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When the question says "What is the value of..." the question is asking if we have enough information to determine a single value. There are 2 variables in the equation provided (x and y) and S1 only gives us a value for x. The equation is not equal to anything, ti's just an equation. IF THE QUESTON HAD provided the equation of \(6x^2 + 9y^2 = 33\), then providing us with the value of a single variable WOULD be enough to find the value of y and therefore would be sufficient, but this information is still missing. Look at every problem as if it has 2 varaibles.
a = b
Sometimes we know one variable, such as a = 2. If a = 2, then b = 2. If we have a more complext problem, we have \(a^2 + b = c\). Now we have 3 variables. This is similar to the equation given. While the question isn't written with that third variable visible, it is present. Its the variable we're trying to solve for. It \(6x^2 + 9y^2 = z\) and we need to find z. So anytime you have 3 variables, in order to solve for the entire equation to a single value, you need to know the value of AT LEAST 2 of those variables. [There are exceptions to this, but as a general rule, knowing the information necessary to solve the equation is a vital step in doing Data Sufficiency questions.]
What is the value of the following expression: \(6x^2 + 9y^2?\)
1. \(x = 2\) 2. \(6y^2 + 4x^2 = 22\)
* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient
Statement 1 provides us with value of x but it is insufficient to answer the whole question
Statement 2 provides us with necessary information: we need to multiply the second statement times 1.5 and we will get our result: \(33 = 9y^2 + 6x^2\)
How is x = 2 no sufficient? If we know the value for x we can solve for y and then add the two.
------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.
smarinov, you could solve for Y ONLY and ONLY provided that you knew the original equation equals zero or any other number. Yes, you know x=2. Just imagine the other side of the equation is 0, you say then you can solve for y and y=square root of 24/9
What if the original equation was 6x^2 + 9y^2=6 ?? Actually the question is asking us to find this 6. Then substituting 2 for x, y would equal 2, which is different from the Y we got by assuming zero is on the other side of the equation.
Hope it helps _________________
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Not sure if this was indeed a very hard DS question. Was relatively straight forward that statement (ii) is sufficient. I had to re-check if I was missing anything with statement (i) since (ii) was rather obvious.
The answer I chose was B. _________________
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Statement 1: Useless. We have no information about y Statement 2: Can be reduced to 2x^2 + 3y^2 = 11. The equation in the question stem is fairly similar to this one ----> by multiplying the equation in statement 2 by 3 we end up with the equation in the stem. Therefore, it must also equal 33. Sufficient.
It's basic algebra; an expression is different than an equation.
"An equation contains an equal sign, expressions do not. An expression, even one that contains variables, represents a value. Even if you don't know that value, nothing you do to an expression can change its value." mgmat