Last visit was: 17 Jul 2024, 06:23 It is currently 17 Jul 2024, 06:23
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
User avatar
Intern
Intern
Joined: 16 Aug 2020
Posts: 4
Own Kudos [?]: 16 [13]
Given Kudos: 9
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641635 [5]
Given Kudos: 85667
Send PM
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641635 [2]
Given Kudos: 85667
Send PM
User avatar
Intern
Intern
Joined: 16 Aug 2020
Posts: 4
Own Kudos [?]: 16 [0]
Given Kudos: 9
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Thanks for the answer!
VP
VP
Joined: 16 Feb 2015
Posts: 1067
Own Kudos [?]: 1051 [0]
Given Kudos: 30
Location: United States
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Explanation:

a + 2b = 3
As all answers in terms of a , so
2b = 3-a
b = (3-a)/2

Substituting value of b in below eqn
a + b < 0
a + (3-a)/2 < 0
(2a + 3 -a)/2 < 0
a+3 < 0
a < -3

So a will be also less than -2.

IMO-C
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7981
Own Kudos [?]: 4227 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
given a+b<0
so sum is -ve and a+2b=3
let a = -5 and b = 4
option C a<-2 is correct



arunkumarzz wrote:
If a + b < 0 and a + 2b = 3, then which of the following must be true?

A. a > 4

B. a < -4

C. a < -2

D. 2 < a < 4

E. None of the above.
Intern
Intern
Joined: 19 Jun 2018
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 174
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
If the answer is indeed, a < -2, that would simply mean even -3 applies.

So in that case,
-3+2b = 3
2b = 6
b = 3.

a+b <0,
-3+3 =0. Right?

Am i going wrong somewhere?
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19148
Own Kudos [?]: 22654 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Expert Reply
arunkumarzz wrote:
If a + b < 0 and a + 2b = 3, then which of the following must be true?

A. a > 4

B. a < -4

C. a < -2

D. 2 < a < 4

E. None of the above.


Solution:

Since a + 2b = 3, b = (3 - a)/2. Substituting this into the inequality, we have:

a + (3 - a)/2 < 0

2a + 3 - a < 0

a < -3

Since a is less than -3, a is also less than -2.

Answer: C

Director
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 233 [0]
Given Kudos: 432
Location: United States
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
a + b < 0 and a + 2b = 3

2b = 3 - a
b = (3 - a) / 2

Plug b into a + b < 0
a + (3 - a) / 2 < 0
2a + 3 - a < 0
a + 3 < 0
a < -3

If a < -3 then a < -2. Answer is C.
SVP
SVP
Joined: 27 May 2012
Posts: 1696
Own Kudos [?]: 1493 [1]
Given Kudos: 639
Send PM
If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
1
Kudos
Bunuel wrote:
arunkumarzz wrote:
If a + b < 0 and a + 2b = 3, then which of the following must be true?

A. a > 4

B. a < -4

C. a < -2

D. 2 < a < 4

E. None of the above.


From a + 2b = 3 we get that b = (3 - a)/2.

Substitute b = (3 - a)/2 into a + b < 0 to get a + (3 - a)/2 < 0. This simplifies in a < -3.

Less than -2 does not mean less than -3 as shown a could be -2.1

Now, if a < -3, then a is also less than -2.

Answer: C.


Bunuel maybe I am missing something or maybe not.
Let take a = -2.1 and check whether equation is satisfied by substituting the value of a in a + 2b = 3,we get \(b= \frac{5.1}{2}=2.55\)
Hence \(-2.1 + 2.55 \nless 0\)

we need \(a<-3 \)
if a<-2 then it need not be less than -3, as shown a could be -2.1 and the equation is not satisfied.
On the other hand if a<-4 then a is definitely less than -3

Wouldn't option B be a better answer choice with no ambiguity?

I guess it is the way we interpret the question, but if ans is C then shouldn't the equation hold true for a=-2.1?
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641635 [0]
Given Kudos: 85667
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Expert Reply
stne wrote:
Bunuel wrote:
arunkumarzz wrote:
If a + b < 0 and a + 2b = 3, then which of the following must be true?

A. a > 4

B. a < -4

C. a < -2

D. 2 < a < 4

E. None of the above.


From a + 2b = 3 we get that b = (3 - a)/2.

Substitute b = (3 - a)/2 into a + b < 0 to get a + (3 - a)/2 < 0. This simplifies in a < -3.

Less than -2 does not mean less than -3 as shown a could be -2.1

Now, if a < -3, then a is also less than -2.

Answer: C.


Bunuel maybe I am missing something or maybe not.
Let take a = -2.1 and check whether equation is satisfied by substituting the value of a in a + 2b = 3,we get \(b= \frac{5.1}{2}=2.55\)
Hence \(-2.1 + 2.55 \nless 0\)

we need \(a<-3 \)
if a<-2 then it need not be less than -3, as shown a could be -2.1 and the equation is not satisfied.
On the other hand if a<-4 then a is definitely less than -3

Wouldn't option B be a better answer choice with no ambiguity?

I guess it is the way we interpret the question, but if ans is C then shouldn't the equation hold true for a=-2.1?


a cannot be -2.1 because we know that a < -3 (-2.1 is not less than -3.).

To understand the concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5291
Own Kudos [?]: 4209 [0]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Asked: If a + b < 0 and a + 2b = 3, then which of the following must be true?

a + b < 0
a + 2b = 2a + 2b - a = 3
2(a+b) = a+3
Since 2(a + b) < 0
a + 3 < 0
a < -3
Since a < -3, it must be <-2

IMO C
User avatar
Intern
Intern
Joined: 19 Nov 2022
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 3
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
yeah...

i still don't get it
why not (b)

if a<-3

then it will be <-4...
if i am wrong can someone explain why ?
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641635 [0]
Given Kudos: 85667
Send PM
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Expert Reply
thelastzedi wrote:
Bunuel wrote:
arunkumarzz wrote:
If a + b < 0 and a + 2b = 3, then which of the following must be true?

A. a > 4

B. a < -4

C. a < -2

D. 2 < a < 4

E. None of the above.


From a + 2b = 3 we get that b = (3 - a)/2.

Substitute b = (3 - a)/2 into a + b < 0 to get a + (3 - a)/2 < 0. This simplifies in a < -3.

Now, if a < -3, then a is also less than -2.

Answer: C.



yeah...

i still don't get it
why not (b)

if a<-3

then it will be <-4...
if i am wrong can someone explain why ?


From a + b < 0 and a + 2b = 3 we can get that a < -3:

--------(-3)--------

C says a < -2. Pick any number from the green zone above. Whatever number you pick, if it's less than -3, then it will also be less than -2.

B says a < -4. If you pick a number from the green zone which is between -4 and -3, it won't be less than -4. Therefore, this option is NOT always true.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.

Hope it helps.
GMAT Club Bot
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
Moderator:
Math Expert
94372 posts