The beautiful thing about Data Sufficiency is that we’re allowed not to do all of the calculations that a Problem Solving problem might require. Still, leave it to the GMAT to try to suck you into doing more than you need to do in order to get to the answer.
Normally, I just toss you into a problem and then we discuss, but today I’m going to warn you: the GMATPrep® problem that I’m about to give you is going to do its best to make you waste time. As you try this problem, ask yourself, “Do I really need to do that calculation? Is there an easier way?”
Try this problem from the GMATPrep free exams.
“If it took Carlos ½ hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5,280 feet)
(1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
(2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.”
(I haven’t put in the DS answer choices. If you don’t know DS well enough to know what the answer choices are already, come back to this article later.)
Ready? Okay, first, let’s understand what’s going on.
Glance: DS. Story problem. 1 mile = 5,280 feet catches my eye and my immediate reaction is, “Ugh,” followed by, “I am not converting stuff in this problem! No thank you!”
(Note: I haven’t even read the problem yet. I’m just annoyed by the idea of conversion in general, and this is DS, so I’m going to do my best to find a way around it.)
Read: C bicycles for half an hour. The question is an inequality … interesting. It’s a yes/no question.
Jot:
Note that I did not jot down the conversion from miles to feet. I’m still determined to avoid having to use that!
Next, I need to think about how to approach this in order to minimize my calculations. There’s not a lot I can do with the question stem, so it’s time to look at the statements.
What now? Think before you work.
Hmm. Each statement is an inequality. Annoyingly, the rate is in feet per second, even though the question stem talks about biking for half an hour. Another conversion!
Okay, think about this. If they gave me an exact number for the rate, I could of course solve. But they only told me that the rate is greater than 16 f/s (for statement 1).
On Data Sufficiency, when they give you an inequality with a yes/no question, the task is to figure out whether the range of possible values is going to give you one definitive answer (either Always Yes or Always No = sufficient), or whether that range will permit a Sometimes Yes, Sometimes No situation (= insufficient).
The key is to test the limit: the integer at the outside edge of the range (even if it is not included in the range!). For statement (1), that means testing r = 16 f/s. If that rate already means that the distance is greater than 6 miles, then all higher rates will also result in a distance greater than 6 miles.
If, on the other hand, r = 16 f/s results in a distance of less than 6 miles, then some higher rates will return that same result … but once the rate gets high enough, the distance will become greater than 6 miles.
Try it out.
Statement (1) : r > 16 f/s
Try r = 16 f/s
Convert to feet per half hour, since we know Carlos rides for half an hour:
=(16 f/sec)(60 sec/min)(30 min/ half hour)
move some zeroes around to get:
=(1600)(18)
Now pause again and think about how to avoid multiplying that out. Also, glance at the conversion for miles to feet: 1 mile = 5,280 feet.
Feet to miles … feet to miles … how to get from feet to miles?
Try multiples of 1600 until you get closer to 1 mile, or 5,280 feet.
1600
3200
4800
Hmm. (1600)(3) = 4800, which is a bit less than 1 mile. But I’ve only multiplied by 3 so far. I also still have a 6 that I need to multiply by, since 18 = (3)(6).
In other words, I have to do this (1600)(3) calculation 6 times. Brainstorm!! The question asked whether he went more than 6 miles. Check this out:
1600(3) = 4800 which is < 1 mi
1600(3) = 4800 which is < 1 mi
1600(3) = 4800 which is < 1 mi
1600(3) = 4800 which is < 1 mi
1600(3) = 4800 which is < 1 mi
1600(3) = 4800 which is < 1 mi
I have to do the calculation 6 times and Carlos is about 500 feet under a mile each “time,” so he will be decently below 6 miles at this rate. (You don’t need to write out all 6 lines. I’m just trying to illustrate the pattern.)
What happens when the rate increases?
At a rate of 16.00001 f/s, Carlos is still going to be under 6 miles. But if that rate gets up to, say, 100 f/s, he’s going to travel more than 6 miles.
Statement (1) is not sufficient to answer the question. Eliminate answers (A) and (D).
Try the same shortcut for the next statement
Statement (2) : r < 18 f/s
Try r = 18 f/s
Convert to feet per half hour again and rearrange the zeros:
=(18 f/sec)(60 sec/min)(30 min/ half hour)
=(1800)(18)
Hmm.
1800
3600
5400
This time, multiplying by 3 puts Carlos over 1 mile! So if he does this 6 times, that’s going to be over 6 miles.
Again, at 17.99999 f/s, Carlos is still going to be over 6 miles. But we know that if he gets down as far as 16f/s, he’ll be under 6 miles.
Statement (2) is also not sufficient; eliminate answer (B).
What happens when you put the two statements together?
Carlos is traveling somewhere between 16 and 18 f/s. If he’s just a little over 16 f/s, then he’s going to travel fewer than 6 miles. But if he makes it to just under 18 f/s, he’s going to be over 6 miles.
Even together, the two statements are not sufficient to answer the question.
The correct answer is (E).
How did I know to break the numbers down exactly the way I did?
I didn’t! I just knew that I wanted to avoid some annoying calculations if possible, so I started looking for ways to approximate what I needed. I wrote out the calculations exactly as I put them up above—and suddenly I had my Eureka! moment and realized that my approximations were good enough.
What if that hadn’t worked? I would’ve shrugged my shoulders, picked my favorite letter (B, for the record), and moved on. I’d rather do that than get super aggravated trying to convert and do all those calculations by hand.
Key Takeaways for Avoiding Calculations on DS:
(1) Let your annoyances work for you. That conversion was one of the first things I noticed, and I hate conversions. (Who doesn’t?) So, from the beginning, I decided that I was committing myself to a “no annoying math” pathway for the problem. (See #3 for more on this.)
(2) When I committed to my “minimal math” path, I knew I wouldn’t have time to go back to the beginning and do all of the real calculations if the “minimal” path didn’t work out. And I was okay with that. Don’t be afraid to guess and move on.
(3) Do set up the beginning math, but don’t automatically do the calculations. I knew I had no interest in multiplying out (16)(60)(30)—and then doing a feet to miles conversion on top of that!—but looking at the math written out gave me an idea about how to approximate my way to an answer.
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California. Stacey has been teaching the GMAT, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. Check out Stacey’s upcoming GMAT courses here.
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