If x = (0.08)^2, y = 1/(0.08)^2 and z = (1 - 0.08)^2 -1, which of the

Question

If x =  (0.08)^2 , y =  \frac{1}{(0.08)^2}  and z =  (1 - 0.08)^2-1 , which of the following is true?

(A) x = y = z
(B) y < z < x
(C) z < x < y
(D) y < x and x = z
(E) x < y and x = z

adkikani · Accepted Answer

pushpitkc niks18 Hatakekakashi
amanvermagmat

How about this approach?

On seeing z, I know I can write it as \(a^2\) - \(b^2\) = (a+b) * (a-b)

or (1 - 0.08 + 1 ) * (1 - 0.08 -1 )

The second bracket gives me a negative value as final answer.

Just by looking at x and y , I know these are positive. So only C holds good.
I do not have to care about inequality between x and y.

GMATNinja Sorry to bother you on qaunt forum

, but is this approch more efficient than one here at 32:05 min

pushpitkc · Answer

The values of x,y, and z are

x =  0.0064 
y =  \frac{1}{0.0064} = \frac{10000}{64}  
z =  (0.92)^2 - 1 = 0.8464 - 1 = -0.1536

Therefore,  Option C(z < x < y)  has to be true for the following values.

abhimahna · Answer

Hey adkikani , I completly agree with this approach and I really like it.

This method is also know as smart way of solving any inequality question.

pushpitkc · Answer

Hi  adkikani

I don't see the problem with using the method you are suggesting to find
the value of z. Also, specific to this problem, we might not need to bother
about the inequality between x and y.

But as far as the GMAT is concerned, it always makes sense to find the 
value of the x and y in case we have both z < x < y and z < y < x as 
answers!

KSBGC · Answer

how do u get z=0.02..........it's given that z=(1-0.08)^2-1...........1-0.08=0.92

pushpitkc · Answer

Have corrected my solution. Thanks for notifying,  selim

KSBGC · Answer

we have to keep in mind that if we square a fraction it would be even smaller. 
start with Z= (1-0.08)^2-1
we don't have calculate anything. just think logically. we will get fractional value inside the bracket. furthermore we are going to square it. the ultimate value will be even more smaller. finally we deduct 1. so, Negative value is a must here. thus it will be the smallest one.

only option C meets the condition.

but for more analyze, y = 1/0.08^2
 
here ultimate value will be more that 1 . how ? coz u are dividing a integer by a fraction . 
 x= 0.08^2
 we will get a fraction but smaller one , positive one. 
so, y>x>z

adkikani · Answer

I agree pushpitkc

but options other than (C) can be eliminated using logic:

two numbers, out of which one is smaller (or negative to be more precise)
CAN NOT BE equal to other one.

Quote:

(A) x = y = z

Nope, I know z is negative and x is positive, rejected.

Quote:

(B) y < z < x

Nope, I know z is negative and y is positive, rejected.

Quote:

(D) y < x and x = z

x and z can not be equal.

Quote:

(E) x < y and x = z

x and z can not be equal.

Hope I am thinking on correct lines

Hatakekakashi · Answer

hey that's a great way to solve the problem but it is problem specific. Great observation .. loved it

JeffTargetTestPrep · Answer

We can observe the following:

Since 0.08 < 1, x = (0.08)^2 will be less than 1 also. However, its reciprocal, y = 1/(0.08)^2 will be greater than 1.

Finally we see that z is negative, since (1 - 0.08)^2 is less than 1. We know that it is less than 1 because (1 - 0.08) is less than 1, and thus, when (1 - 0.08) is squared, the result is also less than 1.

Thus, z < x < y

Answer: C

Kinshook · Answer

Given: 
1. x =  (0.08)^2 
2. y =  \frac{1}{(0.08)^2}  
3. z =  (1 - 0.08)^2 -1

1. x =  (0.08)^2  = 0.0064
2. y =  \frac{1}{(0.08)^2}  = \frac{1}{0.0064} = 156.25
3. z =  (1 - 0.08)^2 -1 = (.92 + 1)(.92-1) = 1.92*(-.08) = -.1536

-.1536(z) < .0064(x) <156.25(y)
z<x<y

Asked: which of the following is true?

(A) x = y = z
NO 
(B) y < z < x
NO
(C) z < x < y
YES
(D) y < x and x = z
NO
(E) x < y and x = z
NO

IMO C

goaltop30mba · Answer

Alternative way , I am no expert so feedback from the experts is most welcome

If 0<x<1, then x>x^2>x^3....so as we increase the power, the value of x decreases

If 1<x, then x<x^2<x^3....... so as we increase the power the value of x increases

Now as per the given question x is between 0 and 1.

Y=1/x or Y=x^-1 —> Y>x.... so a is gone, b is gone and d is gone..

we are left with c and e, we can easily compare c to e.. Clearly x is not equal to z... hence the answer C

I always try to avoid calculations as much as I can.

Give kudos, if you like the above mentioned solution

Experts are most welcome to share their views/feedback

Posted from my mobile device

himanshubhardwaj · Answer

Lets try to solve it verbally... 
x must be less than 1 because whatever quantity less than 1 and greater than zero will be squared then its value will be less than one.
y must be greater than 1 because it is a reciprocal of x
now, comes Z, 1 -0.08 must be less than 1 and its square will also be less than 1 therefore z will be negative

so our answer will be z<x<y

CEdward · Answer

If x = (0.08)^2, y = 1/(0.08)^2 and z = (1−0.08)^2 −1, which of the following is true?

(A) x = y = z
(B) y < z < x
(C) z < x < y
(D) y < x and x = z
(E) x < y and x = z

x = (0.08)^2 = (8/100)^2 = 64/100^2
y = 1/(0.08)^2 = 100^2 /64

z = (1−0.08)^2 −1 = (0.92)^2 - 1 --> Any fraction wherein 0 < fraction < 1 raised to an exponent will become smaller and smaller the larger the exponent becomes

z = -ve

z < x < y

C.

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If x = (0.08)^2, y = 1/(0.08)^2 and z = (1 - 0.08)^2 -1, which of the

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If x = (0.08)^2, y = 1/(0.08)^2 and z = (1 - 0.08)^2 -1, which of the

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