Last visit was: 14 Sep 2024, 07:03 It is currently 14 Sep 2024, 07:03
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If a + (1/b) = 400, and a < -300, then

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 08 Jun 2013
Posts: 456
Own Kudos [?]: 770 [3]
Given Kudos: 118
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
WE:Consulting (Other)
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31311 [4]
Given Kudos: 799
General Discussion
Director
Joined: 20 Feb 2015
Posts: 626
Own Kudos [?]: 742 [2]
Given Kudos: 74
Concentration: Strategy, General Management
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19460
Own Kudos [?]: 23238 [0]
Given Kudos: 286
Location: United States (CA)
Re: If a + (1/b) = 400, and a < -300, then [#permalink]
Harshgmat
If a + (1/b) = 400, and a < -300, then which of the following must be true?

A) b > -700
B) b > 1/(-100)
C) b > 1/ 300
D) b > 700
E) b < 1/700

Since a = 400 - 1/b, we have:

400 - 1/b < -300

700 < 1/b

We note at this point that b is positive (which is because a is negative and a + (1/b) is positive; therefore 1/b must be positive, therefore b must be positive). Let’s multiply each side of this inequality by the positive number b:

700b < 1

b < 1/700

Tutor
Joined: 12 Oct 2010
Status:GMATH founder
Posts: 891
Own Kudos [?]: 1447 [0]
Given Kudos: 56
If a + (1/b) = 400, and a < -300, then [#permalink]
Harshgmat
If a + (1/b) = 400, and a < -300, then which of the following must be true?

A) b > -700
B) b > 1/(-100)
C) b > 1/ 300
D) b > 700
E) b < 1/700

The winning triad asks for DATA connected to FOCUS... but it is the FOCUS the fundamental leg of the triad!

$$?\,\,\,:\,\,\,b\,\,{\rm{inequality}}$$

Hence:

$$a + {1 \over b} = 400\,\,\,\, \Rightarrow \,\,\,{1 \over b} = 400 - a = 400 + \left( { - a} \right)\mathop > \limits^{\left( * \right)} 700$$

$$\left( * \right)\,\,\,a < - 300\,\,\,\, \Rightarrow \,\,\, - a > 300$$

$${1 \over b} > 700\,\,\,\,\mathop \Rightarrow \limits^{{\rm{positives}}!} \,\,\,\,\,?\,\,:\,\,b < {1 \over {700}}$$

Do not forget the two "Golden rules": when numbers have the same signs, the greater has the lower reciprocal... Mathematically speaking:

$$x > y > 0\,\,\,\mathop \Rightarrow \limits^{:\,\,xy\, > \,0} \,\,\,{1 \over x} < {1 \over y}$$

$$q < w < 0\,\,\,\mathop \Rightarrow \limits^{:\,\,qw\, > \,0} \,\,\,{1 \over w} < {1 \over q}$$

$$\left( {x = {1 \over b}\,\,\,{\rm{and}}\,\,y = 700\,\,{\rm{in}}\,\,{\rm{our}}\,\,{\rm{case}}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
Non-Human User
Joined: 09 Sep 2013
Posts: 34832
Own Kudos [?]: 878 [0]
Given Kudos: 0
Re: If a + (1/b) = 400, and a < -300, then [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If a + (1/b) = 400, and a < -300, then [#permalink]
Moderator:
Math Expert
95503 posts