if a+b=10, what is the value of b?

[AsadA969]

If a+b=10, what is the value of b?
1) a=2
2) b=4a

Correct choice D
Source: TargetTestPrep

[AsadA969]

If a+b=10, what is the value of b?
1) a=2
2) b=4a

Correct choice D
Source: TargetTestPrep

I'm little scared about this types of question.
What if a=1 in statement 1? if this is the thing then statement 2 provides a=2 (when it is calculated). Are these different values of a in highlighted part violate the rules of DS? Is this type of question (if a=1) legit for GMAT?

[StaceyKoprince]

The statements are always facts. Since statement (1) says that a = 2, there is no other possible value for a according to this statement.

Statement (2) is a new fact. Statement (2) could be completely different information, it could be information that partially overlaps with the information in statement (1), and sometimes, it actually turns out to be the exact same information as in statement (1).

But when you first get to the second statement, forget about statement (1)—literally pretend you never read it. Evaluate that second statement all by itself.

So in this problem, you would do something like this:
Given (fact): a + b = 10
Question: b = ? (Value)

(1) a = 2
This is a fact. If a = 2, then you can use the formula given in the question stem (a + b = 10) to find the value of b. So this statement is sufficient to answer the question. Eliminate answers (BCE).

(2) b = 4a
This is a fact. Forget what statement (1) said—that doesn't exist.
You do still have the fact given in the question stem: a + b = 10.
Can you combine those two facts to find a single value for b?

These are both linear equations and they are two different equations. So you could substitute one equation into the other:
a + 4a = 10 to solve for a single value for a, and then once you find a, you could plug it into either of the original equations to find a single value for b. So this statement is also sufficient to answer the question. The correct answer is (D).

Only look at the two statements together after you have first looked at them separately and eliminated answers A, B, and D. If you are down to answers C and E, then you can look at the two statements together.

[AsadA969]

The statements are always facts. Since statement (1) says that a = 2, there is no other possible value for a according to this statement.

Statement (2) is a new fact. Statement (2) could be completely different information, it could be information that partially overlaps with the information in statement (1), and sometimes, it actually turns out to be the exact same information as in statement (1).

But when you first get to the second statement, forget about statement (1)—literally pretend you never read it. Evaluate that second statement all by itself.

So in this problem, you would do something like this:
Given (fact): a + b = 10
Question: b = ? (Value)

(1) a = 2
This is a fact. If a = 2, then you can use the formula given in the question stem (a + b = 10) to find the value of b. So this statement is sufficient to answer the question. Eliminate answers (BCE).

(2) b = 4a
This is a fact. Forget what statement (1) said—that doesn't exist.
You do still have the fact given in the question stem: a + b = 10.
Can you combine those two facts to find a single value for b?

These are both linear equations and they are two different equations. So you could substitute one equation into the other:
a + 4a = 10 to solve for a single value for a, and then once you find a, you could plug it into either of the original equations to find a single value for b. So this statement is also sufficient to answer the question. The correct answer is (D).

Only look at the two statements together after you have first looked at them separately and eliminated answers A, B, and D. If you are down to answers C and E, then you can look at the two statements together.

Hello Stacey,
Thanks for the explanation. I read your explanation attentively. Actually, your explanation is totally different to my asking question. Here you go for question again that I intend to mean, please.

The main question is:
If a+b=10, what is the value of b?
1) a=2
2) b=4a
The correct choice is D
---------------------
The changed version of this question is:
If a+b=10, what is the value of b?
1) a=1
2) b=4a
Do you think that the correct choice is D too in this changed version?
Or,
Do you think that the changed version is wrong since the value of a is different (in statement 1, a=1; and in statement 2, a=2) in both statements--the statements in data sufficiency don't contradict each other. In short, is this question legit question for GMAT?

[Whit Garner]

Do you think that the changed version is wrong since the value of a is different (in statement 1, a=1; and in statement 2, a=2) in both statements--the statements in data sufficiency don't contradict each other. In short, is this question legit question for GMAT?

For all Data Sufficiency questions, the two statements are facts; in other words, they both must be based on the same true information. For that reason, the GMAT will never give you a question where the values of certain variables or the answer to the question vary from statement to statement: they cannot give conflicting information!

I hope this helps!