If x/4 = a/b (x ≠ ±4;a ≠±b), which of the following statements could

Question

If  \frac{x}{4} = \frac{a}{b}  ( x ≠ ±4; \ a ≠±b ), which of the following statements could be wrong?

(A)  \frac{x-4}{4} = \frac{a-b}{b}

(B)  \frac{4x}{x+4} = \frac{bx}{a+b}

(C)  \frac{4}{x-4} = \frac{b}{a-b}

(D)  \frac{x}{4+a} = \frac{a}{b+a}

(E)  4a = bx

shantanugaware · Answer

I see variables absolutely everywhere in this question.
My first approach would be to choose numbers, such that those numbers would be ease to work with.
In this case let's assume x=2, a=3, b=6 (NOTE: Followed every constraint in the stem.)

Therefore, we have to find an answer choice which does not equate (i.e. LHS≠RHS).
For given numbers, only option D satisfies the above mentioned condition.

D] x/(4+a)≠a/(b+a)
 2/(4+3)≠3/(6+3)
 2/7≠3/8

It satisfies the condition.
Therefore my answer is Choice *D*

nikorohr · Answer

don't know if quicker or better but i solved using cross multiplication 
therefore seems also possible

OMKARGADKARI · Answer

Given the equation x4=abx^4 = abx4=ab and the conditions x≠±4x 
eq \pm 4x=±4 and a≠±ba 
eq \pm ba=±b, we need to determine which of the given statements could be wrong.

Let's evaluate each option in the context of the given equation.

(A) x−44=a−bb\frac{x - 4}{4} = \frac{a - b}{b}4x−4​=ba−b​

Starting from x4=abx^4 = abx4=ab, let’s test if this equation can be derived from the given statements. Rearranging:

x−44=a−bb\frac{x - 4}{4} = \frac{a - b}{b}4x−4​=ba−b​Rewriting the terms:

x−4=4⋅a−bbx - 4 = 4 \cdot \frac{a - b}{b}x−4=4⋅ba−b​Substituting x=4x = 4x=4, which does not meet the conditions, this equality does not hold for the general case. It could be wrong.

(B) 4xx+4=bxa+b4\frac{4x}{x + 4} = \frac{b x a + b}{4}x+44x​=4bxa+b​

Let's test this expression:

4xx+4=bxa+b4\frac{4x}{x + 4} = \frac{b x a + b}{4}x+44x​=4bxa+b​Cross-multiplying to check consistency:

4⋅(bxa+b)=4x⋅(x+4)4 \cdot (b x a + b) = 4x \cdot (x + 4)4⋅(bxa+b)=4x⋅(x+4)Simplify:

4bxa+4b=4x2+16x4b x a + 4b = 4x^2 + 16x4bxa+4b=4x2+16xThis is complex, and without specific values, it’s hard to verify its consistency. But given the complexity, this statement could potentially be wrong.

(C) 4x−44=ba−b\frac{4x - 4}{4} = \frac{b}{a - b}44x−4​=a−bb​

Testing the validity:

4x−44=ba−b\frac{4x - 4}{4} = \frac{b}{a - b}44x−4​=a−bb​Simplify:

x−1=ba−bx - 1 = \frac{b}{a - b}x−1=a−bb​Substituting into the original problem doesn’t directly help verify, but this equation is plausible based on the given information. It’s not necessarily wrong.

(D) x4+a=ab+ax^4 + a = ab + ax4+a=ab+a

Testing:

x4+a=ab+ax^4 + a = ab + ax4+a=ab+aSubtracting aaa from both sides:

x4=abx^4 = abx4=abThis is consistent with the given x4=abx^4 = abx4=ab. This statement is not wrong.

(E) 4a=bx4a = b x4a=bx

Testing:

4a=bx4a = b x4a=bxRearranging to check consistency:

a=bx4a = \frac{b x}{4}a=4bx​Without specific values, this could be a valid expression if aaa and bbb are proportional to xxx. This statement does not immediately seem to contradict the given information.

Given this analysis,  the statement that could be wrong  is:

(B) 4xx+4=bxa+b4\frac{4x}{x + 4} = \frac{b x a + b}{4}x+44x​=4bxa+b​

If x/4 = a/b (x ≠ ±4;a ≠±b), which of the following statements could

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GMAT Problem Solving (PS) Questions

If x/4 = a/b (x ≠ ±4;a ≠±b), which of the following statements could

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