 will give us a Yes and a No

Now if a < -4 and b>a we know that b will have to be greater than -4 hence it a(a) + b will always be greater than 12.

Hence the answer is C

Divyadisha · Answer

3^2 -b< a^2-3? 1212. Not sufficient. (2) a + 4 < 0 a<-4 a^2> 16 but we don't know the value of b and hence can't get the value of a^2+b>12. Not sufficient Combining both statements:- a^2 > 16 and b> a a^2+b>12 will always be true. C is the answer

MathRevolution · Answer

If we modify the original condition and the question, we get the question as f(3,b)<f(a,3)?, 3^2-b<a^2-3?. In other words, it becomes a^2+b-12>0?. There are 2 variables (a and b) in the original condition. In order to match the number of variables to the number of equations, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. 
Using both the condition 1) and the condition 2), the correct answer is C.

Princ · Answer

OA: C f(x,y) = x^2 - y f(3,b) = 9 -b f(a,3) = a^2-3 Question Stem : Is \quad f(a,3)>f(3,b)? Is \quad a^2-3>9 -b? \quad or \quad Is \quad a^2 +b>12? (1) \quad a < b Taking a = 1 and b = 2 , 1<2 Is \quad a^2 +b>12?\quad No , as 1^2+2 =3 is less than 12 . Taking a = 2 and b = 10 , 2<10 Is \quad a^2 +b>12?\quad Yes , as 2^2+10 =14 is greater than 12 . Statement 1 alone is not sufficient (2) \quad a + 4 < 0 \quad i.e \quad a<-4 Value of b can be anything so Statement 2 alone is not sufficient. Combining (1) and (2) , we get a<-4 and b≥-4 The minimum value of a^2 would be slightly more than 16 . The minimum value of b would be -4 So Minimum value of a^2+b would be 16.X-4 =12.X where X is greater than 0 ,So a^2+b would be always greater than 12 . Combining (1) and (2) Is \quad a^2 +b>12?\quad Yes

bumpbot · Answer

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A function f is defined by f(x,y) = x^2 - y. Is the value of

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