Is ax = 6 - bx ?

Hi All,

The 'algebra approach' to this DS question is pretty straight-forward (and an easy way to get to the correct answer). If you don't recognize that approach though, you can still answer this question by TESTing VALUES.

We're asked if AX = 6 - BX. This is a YES/NO question

Fact 1: A = B

IF....
X = 1
A = B = 3
Then the answer to the question is YES

IF....
X = 1
A = B = 1
Then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: 2AX = 6

Simplifying, we know that AX = 3

IF...
X = 1
A = 3
B = 3
Then the answer to the question is YES

X = 1
A = 3
B = 2
Then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
A = B
AX = 3

Since AX = 3 and A=B, we know that BX also = 3
Plugging those 'values' into the question gives us....
Is 3 = 6 - 3?
The answer is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

1) a= b
2)2ax=6

stem 1:
a=b ; we dont know about X ; not sufficient
stem 2:
2ax=6 ; we dont know about b ; not sufficient
Clubbing stem 1 and stem2 : 2ax=6 ; ie ax= 6-ax and a=b so ax =6-bx hence C is the option

Is ax = 6 - bx ?

(1) a = b
We can rewrite the equation as ax + bx = 6 ?
Since a=b the outcome is dependent on x. Since we have no information on x, this statement is not sufficient.

(2) 2ax = 6
This means ax = 3
bx + 3 = 6 ?
We have no information on b or x so this statement is not sufficient.

Statements 1 and 2 together are sufficient.
ax + bx =6 ? : ax = 3, and a=b therefore bx = ax
3 + 3 = 6

C is correct. Here's why:

(1) a =b

NOT SUFFICIENT - we don't know what 2ax is equal to

(2) 2ax = 6

NOT SUFFICIENT - we don't know what bx is equal to


Together - (1) + (2) - We know ax = bx = 3, so 3 + 3 = 6

SUFFICIENT

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