What is the value of x^2+ 5x +4?

Question

(1) x+1=5
(2) x+4=2

How to answer this DS question?
Does it not matter if the two prompts give two different values to the equation?

piyatiwari · Answer

I think the catch here is that the given equation is not equal to 0.

So this can have two differnt values based on two equations in statements.

Experts, correct me if I'm wrong.

EvaJager · Answer

the given equation is not equal to 0.

An equation cannot be equal to 0. Equation is a statement. The statement is that two algebraic expressions are equal. The equality sign = is used between the two expressions, separating the two sides which should be equal. In particular, one of the sides can be 0. To distinguish it from an identity, which is true for any value of the variable ( x  in our case), an equation has a finite number of solutions, meaning that equality holds only for some specific values of the variable.
 x+1=2x-x+1  is and identity, it holds for any value of  x. 
 x+3=5  is an equation, this equality holds only for  x=2.  We say that 2 is a root of the equation or solution of the equation. You can solve by some method an equation and find the root(s), or if given a root, you can check if the specific number is indeed a root.
If I don't know how to solve the equation  x+3=5  but somebody tells me that  2  is a root of it, I can check by substituting  2  for  x: 
 2+3=5  it is indeed true, so  2  is a solution of the given equation. But if I don't know about methods of solving such equations or I cannot prove whether there might be additional solutions, I am in "trouble", as I cannot check all the real numbers to see whether there is another solution or not.

x^2+ 5x +4  is an algebraic expression, not an equation. The value of this expression is determined by the particular value of  x. 
Obviously, for different values of  x  the expression can take different values. And once  x  is known, the value of the given expression is uniquely determined. That's why the answer to this question is D.

piyatiwari · Answer

The general form of a quadratic equation is ax^2 + bx + c = 0 >>> from GMATclub math book.

https://gmatclub.com/forum/algebra-101576.html#p787276

piyatiwari · Answer

I agree with you on this. What I meant was that the given equation is just an algebraic expression and not a quadratic equation.

KarishmaB · Answer

You need to find the value of  x^2+ 5x +4

Statement 1: x+1=5 which implies x = 4
Put x = 4 and you get the value of  x^2+ 5x +4  as  4^2+ 5*4 +4  which is 40 (a unique value). Hence this statement alone is sufficient.

Statement 2: x+4=2 which implies x = -2
Put x = -2 and you get the value of  x^2+ 5x +4  as  (-2)^2+ 5*(-2) +4  which is -2 (a unique value). Hence this statement alone is sufficient.

The problem here that the statements give different values for  x^2+ 5x +4 . An actual GMAT question does not do that. Both statements are a part of the same puzzle and hence lead to the same answer. 
This problem will not occur in actual GMAT. If both statements individually lead you to a unique solution of the question asked, the unique solutions will be the same.

EvaJager · Answer

Be careful! An equation needs two algebraic expressions with the equal sign between. You are not given an equation! 
You are given an algebraic expression.

EvaJager · Answer

The general form of a quadratic equation is  ax^2 + bx + c = 0  where  a
eq0. 
You must have a quadratic term, otherwise your equation is not quadratic.

2x^2+3x-1=4x+2  is also a quadratic equation even it is not written in the "general form".
Obviously, any algebraic equation  E_{1}(x)=E_{2}(x)  can be written in the form  E_{1}(x)-E_{2}(x)=0. 
So,  2x^2+3x-1=4x+2  can be written as  2x^2+3x-1-(4x+2)=4x+2-(4x+2)  or  2x^2-x-3=0.

ax^2 + bx + c = 0  is an algebraic equation

ax^2 + bx + c  is an algebraic expression. You can use it to build algebraic equations, like  ax^2 + bx + c=0  or  ax^2 + bx + c=dx+e,  etc.

EvaJager · Answer

Answer choice D states (OG13 page 272):
(D) EACH statement ALONE is sufficient to answer the question asked
There is also a note:
NOTE: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

In our case, exactly one value can be determined when each statement is considered regardless of the other statement.
Nowhere is claimed that the answer should be the same value when the two statements are considered separately. 
It might be that most of the DS questions have a unique answer when the two statements are considered separately, but there is no justification to assume that "Both statements are a part of the same puzzle and hence lead to the same answer."

The given question tested just a simple fact: the value of an algebraic expression in one variable ( x  in our case) is uniquely determined once the value of the variable is known.

Bunuel · Answer

Actually Karisham is absolutely right.

The data sufficiency statements  are ALWAYS true  and  NEVER contradict one another .

EvaJager · Answer

Bunuel wrote:
 Actually Karisham is absolutely right.

The data sufficiency statements  are ALWAYS true  and  NEVER contradict one another.

Where is the contradiction? When treated separately, there is no contradiction as you don't have two statements simultaneously.
If the statements contradict each other, the answer should be E, unless either one is sufficient to answer the question.
I don't see any violation of the definition of a DS question here.

PS GMAT questions are always correct...unless proven otherwise (you know what I mean). Be careful when you say never...

Bunuel · Answer

Eva, the two statements in the question contradict because from (1) we have that x=4 and from (2) we have that x=-2, that's why the question if flawed.

EvaJager · Answer

Bunuel,
I can grasp the idea that x cannot be simultaneously 4 and -2. But why should we consider the two statements simultaneously?
 Option (D) - EACH statement ALONE is sufficient to answer the question asked 
Does it state that the two answers should be identical? NO! When considered alone, other statement/option/answer doesn't exist.

I always thought of DS questions as mimicking decision making.
The issue is whether you can answer a certain question based on a specific piece of information. That's all.
It is your assumption (and Karishma's) that the two statements (should) never contradict each other. 
I read through the explanation again (in OG 13) and I could find nothing about the two statements whether they should necessarily be non-contradictory.

Bunuel · Answer

Eva, it's not our assumption it's a fact.

EvaJager · Answer

Bunuel wrote:
Eva, it's not our assumption it's a fact.

Once it was also a fact that the Earth is the center of the Universe...

AbhiJ · Answer

Would suggest you to give one example in any published official problem where the two statements give contradictory values. GMAC has never stated this. However in all published problems this convention is followed.

What is the value of x^2+ 5x +4?

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