Last visit was: 23 May 2024, 12:02 It is currently 23 May 2024, 12:02
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93435
Own Kudos [?]: 626111 [110]
Given Kudos: 81940
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30308 [36]
Given Kudos: 799
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Own Kudos [?]: 1785 [8]
Given Kudos: 26
General Discussion
Intern
Joined: 24 Apr 2019
Posts: 12
Own Kudos [?]: 92 [1]
Given Kudos: 2
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
1
Kudos
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

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.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 8028
Own Kudos [?]: 4127 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
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

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

#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
Manager
Joined: 25 Jul 2018
Posts: 53
Own Kudos [?]: 402 [1]
Given Kudos: 257
Location: Uzbekistan
Concentration: Finance, Organizational Behavior
GRE 1: Q168 V167
GPA: 3.85
WE:Project Management (Investment Banking)
If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
1
Kudos
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

Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18899
Own Kudos [?]: 22304 [5]
Given Kudos: 285
Location: United States (CA)
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
2
Kudos
2
Bookmarks
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 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.

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11693 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
2
Kudos
1
Bookmarks
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

GMAT assassins aren't born, they're made,
Rich
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3723
Own Kudos [?]: 17017 [0]
Given Kudos: 165
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]

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.
Intern
Joined: 09 Mar 2020
Posts: 1
Own Kudos [?]: 2 [2]
Given Kudos: 0
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
2
Kudos
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) ?
Math Expert
Joined: 02 Sep 2009
Posts: 93435
Own Kudos [?]: 626111 [0]
Given Kudos: 81940
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
Daph wrote:
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) ?

The correct answer to this question is B, not D. This is explained above in several posts. Please re-read the thread carefully. Hope it helps.
Tutor
Joined: 17 Jul 2019
Posts: 1301
Own Kudos [?]: 2227 [5]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
3
Kudos
2
Bookmarks
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

Originally posted by avigutman on 18 Oct 2020, 18:39.
Last edited by avigutman on 30 Nov 2020, 14:10, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10149
Own Kudos [?]: 16720 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
1
Bookmarks
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.

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

Originally posted by MathRevolution on 19 Oct 2020, 00:10.
Last edited by MathRevolution on 08 Jan 2021, 00:00, edited 1 time in total.
Intern
Joined: 06 Jul 2020
Posts: 12
Own Kudos [?]: 4 [3]
Given Kudos: 74
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
3
Kudos
Bunuel wrote:
Daph wrote:
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) ?

The correct answer to this question is B, not D. This is explained above in several posts. Please re-read the thread carefully. Hope it helps.

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!
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11693 [4]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
3
Kudos
1
Bookmarks
Irising wrote:
Bunuel wrote:
Daph wrote:
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) ?

The correct answer to this question is B, not D. This is explained above in several posts. Please re-read the thread carefully. Hope it helps.

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!

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
Intern
Joined: 06 Jul 2020
Posts: 12
Own Kudos [?]: 4 [0]
Given Kudos: 74
If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
Thank you very much, Rich! It makes sense now!!
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5985
Own Kudos [?]: 13505 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
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

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Intern
Joined: 31 Aug 2016
Posts: 7
Own Kudos [?]: 2 [0]
Given Kudos: 138
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 33151
Own Kudos [?]: 829 [0]
Given Kudos: 0
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ? [#permalink]
Moderator:
Math Expert
93435 posts