joshbeall wrote:
Hi,
After taking a few practice GMAT exams, it's been clear I'm not fast enough on the quant section. I am used to having more time to work through problems, and I'm struggling with my pacing and strategy for the quant section.
I was just working on the following practice problem, after doing some quick math and going with what seemed reasonable, I picked the wrong answer (C, both statements together).
I went back and tried going through the complete process of figuring out the answer, but it took me several minutes, which highlights my problem. To those of you that did well on the GMAT quant section, what's your strategy for tackling a question like this and getting it in time? Is it just about being able to grind out the math faster?
Quote:
For integers a, b, x, and y, ab + yb = xy - yb. If a - b = 0, and x + y = 0, what is the value of x?
(1) a = 3
(2) y = -3
I started working my way through this problem and found that I found up with a squared value (in my case, \(y^2\)), and so I immediately figured "insufficient, because we could have a positive or negative root."
Well, I was wrong, and when I went back and reworked the problem more thoroughly, I think I found my issue:
ab + yb = xy - yb
ab + 2yb = xy
a - b = 0
a = b
x - y = 0
x = -y
Now, we're letting a = 3 (according to statement (1)), and we know a = b and x = -y, so we'll make those substitutions on the first equation:
3 * 3 + 2 * y * 3 = (-y) * y
9 + 6y = (-1)\(y^2\)
9 + 6y + \(y^2\) = 0
I looked at that for a 30 to 60 seconds and thought about how to factor it (maybe that's my problem?), and got:
(y + 3)(y + 3) = 0
And from that, I can see that y = -3, and with that you can solve for x. And a similar method could be used if you started with the value of y instead of a.
So, I'm left with two questions:
1) Did I solve this correctly? The
Veritas prep material tells me that both statements are sufficient, but it doesn't provide the details, so while I reached a definite answer, I'm not positive I got that definite answer via the correct mathematical process.
2) Do I just need to drill these types of problems so I can get faster at them, or am I missing a faster way to tackle these problems?
-Josh
p.s. I'm not sure the difficulty level, the prep material I'm using doesn't indicate the difficulty level.
DS is a very different and tricky beast to tame. You need to do the following things:
1. Understand the given statements, try to explain to yourself what is given
2. Then, explain in your own words what is asked Is it asking for a unique value or is it a yes/no type of DS question.
3. Analyse the statements given individually and to completion (this is where you made a mistake!)
4. Only when you are sure that statements are not sufficient on their own, go to combining the 2 statements.
Coming back to your question.
1. You are given that a,b,x,y are integers and ab+by=xy-by
Always try to simplify any given alegbraic equations given to you to whatever extent you can.
For this particular one, you get, ab+2by=xy. Additionally, you are given x+y=0 ---> x=-y or y=-x (just because we need x). Also given to us is a-b=0 ---> a=b. Substitute these values in the given algebraic equation, \(ab+2by=xy ---> a^2-2ax=-x^2 ---> a^2-2ax+x^2=0 ---> (a-x)^2=0 ---> a=x\)
Thus, after simplification you see that x=-y and x=a ---> any statement giving any of these 2 values will thus be sufficient.
You can not do anything more than what I have mentioned for this step.
2. The question is asking you about the value 'x'. Thus a statement giving you 1 and only 1 value will be sufficient. Otherwise, itll not be sufficient.
3. Per the analysis in step 1 above, a statement mentioning the value of a or y will be sufficient. Both statements individually provide both and hence both are sufficient ---> D is thus the correct answer.
4. No need for this step as both statements are sufficient on their own.
DS demands a lot of timed practice and making notes of typical traps in DS. Although this question did not require the use of the information about the 4 variables being integers, you should nonetheless always remember these small markers whenever you solve any DS question (or any GMAT question for that matter). Timing will be taken care of once you start recognising these things and applying the correct sequence of steps.
Hope this helps.
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