|2a| + |6a + b| = 24, what is the value of 4a + b?

Question

(1) 4a + b > 0
(2) 8a + b > 0

yashikaaggarwal · Answer

|2a| + |6a + b| = 24, what is the value of 4a + b?

(1) 4a + b > 0
Even if A and B both are positive, they could hold a series of values.
Can't specifically tell the value of 4a+b. (Insufficient)

(2) 8a + b > 0
Similar to 1st statement, A and B could hold a series of values.
Can't specifically tell the value of 4a+b. (Insufficient)

Combining both,
Still no specific value of either of a and b to determine value.

Answer is E

Posted from my mobile device

gloomybison · Answer

I would say looking at it from a scenario perspective may work;
so we don't know the signs of 2a and 6a+b, hence we need to employ different scenarios to see the one that would give us a value for 4a + b

Scenario 1
2a<0
6a+b<0

This scenario would give us
-2a-6a-b=24
-8a-b=24

Scenario 2
2a>0
6a+b<0

This scenario would give us
2a-6a-b=24
-4a-b=24

Scenario 3
2a<0
6a+b>0

This scenario would give us
-2a+6a+b=24
4a+b=24

Scenario 4
2a>0
6a+b>0

This scenario would give us
2a+6a+b=24
8a+b=24

As you can see only scenario 2 & 3 tell us a potential value for 4a+b
so looking at them
Scenario 3
2a<0 -> we can write it as -2a>0
6a+b>0

summing both conditions will give us 4a+b>0
mind that this scenario gave us the value for 4a+b as 24

Scenario 2
2a>0 -> we can write it as -2a<0
6a+b<0

summing both conditions will give us 4a+b<0
mind that this scenario gave us the value for 4a+b as -24

so whether 4a+b is positive or negative it would give us a value
so IMO the answer is A

TarunKumar1234 · Answer

|2a| + |6a + b| = 24, what is the value of 4a + b?

(1) 4a + b > 0
Even if A and B both are positive, they could hold a series of values.
Can't specifically tell the value of 4a+b. (Insufficient)

(2) 8a + b > 0
Similar to 1st statement, A and B could hold a series of values.
Can't specifically tell the value of 4a+b. (Insufficient)

Combining both,
Still no specific value of either of a and b to determine value.

Answer is E

Posted from my mobile device

umangshah · Answer

|2a| + |6a + b| = 24, what is the value of 4a + b?

(1) 4a + b > 0
(2) 8a + b > 0

Bunuel

Hi, Can you explain why OE is E.
Upon evaluating the equation we can find that 4a+b=+/-24 and by using statement 1 we get one unique solution to the question which is 4a+b=24. 
Isn't Statement 1 sufficient to answer the question?

Thanks

Bunuel · Answer

Not sure how you got that 4a + b is either 24 or -24 bur the OA is E. For instance, if a = 1 and b = 16, then 4a + b ≠ 24.

Score-Quest · Answer

TarunKumar1234 , Statement 1 does not imply that a<0 and (6a+b)>0. Case 1 could also potentially be true because 4a+b>0 could also occur when a>0 and (6a+b) >0. For e.g., if a=2 and b=8, Case 1 will be satisfied but 4a+b will also be greater than 0

umangshah  hope this helps you as well!

Apeksha2101 · Answer

I followed the same approach, then why answer E is right?

rahulsinha21 · Answer

Bunuel  - If you create 4 scenarios and simply the equations you will get 4a+b=24 or -24 for (+,-) and (-,+) case.

So if you get an out right value of 24 after keeping (a), should the answer be A.

If no, can you please explain how to solve this.

|2a| + |6a + b| = 24, what is the value of 4a + b?

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