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Manager  Joined: 14 Feb 2010
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If y=root(3y+4), then the product of all possible solution  [#permalink]

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Question Stats: 43% (01:18) correct 57% (01:09) wrong based on 805 sessions

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If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:

A. -4
B. -2
C. 0
D. 4
E. 6
Math Expert V
Joined: 02 Sep 2009
Posts: 59720
If y=root(3y+4), then the product of all possible solution  [#permalink]

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14
18
Prax wrote:

If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:
-4
-2
0
4
6

Square both sides: $$y^2=3y+4$$ --> $$(y+1)(y-4)=0$$ --> $$y=-1$$ or $$y=4$$, but $$y$$ cannot be negative as it equals to square root of some expression ($$\sqrt{expression}\geq{0}$$), so only one solution is valid $$y=4$$.

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Math Expert V
Joined: 02 Sep 2009
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If y=root(3y+4), then the product of all possible solution  [#permalink]

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12
5
Prax wrote:
But don't we consider negative sq. root as well?

This issue was discussed several times lately on the forum and let me assure you: square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

So when we see $$y=\sqrt{3y+4}$$ we can deduce TWO things:
A. $$y\geq{0}$$ - as square root function cannot give negative result;
B. $$3y+4\geq{0}$$ - as GMAT is dealing only with real numbers and even roots of negative number is undefined ($$3y+4$$ is under square root so it must be $$\geq{0}$$).

Hope it's clear.
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Manager  Joined: 14 Feb 2010
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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1
But don't we consider negative sq. root as well?
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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1
rakeshd347 wrote:
noboru wrote:
If y=sqrt(3y+4) then the product of all possible solution(s) for y is

a -4
b -2
c 0
d 4
e 6

The two solutions are 4 and -1 then -1 doesn't satisfy the equation so the only solution is 4.
D is correct.

Hello rakeshd347.,

If the two solutions are 4 and -1, that would mean that they both satisfy the equation and that is why they are the solutions. The product of all possible solutions is hence 4*-1 = -4.

If it helps, in an equation $$ax^2 + bx + c = 0$$, the sum of the roots is $$\frac{-b}{a}$$ and the product of the roots is $$\frac{c}{a}$$
Manager  Joined: 14 Feb 2010
Posts: 50
Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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Thanks a lot Bunuel. its absolutely clear Manager  Joined: 20 Dec 2013
Posts: 116
Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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Prax wrote:

If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:

A. -4
B. -2
C. 0
D. 4
E. 6

y has to be a non negative value as y = square root of something hence we can eliminate A and B.

squaring both sides we get:
y^2 - 3y - 4 = 0
y^2 - 4y + y - 4 = 0
y(y-4) + 1(y - 4) = 0
(y-4) (y+1) = 0
y can be equal to 4 or -1.

Now -1 is not possible as -1 is not equal to square root of -1. Hence answer is 4. (D)
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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Bunuel wrote:
Prax wrote:

If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:
-4
-2
0
4
6

Square both sides: $$y^2=3y+4$$ --> $$(y+1)(y-4)=0$$ --> $$y=-1$$ or $$y=4$$, but $$y$$ cannot be negative as it equals to square root of some expression ($$\sqrt{expression}\geq{0}$$), so only one solution is valid $$y=4$$.

I don't understand why y = -1 is not a valid solution. Let's evaluate the equation with y = -1.
LHS = y = -1.
RHS = sqrt(3y+4) = sqrt(3*(-1)+4) = sqrt(-3+4) = sqrt(1) = -1 = LHS. Where's the problem? It perfectly satisfies the equation.

Just saying that for y = -1 the sqrt is not valid is incorrect coz for y = -1 the expression under sqrt equals 1 which is +ve. Hence y = -1 is valid solution and answer for this question should be -1*4 = -4.

Hope I'm clear. Justify if I'm not.
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Math Expert V
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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rahulforsure wrote:
Bunuel wrote:
Prax wrote:

If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:
-4
-2
0
4
6

Square both sides: $$y^2=3y+4$$ --> $$(y+1)(y-4)=0$$ --> $$y=-1$$ or $$y=4$$, but $$y$$ cannot be negative as it equals to square root of some expression ($$\sqrt{expression}\geq{0}$$), so only one solution is valid $$y=4$$.

I don't understand why y = -1 is not a valid solution. Let's evaluate the equation with y = -1.
LHS = y = -1.
RHS = sqrt(3y+4) = sqrt(3*(-1)+4) = sqrt(-3+4) = sqrt(1) = -1 = LHS. Where's the problem? It perfectly satisfies the equation.

Just saying that for y = -1 the sqrt is not valid is incorrect coz for y = -1 the expression under sqrt equals 1 which is +ve. Hence y = -1 is valid solution and answer for this question should be -1*4 = -4.

Hope I'm clear. Justify if I'm not.

$$\sqrt{1}=1$$, not 1 and -1.
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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Bunuel wrote:
rahulforsure wrote:
Bunuel wrote:

I don't understand why y = -1 is not a valid solution. Let's evaluate the equation with y = -1.
LHS = y = -1.
RHS = sqrt(3y+4) = sqrt(3*(-1)+4) = sqrt(-3+4) = sqrt(1) = -1 = LHS. Where's the problem? It perfectly satisfies the equation.

Just saying that for y = -1 the sqrt is not valid is incorrect coz for y = -1 the expression under sqrt equals 1 which is +ve. Hence y = -1 is valid solution and answer for this question should be -1*4 = -4.

Hope I'm clear. Justify if I'm not.

$$\sqrt{1}=1$$, not 1 and -1.

Ok. Got it. But does this apply to DS as well. E.g., if the deduction of any statement boils down to, say, x= sqrt(4), then can we say that that statement would be sufficient since it would yield just one value (i.e. the principal root)?

I'm a bit confused coz I remember coming across questions where both +ve & -ve values have been considered. Please help clarify my confusion. Thanks in advance. _________________
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Math Expert V
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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rahulforsure wrote:
Ok. Got it. But does this apply to DS as well. E.g., if the deduction of any statement boils down to, say, x= sqrt(4), then can we say that that statement would be sufficient since it would yield just one value (i.e. the principal root)?

I'm a bit confused coz I remember coming across questions where both +ve & -ve values have been considered. Please help clarify my confusion. Thanks in advance. This applies to math generally. The square root cannot give negative result.
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GMAT 1: 750 Q49 V43 If y=root(3y+4), then the product of all possible solution  [#permalink]

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Prax wrote:
If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:

A. -4
B. -2
C. 0
D. 4
E. 6

The two roots y=4 and -1
Since y is coming out of a square root it cannot be -ve
Therefore the root y=-1 is not valid leaving us with only one root y=4
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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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y^2 = 3y+4.. solving the quadratic we get two values for Y : -1 or 4

But as Y is a root of something it cant take the negative value, hence only solution is 4

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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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If $$y=\sqrt{3y+4}$$, then the product of all possible solution(s) for y is:

$$y=\sqrt{3y+4}$$

Squaring on both sides.

$$y^2 = 3y + 4$$

$$y^2 - 3y - 4 = 0$$

$$(y - 4) (y + 1) = 0$$

$$y = 4$$ or

$$y = -1$$

As per the given equation for y we know that the value was in Square Root

As the value of square root cannot be negative, there can be only value for y here and that is y =4

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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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y^2=3y+4
y^2-3y-4=0
(y+1)(y-4)=0
y=-1,4
y can't be negative because it's the result of a square root

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Re: If y=root(3y+4), then the product of all possible solution  [#permalink]

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Solution

Given
• y=√(3y+4)

To find
• The product of all the possible values of y.

Approach and Working out

Squaring on all the sides of y=√(3y+4), we get:
• y^2 = 3y +4
• y^2 -3y -4 =0
• y^2 – 4y + y -4 =0
• y(y-4) +1(y-4) =0
• y = -1 and 4

Since y is equal to the square root of one number, it cannot be negative.
Hence, y =4
Thus, option D is the correct answer.

_________________ Re: If y=root(3y+4), then the product of all possible solution   [#permalink] 30 Sep 2019, 07:28
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