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We are GMAT Mentors, a non-profit focused on facilitating the free exchange of GMAT knowledge, support, and advice through one-on-one mentoring.
Since launching our service, we have gotten a lot of positive feedback from both mentees and mentors! We have had requests to start a tip/principle of the week, so we have decided to do just that. Each week we post a tip, trick, or principle focusing in either Verbal or Quant. You may already know some of these, but hopefully you will see something new! Check our posts for prior weeks tips!
Quant - Breaking down inequalities and absolute values in data sufficiency
A lot of people can get overwhelmed and confused when faced with absolute values within inequalities in data sufficiency. Below are some key points and reminders that can help you quickly and confidently solve these problems.
Write the absolute value as two scenarios, 1 positive and 1 negative, as in the below example. Breaking down the inequalities in this way will allow you to quickly and simply understand the values of X. Remember, you want to get through problems as quickly and efficiently as possible, while being confident you are getting the right answer.
Example:
|x-5|<4 can be broken into “x-5<4” and “-x+5<4”
“x-5<4” then becomes x<9
“-x+5<4” then becomes 1<x
Combining the two segments we get 1<x<9
Using the breakdown done in the above example, you can quickly and more confidently figure out the answer to a data sufficiency problem with absolute values and inequalities
Question: Is |x-6|>2?
Statement 1: |x-4|>3
Statement 2: |x-8|>1
Evaluating the question
(x-6)>2 results in x>8
-x+6>2 results in 4>x
This means that x is either greater than 8 or less than 4
Evaluating statement 1:
(x-4)>3 results in x>7
-x+4>3 results in 1>x
This means that x is either greater than 7 or less than 1. When you try 7.5 and 10, you quickly see that statement 1 is not sufficient (i.e., 7.5 the answer is no, 10 answer is yes)
Evaluating statement 2:
(x-8)>1 results in x>9
-x+8>1 results in 7>x
This means x can either be greater than 9 or less than 7. Again, you can use 5 and 10 to quickly see this doesn't work (i.e., 5 results in no, 10 results in yes)
Evaluating the statements combined
We now understand from statement 1 that X>7 and 1>x
From statement 2 we understand that X>9 and 7>x
When you combine statements, use the more limiting inequality for each direction X can go (i.e., use X>9 because less large values of X can be used, and use 1>x because less small values can be used)
This results in X>9 and 1>x, which now answers yes to the question in every scenario - the answer is C
Thanks for reading and please let us know if you have any questions!
If you would like to become a mentee and receive personalized support or become a mentor and help others, please check out our website or email us!
Email: [email protected]
Website: https://www.gmatmentors.com
Since launching our service, we have gotten a lot of positive feedback from both mentees and mentors! We have had requests to start a tip/principle of the week, so we have decided to do just that. Each week we post a tip, trick, or principle focusing in either Verbal or Quant. You may already know some of these, but hopefully you will see something new! Check our posts for prior weeks tips!
Quant - Breaking down inequalities and absolute values in data sufficiency
A lot of people can get overwhelmed and confused when faced with absolute values within inequalities in data sufficiency. Below are some key points and reminders that can help you quickly and confidently solve these problems.
Write the absolute value as two scenarios, 1 positive and 1 negative, as in the below example. Breaking down the inequalities in this way will allow you to quickly and simply understand the values of X. Remember, you want to get through problems as quickly and efficiently as possible, while being confident you are getting the right answer.
Example:
|x-5|<4 can be broken into “x-5<4” and “-x+5<4”
“x-5<4” then becomes x<9
“-x+5<4” then becomes 1<x
Combining the two segments we get 1<x<9
Using the breakdown done in the above example, you can quickly and more confidently figure out the answer to a data sufficiency problem with absolute values and inequalities
Question: Is |x-6|>2?
Statement 1: |x-4|>3
Statement 2: |x-8|>1
Evaluating the question
(x-6)>2 results in x>8
-x+6>2 results in 4>x
This means that x is either greater than 8 or less than 4
Evaluating statement 1:
(x-4)>3 results in x>7
-x+4>3 results in 1>x
This means that x is either greater than 7 or less than 1. When you try 7.5 and 10, you quickly see that statement 1 is not sufficient (i.e., 7.5 the answer is no, 10 answer is yes)
Evaluating statement 2:
(x-8)>1 results in x>9
-x+8>1 results in 7>x
This means x can either be greater than 9 or less than 7. Again, you can use 5 and 10 to quickly see this doesn't work (i.e., 5 results in no, 10 results in yes)
Evaluating the statements combined
We now understand from statement 1 that X>7 and 1>x
From statement 2 we understand that X>9 and 7>x
When you combine statements, use the more limiting inequality for each direction X can go (i.e., use X>9 because less large values of X can be used, and use 1>x because less small values can be used)
This results in X>9 and 1>x, which now answers yes to the question in every scenario - the answer is C
Thanks for reading and please let us know if you have any questions!
If you would like to become a mentee and receive personalized support or become a mentor and help others, please check out our website or email us!
Email: [email protected]
Website: https://www.gmatmentors.com
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