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

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arunkumarzz
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If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   14 Oct 2020, 02:25
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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.
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C
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Bunuel
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   14 Oct 2020, 02:32
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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.
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   14 Oct 2020, 02:33
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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.


To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   14 Oct 2020, 02:36
Thanks for the answer!
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   14 Oct 2020, 02:48
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
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   14 Oct 2020, 04:15
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.
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   15 Oct 2020, 00:24
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?
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   17 Oct 2020, 13:08
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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
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   17 Oct 2020, 13:30
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.
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If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   18 Oct 2020, 10:19
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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?
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   18 Oct 2020, 10:30
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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.
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   18 Oct 2020, 10:37
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
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   06 Mar 2023, 10:50
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 ?
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink] New post   18 Mar 2023, 02:02
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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.
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true? [#permalink]
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