If a + b

Question

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.

Bunuel · Accepted Answer

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.

Bunuel · Answer

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

arunkumarzz · Answer

Thanks for the answer!

rajatchopra1994 · Answer

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

Archit3110 · Answer

given a+b<0
so sum is -ve and a+2b=3
let a = -5 and b = 4
option C a<-2 is correct

Adithyasirish · Answer

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?

ScottTargetTestPrep · Answer

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

Basshead · Answer

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.

stne · Answer

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 
less 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?

Bunuel · Answer

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 .

Kinshook · Answer

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

thelastzedi · Answer

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 ?

Bunuel · Answer

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.

Kinshook · Answer

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

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

3-a < -2a
a < - 3 < - 2

IMO C

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

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GMAT Problem Solving (PS) Questions

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

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