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# Is it true that a > b? (1) 2a > 2b (2) a + c > b + c

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Is it true that a > b? (1) 2a > 2b (2) a + c > b + c [#permalink]
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briozeal wrote:
Is it true that a > b?

(1) 2a > 2b
(2) a + c > b + c

Target question: Is a > b?

Statement 1: 2a > 2b
Divide both sides by 2 to get: a > b
The answer to the target question is YES, a IS greater than b
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a + c > b + c
Subtract b from both to get: a > b
The answer to the target question is YES, a IS greater than b
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Originally posted by BrentGMATPrepNow on 30 Jun 2019, 10:28.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:31, edited 1 time in total.
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Re: Is it true that a > b? (1) 2a > 2b (2) a + c > b + c [#permalink]
Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables and 1 Equation: Let the original condition in a DS question contain 2 variables and 1 Equation. Now, 2 variables and 1 Equation would generally require 1 more equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 1 more equations to match the numbers of variables and equations in the original condition, the logical answer is D.

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

Let’s apply the 3 steps suggested previously. [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 Is it true that a > b.

=> a > b OR a - b > 0

Second and the third step of Variable Approach: From the original condition, we have 2 variables (a and b) and 1 Equation(a - b > 0). To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take a look at each conditions .

Condition(1) tells us that the 2a > 2b = .

=> 2a > 2b = a > b => a - b> 0 - YES

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

Condition(2) tells us that a + c > b + c.

=> a + c > b + c => a > b => a - b > 0

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

Each condition alone is sufficient.

So, D is the correct answer.

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Re: Is it true that a > b? (1) 2a > 2b (2) a + c > b + c [#permalink]
Correct Option D

Is it true that a > b?
(1) 2a > 2b - Sufficient Divide both side by 2, we have a>b, here constant is Value "2"
(2) a + c > b + c - Sufficient Substract both side by c, we have a>b, here constant is Value "C"

Learning: Integer properties of operations :
Commutative Property: Property of addition and multiplication states that
the order of terms doesn’t matter,
the result will be the same.
Whether it is addition or multiplication,
swapping of terms will not change the sum or product.
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Re: Is it true that a > b? (1) 2a > 2b (2) a + c > b + c [#permalink]
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Re: Is it true that a > b? (1) 2a > 2b (2) a + c > b + c [#permalink]
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