### GMATPrep Data Sufficiency: Maria’s Books

The other week, we discussed the overall process for Data Sufficiency. This week, we’re going to test out the process using a GMATPrep question “ and take a look at a couple of *very* common DS traps.

Set your timer for 2 minutes. and GO!

* A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul all bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.

(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.

Note that I haven’t listed the answer choices for you. Because DS answers are always the same, we should memorize them. If you don’t have them memorized yet, look back at the How DS Works article linked in the first paragraph.

All right, let’s tackle this problem.

Step 1: Read the Question Stem

The first sentence tells us that each paperback book sells for the same price and each hardcover book also sells for the same price (but possibly a different price than the paperback books).

The question asks how much Maria paid for 1 of each type of book. Is this a value or a yes/no question?

They’re asking for a specific amount; this is a value question. We’ve also got lots of words; we’re going to have to translate.

Step 2: Glance *Briefly* at Both Statements

What have we got in general? More words. We’ve just confirmed that translation is our first step.

Step 3: Examine / Rephrase the Question Stem

To translate, we’re going to need some variables. Let’s set *p* for the price of the paperback book and *h* for the price of the hardcover book.

We can translate the question in this way:

p+h= ?

Note that we don’t necessarily have to be able to find *p* and *h* individually. If we can find a value for the combination *p* + *h*, then that’ll be good enough.

Step 4: Tackle the Statements

Statement 1 doesn’t seem horrible, so start with it. Write down the answer grid (AD, and then underneath, BCE).

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.

Translate using the set variables:

J: 2

p+ 3h= 12.5

Okay. We’ve got a formula with our two desired variables. Is there any way to manipulate that formula to get *p* + *h* on one side and a value on the other?

Nope. There’s one extra *h* hanging around. If it had said something like 2*p* + 2*h* = 12.5, where the coefficients (the numbers before the variables) were the same, then we could get a value for *p* + *h*. But there’s no way to get the two different coefficients to be the same *and* have only a numerical value on the other side of the equation.

Statement 1 is not sufficient. Cross off the top row (answers A and D) and move to statement 2.

(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.

Oh, I can see where this is going. I’m going to get a formula for Paul and, look, it also includes the *p* and *h* variables. By itself, that won’t be enough, but if I combine it with statement 1, then I’ll be able to solve. The answer must be C.

Careful! That’s wrong; C is a trap answer. We’re always trying to save time on DS by not calculating things or stopping calculations before we’re done but don’t cut things down *too* much. Translate this formula.

P: 4

p+ 6h= 25

(Note: because Paul’s name starts with P and I’ve also chosen *p* to represent the price of a paperback, I’d probably do something like put a circle around P “ and go back up to do the same with J “ so that I don’t confuse anything.)

Once again, by itself, this won’t work (I can’t find the variables individually and there’s no way to get the two coefficients to be the same, so I can’t solve for the combination *p* + *h*). Cross off answer B.

Now, look at those two equations together. Notice anything?

They look strangely similar, don’t they? Here they are side by side:

2

p+ 3h= 12.54

p+ 6h= 25

Let’s see yep, if we multiply each term in the first equation by 2, we’ll get the second equation.

In other words, these two equations are identical “ they’re the same equation! In order to solve for these two variables, we would need two *different* equations (or an equation in which the coefficients before *p* and *h* were the same).

Using the two statements together still doesn’t allow us to figure out a value for *p* + *h*. Cross off answer C.

The correct answer is E.

**Key Takeaways for Algebra Word Problems**

(1) Translate. Get everything on paper in math form so that you can look at it. If you do too much in your head, you’ll be much more likely to make a mistake with the math. (Looking for more on translation? Read this introduction to translation or dive into the Algebraic Translations chapter of our Word Problems book.)

(2) Watch out for the stopping too early trap: this trap involves thinking that we know whether something is sufficient even though we haven’t done enough work yet. As a general rule, if something requires any kind of translation or manipulation at all, don’t do that in your head. Write it down. If you find, through review, that you often make the mistake of stopping too early, then vow to go one step further every single time from now on. With enough practice, you’ll then learn where you really can stop and where you can’t.

(3) Watch out for the combo trap: this trap involves thinking that we need to be able to find each individual variable when it’s actually sufficient to find a *combination* of the variables (such as *p* + *h*). This particular trap didn’t show up on the above problem, but it shows up on many others; keep an eye out for it!

* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

I got

2p + 3h =12.50 …. e1

4p+6h=25.00 ……e2

e1 = p= (12.50-3h)/2

4((12.50-3h)/2) + 6h =25.00

h= 2.8205

p=((12.50-2(2.8205))/2

p = 2.01925