The GMAT Official Guides 2017 Edition - Part 2

by , Jun 10, 2016

The new Official Guide books have landed! In part 1, we talked about the changes to the quant portions of the guides.

Already read that part? Then lets talk about those interesting problems I mentioned last time! Note: I cant reprint the problems here for copyright reasons. You will actually have to have a copy of the book in order to follow along. If you dont have a copy, skip ahead to part 3, where well talk about verbal.

Note: I strongly recommend that you not read this until you have worked on these problems yourself! If you can figure out whats going on yourself, the lesson will stick much better in the end. :)

Big Book #116 and #140

Guiding principle: Do NOT do textbook math. Work backwards.

My colleague Whitney Garner and I both snorted when we saw the first one of these, #116. The math is truly ridiculous unless you approach it as a real-world problem, not a textbook math problem. The problem talks about 1/3 of the total, but we dont have a real number for the total (we only know its [pmath]37 + x + 32[/pmath]). So the math could get crazy messy unless you work backwards from the answer choices. Even then, the math is messy unless you also estimate at one point.

So lets take answer (B) 9. (When working backwards, start with B or D.) If [pmath]x = 9[/pmath], then there are a total of 78 marbles. One-third are blue, so 78/3 = 26. Now we have to test these numbers with the percentages listed in the final column to see whether we have a match. Dont calculate 10.8% of anythingestimate! (By the way it makes sense that you can do this because you shouldnt have only part of a marble )

A little more than 10% of 37 is 4. 50% of 32 is 16. And 66.7% of [pmath]x = 9[/pmath] is 6. Does that add up right? Yep. 26 blue ones. Weve found the answer!

#140 is equally weird until you treat the answer choices as your starting point. The question asks for the least and greatest possible values of [pmath]n[/pmath]. Look at those answers.

There are only three possibilities for the least value: 0, 1, or 2. Since they're asking for the least, try the smallest one (0) first to see whether its possible.

Once you figure out whether the lower bound is 0, 1, or 2, that leaves you with either one or two remaining answers. At most, youll need to test one of the upper bound numbers and youre done. (This time, test the larger number first, since youre looking for the greatest possibility.)

Big Book #194 and #283:

Guiding principle: know how to think about probability.

#194 is a PS problem and the answers range from really small to just under half to just over half to decently bigger than half. So you might be able to narrow down by estimating.

Pretend youre the one going camping. Hows it going to work out?

Saturday: no rain

Sunday: no rain

Monday: rain!

The probability of rain is 0.2, so the probability of no-rain is 0.8. Youve got a really good chance to stay on Saturday. On Sunday, theres a decent chance that you can still stay but its a bit worse than it was solely on Saturday. Still more than 50% though.

It does rain Monday, however, so youve got to factor in that low probability of 0.2. That should drop your odds below half. Answers (D) and (E) are out and even (C) is probably too close to half. And (A) is vanishingly small, so its probably (B).

The actual math would be (0.8)(0.8)(0.2) for the scenario described (no rain, no rain, rain). Ignore the decimals and multiply out the numbers: (8)(8)(2) = 128. Only one answer matches that digit sequence: (B)!

The second problem here, #283, is a DS. Lets call a job offer a Yes answer (ie, yes the company wants Jill). In order to calculate the probability, we need to know the probability of earning a Yes from each, or (Yes)(Yes).

Notice that the statements combine the info about the two companies. Statement (1) is the equivalent of (No)(No). What are the other possible outcomes?

(No)(No)

(Yes)(No)

(No)(Yes)

(Yes)(Yes)

So statement (1) doesnt give us enough to get to (Yes)(Yes). What about statement (2)?

Interesting! This one is (Yes)(No) + (No)(Yes). She gets an offer from the first one but not the second one or she gets an offer from the second one but not the first one.

By itself, thats not enough, but it you put the two statements together, you have the probabilities for three out of the four possible scenarios.

All of the possible scenarios must add up to a probability of 1, so you can subtract the other three scenarios to find the probability of the one desired scenario (Yes)(Yes). Sufficient! The answer is (C).

In both cases, these two problems are medium to higher-level, but they dont require crazy calculations. They do require, though, that you know how to think about probability in general. For instance, if you know the probability of all possible scenarios except for one, then you can always find the probability of the one missing scenario.

Big Book #310 and #???

Guiding principle: try to use what youve already figured out to help give you a boost on harder problems.

This is the one where I wouldnt tell you the second question number beforeI suggested you try to find something similar to 310 yourself. I'll be honest: this was a really challenging assignment. If you can do this, you have a good shot to get a really high quant score on the GMAT.

To me, these two were the most intriguing of all of the new quant problems. I havent seen prior problems test these principles in quite this way. Lets start with the first one, 310. When I first saw it, I wanted to throw in the towel. Even just Testing Cases was going to be really tedious and annoying on this one.

I knew, though, that this test doesnt ever require us to do super-tedious math. So I took another look at what they gave me and realized there was a really interesting hidden pattern.

The question stem asks me to add the same value, n, to each of 3 numbers. Thats a really weird request, so it caught my attention. I noticed that, since Im adding [pmath]n[/pmath]to each one, the differences between those three numbers never change. 94 is 25 larger than 69 and [pmath]94 + n[/pmath] is 25 larger than [pmath]69 + n[/pmath]. I had no idea what that meant; I just noticed it.

Statement (1) brings in what seems like crazy info: [pmath]69 + n[/pmath] and [pmath]94 + n[/pmath] both represent the squares of two consecutive integers.

Ah! Thats what did it for me. I already knew another principle that Ill explain to you right now. Square some consecutive positive integers. Notice anything?

1, 4, 9, 16, 25, 36, 49,

As you get bigger, the difference between the numbers always gets larger. The difference between 1 and 4 is 3, the difference between 4 and 9 is 5, and the difference between 9 and 16 is 7. And that keeps going. The key detail: each pair of consecutive integers-squared has its own unique difference.

So [pmath]69 + n[/pmath] and [pmath]94 + n[/pmath] represent the squares of two consecutive integers. Whatever those two squares are, they are 25 apart. Their difference is 25. Theres only one pair of positive consecutive integers-squared that are 25 apart. (Im not going to go figure out what they are, of course. This is DS. But I know from the pattern that there can be only one pairing with a difference of 25.) Done! Sufficient.

What about statement (2)? Same deal. This time, weve got two different numbers (and a difference of [pmath]121 - 94 = 27[/pmath]), but the same principle: theres only one pairing of consecutive integers-squared that has a difference of 27. Sufficient!

Which other problem later in this same chapter touches on similar principles? Drum-roll please: its 327. Check it out.

In this case, though, the problem cannot be solved via the given information. The two statements each tell you that one of the terms is a perfect square. The problem mentions nothing about the two terms being consecutive, though, nor could they be, since the difference between consecutive squares is always odd and the difference between the two terms here is 24, an even number.

Each statement cant be sufficient by itself because the other term could be a non-integer; there are infinite possibilities. That knocks out answers (A), (B), and (D). The real question is whether putting the two statements together will narrow things down to just one possible value.

At this point, its a judgment call whether you want to take the time to see whether you really can find two different cases (using real numbers). Its tricky on this problem, since both [pmath]x[/pmath] and [pmath]x + 24[/pmath] have to be perfect squaresbut that right there is your clue. Test out small perfect squares to find ones that are exactly 24 apart and don't bother trying to test consecutive pairings, since you know those will be an odd number apart, not an even number. Try numbers that are 2 apart, 4 apart, 6 apart

1 and 3 are too close for their squares to be 24 apart. What about 1 and 5? Bingo! That pairing actually works.

What about 2 and 4 or 3 and 5? Too close. 4 and 6? Almost 5 and 7? Bingo! At least two pairings work, so even together, these guys arent sufficient. The answer is (E).

You could also just gamble that, without the consecutive constraint, chances are that more than one combo workssince it seems as though the constraint is now so specific that only one number could work. (ie, its a trap.)

The key takeaway: having thought through the first one already, I actually had a shot at figuring out the more complicated second one in a reasonable amount of time. If Id seen the second one first, I likely would have decided the problem wasnt worth it once I got to (C) and (E).

What about Verbal?

Next time, well dive into the verbal sections of the Big OG and the verbal review. In some later articles, Ill also provide you with lists of the new questions in each book.

Happy studying!