If z is not equal to zero, and z = 6zs - 9s^2, then z equals:

Question

Tough and Tricky questions: Algebra.

If z is not equal to zero, and  z = \sqrt{6zs - 9s^2} , then z equals:

A. s 
B. 3s 
C. 4s 
D. -3s 
E. -4s

Kudos for a correct  solution .

PareshGmat · Accepted Answer

z = \sqrt{6zs - 9s^2}

Squaring both sides

z^2 = 6zs - 9s^2

z^2 - 6zs + 9s^2 = 0

The LHS is a perfect square of (z - 3s)

(z - 3s)^2 = 0

z = 3s

Answer = B

adymehta29 · Answer

This is how i got the answer. squaring on both the sides gives Z^2 = 6ZS -9S^2 = Z^2-6ZS+9S^2 = Z(Z-3S) -3S(Z-3S) = (Z-3S) (Z-3S) = Z = 3S i will go with B

mau5 · Answer

One can easily eliminate A,D and E, as because for any of the values of z for these options, the expression under the root would equal a negative integer. Thus, we are left with only B or C. Easily start with any one, plug-in the value of z(say z=4s), this gives the expression under the root as  5s^2 , which is obviously not correct.

B.

LighthousePrep · Answer

Agree with your answer. I just think you had some typo (Z mixed with S) in there that might confuse people.

https://i.imgur.com/wCYKilG.png

stonecold · Answer

Here z^2 = 6zs -9s^2 
now using the quadratic formula => z = 6s /2 = 3s 
hence B

AJ1012 · Answer

One can easily eliminate D and E as value of z can not be negative because of Square root.
By plugging, z = 3s, 3s = \sqrt{6*3s*s - 9s^2}
then, squaring on both side: 9s^2 = 18s^2 - 9s^2,
we get both sides equal.

nik256 · Answer

z=\sqrt{6zs-9s^2}

Sq both sides

z^2 = 6zs-9s^2
z^2-6zs+9s^2=0

Now we know that we can factorize 
(Z-3s)(Z-3s)

Z=3s

wilsonprj · Answer

Trick, but whenever you see:

- First ter is square -> Z^2
- last term is a square - 9s^2
- middle term 2*(square roots multiplied)

We can test: (sqr(first) - sqr(last)^2

egmat · Answer

Let's walk through this step by step.

We're given: z = √( 6 zs -  9 s2), and z ≠  0 .

Step 1:  Square both sides to remove the square root.
z2 =  6 zs -  9 s2

Step 2:  Move everything to one side.
z2 -  6 zs +  9 s2 =  0

Step 3:  Recognize this is a  perfect square trinomial . It follows the pattern a2 -  2 ab + b2, where a = z and b =  3 s.
(z -  3 s)2 =  0

Step 4:  Solve.
z -  3 s =  0 
z =  3 s

Answer: B

Common mistake : Some students try to divide both sides of z2 =  6 zs -  9 s2 by z early on. While that can work, you have to be careful not to lose solutions.  The safest approach is to move everything to one side and factor, as we did above.

Key principle to remember:   Whenever you see an expression like a2 -  2 ab + b2, recognize it as  (a - b)2 . Here, z2 -  6 zs +  9 s2 = z2 -  2 (z)( 3 s) + ( 3 s)2 = (z -  3 s)2. Spotting these  perfect square patterns  saves a lot of time on the GMAT.

If z is not equal to zero, and z = 6zs - 9s^2, then z equals:

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GMAT Problem Solving (PS) Questions

If z is not equal to zero, and z = 6zs - 9s^2, then z equals:

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