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Negative Values

This topic has 4 expert replies and 0 member replies
kamalakarthi Senior | Next Rank: 100 Posts Default Avatar
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Negative Values

Post Mon Aug 07, 2017 10:51 am
Hi,

This is from MCAT test.

In this below question, I got to the right answer after testing for various numbers. But I took long time to solve this question.
How can I improve my choosing the right numbers.

I tried with a=5 and b=3 then I tried with A=1 and B=-1 then I tried with A=-2 and B=-3





ttps://postimg.org/image/esv38uxhh/" target="_blank">

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Post Fri Aug 18, 2017 1:18 pm
We could take a conceptual approach too. Remembering that |x - y| = the distance from x to y on the number line, we could say

A::
|a + b| - |a - b| < 0
|a + b| < |a - b|
the distance from a to -b < the distance from a to b

This is definitely possible.

B::

|a + b| < |a|
the distance from a to -b < the distance from a to 0

Also totally possible!

C::

|2a + b| < |a + b|
the distance from 2a to -b < the distance from a to -b

Yup, works!

D::

a² - 2|ab| + b² < 0

(|a| - |b|)² < 0

Aha! No such thing as a negative square - at least not in GMAT math - so we've found our answer.

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Post Fri Aug 18, 2017 1:13 pm
Let me add a (semi-)algebraic approach too.

Suppose that each answer is negative. For instance, for answer B that would give us

|a + b| - |a| < 0, or

|a + b| < |a|

This is obviously possible, if a = 3 and b = -1, so a negative result could work here.

Continuing this way through the other answers, you might find plugging in faster and simpler.

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Matt@VeritasPrep GMAT Instructor
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Post Fri Aug 18, 2017 1:18 pm
We could take a conceptual approach too. Remembering that |x - y| = the distance from x to y on the number line, we could say

A::
|a + b| - |a - b| < 0
|a + b| < |a - b|
the distance from a to -b < the distance from a to b

This is definitely possible.

B::

|a + b| < |a|
the distance from a to -b < the distance from a to 0

Also totally possible!

C::

|2a + b| < |a + b|
the distance from 2a to -b < the distance from a to -b

Yup, works!

D::

a² - 2|ab| + b² < 0

(|a| - |b|)² < 0

Aha! No such thing as a negative square - at least not in GMAT math - so we've found our answer.

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GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
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625
Target GMAT Score:
V51
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780
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Post Fri Aug 18, 2017 1:13 pm
Let me add a (semi-)algebraic approach too.

Suppose that each answer is negative. For instance, for answer B that would give us

|a + b| - |a| < 0, or

|a + b| < |a|

This is obviously possible, if a = 3 and b = -1, so a negative result could work here.

Continuing this way through the other answers, you might find plugging in faster and simpler.

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

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