If a/b = 2/3 Which of the Following is Not True? GMAT Problem Solving

Question: If a/b = 2/3 which of the following is not true?

1. \(\frac{a+b}{a}=\frac{5}{3}\)
2. \(\frac{b}{b-a}=3\)
3. \(\frac{a-b}{b}=\frac{1}{3}\)
4. \(\frac{2a}{3b}=\frac{4}{9}\)
5. \(\frac{a+3b}{a}=\frac{11}{2}\)

“If a/b = 2/3 which of the following is not true?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

The question states that that a/b = 2/3 or 3a = 2b.

In order to gather the correct answer regarding which one of the options are not true, it is important to simplify these options. However, once the result is achieved in any one of the five options, no further evaluations are needed to be carried out. Hence, in order to yield 3a = 2b, the following simplification is needed-

1. A) (a + b)/b = 5/3

=3(a + b) = 5b

=3a + 3b = 5b

= 3a = 2b

Since we have 3a = 2b, answer choice A is not correct and hence, is true to the given condition.

1. B) b/(b - a) = 3

= b = 3(b - a)

= b = 3b - 3a

= 3a = 2b

Since we have 3a = 2b, answer choice B is not correct hence, can be stated to be true in terms of the given condition.

1. C) (a - b)/b = 1/3

= 3(a - b) = b

= 3a - 3b = b

= 3a = 4b

Since we have 3a = 4b, answer choice C is correct which implies that this equation does not stand in line with the character.

Correct Answer: C

Approach Solution 2:

To find which one of the following options given for the question stating a/b = ⅔, is not true, the options need to be divided.

Accordingly, all the options need to be simplified as well as evaluated in order to find if the required results is not true to the given condition of a/b = ⅔.

1. A) (a + b)/b = 5/3

= (a + b)/b = a/b + b/b

= 2/3 + 1 = 5/3

= This is true and hence, is the wrong answer for the question.

1. B) b/(b - a) = 3

Notice that b/(b - a) = 3 means (b - a)/b = 1/3 when we reciprocate both sides of the equation.

(b - a)/b = b/b - a/b = 1 - 2/3 = ⅓ → This is true.

1. C) (a - b)/b = 1/3

(a - b)/b = a/b - b/b

= 2/3 - 1 = -1/3

→ So (a - b)/b = 1/3 is not true.

Hence, since this option is not true for a/b = 2/3, hence, this is the correct answer choice.

Correct Answer: C

Approach Solution 3:

The answer is either 3a = 2b or a/b = 2/3.

It is crucial to simplify these options in order to determine the correct response on which of the possibilities is untrue. However, no more assessments are required to be carried out after the outcome is attained in any of the five choices. Consequently, the following simplification is required to produce 3a = 2b:

1.  5/3 = (a + b)/b = a/b + b/b = (a + b)/b = (a + b)/b

= 2/3 + 1 = 5/3

= This is accurate, making it the incorrect response to the question.

2.  b/(b - a) = 3
   When we reciprocate both sides of the equation, we find that b/(b - a) = 3 indicates that (b - a)/b = 1/3.

This is correct: (b - a)/b = b/b - a/b = 1 - 2/3 = 13.

100. (a - b)/b = a/b - b/b (a - b)/b = 1/3

= 2/3 - 1 = -1/3

This means that (a - b)/(b) is not true.

This is the right response option because this option is false for a/b = 2/3.

Correct Answer: C

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