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Math Expert V
Joined: 02 Sep 2009
Posts: 60646
If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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12 00:00

Difficulty:   35% (medium)

Question Stats: 66% (01:37) correct 34% (02:05) wrong based on 570 sessions

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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

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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1155
If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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3
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.

EDIT: fixed typos
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Originally posted by DavidTutorexamPAL on 26 Apr 2019, 14:34.
Last edited by DavidTutorexamPAL on 07 May 2019, 06:39, edited 2 times in total.
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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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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

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.
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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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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

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

#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
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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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2
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

Cheers,
Brent

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

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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

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

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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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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 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.

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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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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

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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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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.
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Re: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?  [#permalink]

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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

Cheers,
Brent

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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?

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