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If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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Updated on: 07 May 2019, 06:39

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Bunuel wrote:

If a and b are integers, and b > 0, does \(\frac{a - 1}{b + 1} = \frac{a}{b}\) ?

(1) a = b − 4 (2) a = –b

DS81602.01 OG2020 NEW QUESTION

We'll simplify the fraction so we can better SEE the logic. This is a Precise approach.

Multiplying the two fractions by their common denominator gives ab - b = ab + a --> -b = a. So (2) is certainly sufficient. (1) does not tell us if -b = a or not: this could be true for b = 2, a = -2 and could be false for b = 4, a = 0.

Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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27 Apr 2019, 10:30

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Top Contributor

Bunuel wrote:

If a and b are integers, and b > 0, does \(\frac{a - 1}{b + 1} = \frac{a}{b}\) ?

(1) a = b − 4 (2) a = –b

Given: a and b are integers, and b > 0

Target question:Does (a - 1)/(b + 1) = a/b? This is a good candidate for rephrasing the target question.

Take the equation: (a - 1)/(b + 1) = a/b Cross multiply to get: (b)(a - 1) = (a)(b + 1) Expand both sides to get: ab - b = ab + a Subtract ab from both sides to get: -b = a Add b to both sides to get: 0 = a + b REPHRASED target question:Does a +b = 0?

Aside: The video below has tips on rephrasing the target question

Statement 1: a = b − 4 Let's TEST some values. There are several values of a and b that satisfy statement 1. Here are two: Case a: a = -2 and b = 2. In this case, a + b = (-2) + 2 = 0. So, the answer to the target question is YES, a+b = 0 Case b: a = -1 and b = 3. In this case, a + b = (-1) + 3 = 2. So, the answer to the target question is NO, a+b does NOT equal 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a = –b Add b to both sides to get: a + b = 0 The answer to the target question is YES, a+b = 0 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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29 Apr 2019, 02:51

Bunuel wrote:

If a and b are integers, and b > 0, does \(\frac{a - 1}{b + 1} = \frac{a}{b}\) ?

(1) a = b − 4 (2) a = –b

DS81602.01 OG2020 NEW QUESTION

Hola amigos

Is \(\frac{a - 1}{b + 1}\) equal to \(\frac{a}{b}\) ?

1. \(a = b − 4\) Substituting \(a\) for \(b - 4\), we get the question - is \(\frac{b - 5}{b + 1}\) equal to \(\frac{b - 4}{b}\) ? If \(b = 1\), then NO If \(b = 2\), then YES Insufficient

2. \(a = -b\) Substituting \(a\) for \(-b\), we get \(\frac{-(b + 1)}{b + 1} = \frac{-b}{b}\). Since \(b > 0\), denominators can't be \(0\) and we can reduce both fractions to \(-1 = -1\) Sufficient

Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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20 May 2019, 13:45

Hi All,

We're told that A and B are INTEGERS, and B > 0. We're asked if (A-1)/(B+1) = A/B. This is a YES/NO question and can be approached in a number of different ways, including by TESTing VALUES.

(1) A = B - 4

IF.... B = 1, A = -3, then (-4)/(2) = -2 and (-3)/(1) = -3 and the answer to the question is NO B = 2, A = -2, then (-3)/(3) = -1 and (-2)/(2) = -1 and the answer to the question is YES Fact 1 is INSUFFICIENT

(2) A = -B IF.... B = 1, A = -1, then (-2)/(2) = -1 and (-1)/(1) = -1 and the answer to the question is YES B = 2, A = -2, then (-3)/(3) = -1 and (-2)/(2) = -1 and the answer to the question is YES B = 3, A = -3, then (-4)/(4) = -1 and (-3)/(3) = -1 and the answer to the question is YES This result occurs with any values you use, so the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT

Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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31 May 2019, 11:31

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• The numbers a and b are integers • Also, b > 0

We need to determine whether (a-1)/(b+1) = a/b Simplifying the given expression above, we get

• ab – b = ab + a

Or, a = -b

Hence, we need to determine whether a = -b or not. With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, a = b – 4

• However, from this statement we cannot determine whether a = -b or not.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, a = -b

• Therefore, we can say the given expression (a-1)/(b+1) = a/b is true

Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 2 individually, this step is not required. Hence, the correct answer choice is option B.
_________________

Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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09 Jul 2019, 10:01

GMATPrepNow wrote:

Bunuel wrote:

If a and b are integers, and b > 0, does \(\frac{a - 1}{b + 1} = \frac{a}{b}\) ?

(1) a = b − 4 (2) a = –b

Given: a and b are integers, and b > 0

Target question:Does (a - 1)/(b + 1) = a/b? This is a good candidate for rephrasing the target question.

Take the equation: (a - 1)/(b + 1) = a/b Cross multiply to get: (b)(a - 1) = (a)(b + 1) Expand both sides to get: ab - b = ab + a Subtract ab from both sides to get: -b = a Add b to both sides to get: 0 = a + b REPHRASED target question:Does a +b = 0?

Aside: The video below has tips on rephrasing the target question

Statement 1: a = b − 4 Let's TEST some values. There are several values of a and b that satisfy statement 1. Here are two: Case a: a = -2 and b = 2. In this case, a + b = (-2) + 2 = 0. So, the answer to the target question is YES, a+b = 0 Case b: a = -1 and b = 3. In this case, a + b = (-1) + 3 = 2. So, the answer to the target question is NO, a+b does NOT equal 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a = –b Add b to both sides to get: a + b = 0 The answer to the target question is YES, a+b = 0 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers, Brent

RELATED VIDEO FROM MY COURSE

Hi Brent !

Thankyou for the solution !! Wanted to know, 1) Are there any rules that we should keep in mind while cross multiplying variables ? For eg; all the variables must be positive, etc?

I know that in inequalities we do not cross multiply because of more than 1 possible answers.

2) Also, what is the significance of b>0 while solving this question? What if b>0 was not given to us?

Hope to see a reply!

Thanks

gmatclubot

Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?
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09 Jul 2019, 10:01