If a and b are integers, and b 0, does (a - 1)/(b + 1) = a/b ?

Question

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

BrentGMATPrepNow · Accepted Answer

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
 https://www.youtube.com/watch?v=MyG1K3ee69w

DavidTutorexamPAL · Answer

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.

(B) is our answer.

EDIT: fixed typos

TornDilemma · Answer

On Simplifying, the statement reduces to find whether a=-b

Statement 1:

If b=2, a=-2, here a=-b, but if a=3, b=-1, here a is not equal to -b. Insufficient.

Statement 2:
a=-b, that's what is being asked. Sufficient.

IMO, Option B.

Archit3110 · Answer

\frac{a - 1}{b + 1} = \frac{a}{b}  ?

#1
a=b-4
we get
b-3/b+1 = b-4/b
not sufficeint
#2
a=-b
-b-1/b+1 = -b/b = -1
sufficient
IMO B

ShukhratJon · Answer

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 The answer is B

ScottTargetTestPrep · Answer

We are given that a and b are integers and need to determine whether (a -1)/(b + 1) = a/b.

Since we also know b is greater than zero, we can multiply both sides by b, and we have:

ab - b = ab + a

-b = a

Therefore, if a = -b, then (a -1)/(b + 1) = a/b.

Statement One Alone:

a = b - 4

This does not mean a = -b. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

a = -b

This exactly what we have concluded in the stem analysis. Statement two alone is sufficient to answer the question.

Answer: B

EMPOWERgmatRichC · Answer

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

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

EgmatQuantExpert · Answer

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.

Daph · Answer

If we solve the equation using a = b-4, it gives b=2 , a=-2, which holds true for (a - 1)/(b + 1) = a/b ?
Doesn't this mean each answer choice alone is sufficient (D) ?

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=qliQEi7YsB0

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

The first step of the Variable Approach: The first step and the priority is to modify and recheck the original condition and the question to suit the type of information given in the condition.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Learn the 3 steps. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find does \(\frac{(a -1)}{(b + 1)} = \frac{a}{b}\). - where 'a' and 'b' are integers and b > 0

=> \(\frac{(a -1)}{(b + 1)} = \frac{a}{b}\)

=> b * (a - 1) = a * ( b + 1)

=> ab - b = ab + a

=> a + b = 0 or a = -b

We have to find whether a = -b

Condition(1) tells us that a = b - 4.

=> If a = -2 and b = 2 then a = b - 4 and a + b = (-2) + 2 = 0 - YES

=> But if a = -1 and b = 3 then a = b - 4 and a + b = (-1) + 3 ≠ 0 - NO

Since the answer is not a unique YES or NO , condition(1) alone is not sufficient by CMT 1.

Condition(2) tells us that a = -b .

=> This is what we are asked in the question stem. - YES

Since the answer is a unique YES , condition(2) alone is sufficient by CMT 1.

Condition(2) alone is sufficient.

So, B is the correct answer.

Answer: B

SAVE TIME: By Variable Approach[MODIFICATION], check the condition quickly and separately and mark answer as A or B.

Irising · Answer

I have the same question as Daph. I read all posts carefully and still can't understand why.

From the given equation, I was able to get a+b=0 or a=-b. Several expert posts got this too. Then based on statement 1, given that a=b-4, I substituted a for -b, -b=b-4 and solved for b, b=2. Then a = -2. Why is this approach wrong? I am confused as to why we can't solve for a and b when it is given that a=-b. I don't understand why people are using testing case a=-3 and b=1 when clearly in this case a does not equal to -b. The more I say it, the more confused I am. Please help!

EMPOWERgmatRichC · Answer

Hi Irising,

In DS questions, you have to be careful about confusing information that you are given with the specific QUESTION that is asked. In this prompt, you can 'rewrite' the question by cross-multiplying the fractions, so that the question becomes "Does A = -B?" To be clear, that is a QUESTION; that is NOT information for you to use.

The prompt does give us some information to start off with though: both A and B are INTEGERS and B > 0.

In Fact 1, we're given additional information: A = B - 4

Here, we can choose values for A and B that fit THIS equation - but you can probably see that there are several values for A and B that will fit what we're told (A = -2 and B = 2 is one of the possible pairs of numbers, but it is NOT the only one). With the information in Fact 1, depending on the values for A and B, the answer to the question will sometimes be 'YES', but it will also sometimes be 'NO.'

GMAT assassins aren't born, they're made,
Rich

Irising · Answer

Thank you very much, Rich! It makes sense now!!

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=7osxgcu0kQg

Ceekey · Answer

There are a lot of explanations on approaches, so I wont line out another approach.

However, what I often ask myself when reading such questions in DS is:  What is the actual question?

The term provided in the question is obviously a flashbang to confuse people. By thinking about the actual question (simplifying), these problems get a lot easier.

RRINSEAD2025 · Answer

Scott,

If -b = a or b = -a and if statement one is telling us that b = a + 4, why is statement one not sufficient? I've read the explanations but I'm not quite sure why 1 alone isn't suficient. Since statement one is giving us a clear answer that b is not equal to -a?

Thank you,

Bunuel · Answer

Why not? What if a = -2 and b = 2? In this case a = -b and a = b - 4.

If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?

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