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

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by AbeNeedsAnswers » Sun Apr 28, 2019 3:15 pm

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

(1) a = b − 4
(2) a = -b

B

Source: Official Guide 2020
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Source: — Data Sufficiency |

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by Ian Stewart » Mon Apr 29, 2019 3:12 am
We can rewrite the question:

Is (a-1)/(b+1) = a/b ?
Is ab - b = ab + a ?
Is -b = a?

from which we can see that Statement 2 tells us exactly what we want, while Statement 1 does not (if Statement 1 is true, the answer may be 'yes', if b = 2 and a = -2, but can also be no for any other values).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by Brent@GMATPrepNow » Mon Apr 29, 2019 8:20 am
AbeNeedsAnswers wrote:If a and b are integers, and b > 0, does (a−1)/(b+1) = a/b ?

(1) a = b − 4
(2) a = -b

B

Source: Official Guide 2020
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: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Mon May 20, 2019 11:36 am
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
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