1

Question

-1 = -2, which of the following could have the largest value?

a. x^2 + y ^2
b. x^2 - z^2
c y^2 - z ^2
d. x^2 + y^2 -z^2
e. 2 *( x-z)*(x+z) + 2*y^2

vastav · Answer

Another vote for A.

rakesh1239 · Answer

agree with kpadma. Answer should be E.

gmatblast · Answer

Another vote for E. The greatest possible value for the expression in E is +infinity.

The greatest value for A is just 2.

Batliwala,

I have seen that you are positing a lot of good question these days. Most of them may not need to be confirmed with official naswer. However, there are few questions where official answer is required. 

It would be great if you could publish official answer where there is a diagreement among the members.

BG · Answer

Please note that 2*(X-Z)*(X+Z)+2Y^2=2X^2-2Z^2+2Y^2 so no matter if Z>= -2 or <=-2 it is always negative, as with the example of gmatblast it should be -inf.Also think it should be A)

batliwala · Answer

correct ans is E.

substituting values for x, y, and z and limiting conditions E. has the greatest value =4.

gmatblast · Answer

Well I agree with the answer E but I think the value of the expression in E will be +inf.

Here is how I thought of it:

2 *( x-z)*(x+z) + 2*y^2

To get the maximum value of this expression, we need to select the values as follws:

Maximum possible value of (x-z)
Maximum possible value of (x+z) 
Maximum possible value of y


To get the Maximum possible value of (x-z):

 Take the maximum possible value of x = 0
 Take the minimum possible value of z = -2
 
 Hence, maximum possible value of (x - z) =   = 2

To get the Maximum possible value of (x+z):

 Take the maximum possible value of x = 0
 Take the maximum possible value of z = +inf

 Hence, the maximum possible value of (x + z) = +inf

To get the Maximum possible value of y:

 Take the maximum possible value of y = 1

So the maximum possible value of the given expression = 2 (2) (+inf) + 2(1) = +inf.

What am I missing?




Maximum possible value for x = 0
Minimum possible value for z = +inf

lastochka · Answer

You can't have z equal -2 and +inf in the same equation.

kpadma · Answer

I'm changing my answer to A. A simple question and I scrowed up!! God, Show mercy on my Soul in the GMAT exam !!! -1 < = x < =0, ==> 0 =< X^2 =< 1 -1 < = y < = 1, ==> 0 =< Y^2 =< 1 z > = -2 ==> 4 =< Z^2 =< +INF a. x^2 + y ^2 ==> 1 + 1 = 2 b. x^2 - z^2 ==> 1 - 4 = -3 c y^2 - z ^2 ==> 1 - 4 = -3 d. x^2 + y^2 -z^2 ==> 1 + 1 - 4 = -2 e. 2 *( x-z)*(x+z) + 2*y^2 2 ( X^2 + Y^2 - Z^2) ==> 2( 1 + 1 - 4) = -4 So, the answer is A. Dear Batliwala, the unoffical ETS question banker, What is the official answer?

gmatblast · Answer

YES. Kpadma!! I think the answer should be A. 

Such a simple problem and got screwed up. Thanks for the follow up.

batliwala · Answer

Here's the unofficial answer.
The correct choice is E.
x^2 < = 1, Y^2 <=1, Z^2 >=0

Evaluating the maximum value of the answer choices:
a. 1+1 = 2
b. 1-0 =1
c. 1- 0 = 1
d. 1+1 -0 = 2
e. 2(x^2-Z^2) + 2y^2 = 2(1-0)+ 2*1 = 4.

aayi maala wanchwa.

kpadma · Answer

Yes, In deed, Man, Simple problems tend to confuse me! :oops:

Yogendras · Answer

*********************************************************** Step 1: 2 *( x-z)*(x+z) + 2*y^2 = 2* (x^2 - z^2) + 2*y^2 Using : (a+b)*(a-b) = a^2-b^2 Step 2: 2* (x^2 - z^2) + 2*y^2 = 2(x^2+y^2-z^2) Taking 2 as common Step 3: 2(x^2+y^2-z^2) = 2( (-1^2) + (1^2) - (0^2)) Selecting maximum values for x and y and minimum value for z (Here sign doesnt make any diffrence, since we are squaing the values :-D) i.e. x = -1; y = 1 or -1; z = 0 Step 4: 2( (-1^2) + (1^2) - (0^2)) = 4 Solving

************************************************************ Note here the maximum value the option A can give is 2 since it is x^2 + y^2 and max values for x and y (ignoring the sign) is 1

1 < = x < =0, -1 < = y < = 1, z > = -2, which

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