If x and z are positive constants, for how many values of y is

Question

If x and z are positive constants, for how many values of y is x(y)^2 = z(y)^4?

(A) 1 
(B) 2 
(C) 3 
(D) 4
(E) 5

gmatophobia · Answer

Given

x and z are positive constants

xy^2 = zy^4

y^2(x - zy^2)=0

Case 1: y = 0

Case 2:  x - zy^2 = 0

x = zy^2

y^2 = \frac{x}{z}

|y| = \sqrt{\frac{x}{z}}

y can either take a positive or negative value.

Hence, three values of y are possible.

Option C

Can,Will · Answer

gmatophobia  Have a little doubt. how root x/z is negative ? underroots are always positive. In order to have both positive and negative value, x and z must be perfect square ?

Bunuel · Answer

You are right; the square root of a number cannot be negative, but we have a different case here.

When the GMAT provides the square root symbol for an even root, like a square root, fourth root, etc., only the non-negative root is accepted as the answer. For example:   That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2;
Similarly  \sqrt{\frac{1}{16}} = \frac{1}{4} , NOT +1/4 or -1/4.

Notice that in contrast, the equation  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

So here we have  y^2 = \frac{x}{z} , which gives  y = \sqrt{\frac{x}{z}}  or  y = - \sqrt{\frac{x}{z}} .

Hope it's clear.

If x and z are positive constants, for how many values of y is

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If x and z are positive constants, for how many values of y is

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards