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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 \(y=4\).

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 \(\sqrt[4]{x}\), 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, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

So when we see \(y=\sqrt{3y+4}\) we can deduce TWO things: A. \(y\geq{0}\) - as square root function can not 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 \(\geq{0}\)).

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

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19 Apr 2013, 02:02

1

This post received KUDOS

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

D is the correct answer. 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 \(\frac{c}{a}\)
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Re: If y=root(3y+4), then the product of all possible solution [#permalink]

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12 May 2014, 00:10

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18 Jun 2015, 11:17

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

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06 Jul 2016, 23:44

Bunuel wrote:

Prax wrote:

Can you please help me with this question:

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 \(y=4\).

Answer: D.

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.

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 \(y=4\).

Answer: D.

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.

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

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07 Jul 2016, 00:27

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.

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.

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

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07 Jul 2016, 01:09

Prax wrote:

Can you please help me with this question: 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

It's a quadratic equation (y-4)(y+1)=0 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 The answer is D
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Last edited by LogicGuru1 on 25 Jul 2016, 22:31, edited 1 time in total.

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