Hi Zeke,

I took a GMAT Prep Practice test the other day and I struggled with a couple of question. Please help:

Question 1:

If ab != 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?

(1) xy > 0

(2) ax > 0

Question 2:

Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each.

If Juan bought more than 10 paper books, how many hardcover books did he buy?

(1) total cost of hardcover books that Juan bought was at least $150

(2) total cost of the books that Juan bought was less than $260

Thanks,

xxxxxx

Modupe,

Question 1:

It looks like this question is about signs.

ab!=0 tells us that neither a nor b is zero. On a graph, the points a and b do not lie on either the x axis or y axis. It’s everything else that it can be.

**Let’s see what our possibilities are, we’ll run 4 scenarios for a and b:**

positive, positive

positive, negative

negative, negative

negative, positive

**Let’s take a=5, b=3.
(-a, b) is (-5, 3) – upper left quadrant
(-b, a) is (-3, 5) – upper left quadrant.**

Thus, same quadrant, quadrant 2.

However, if we have a=5 b=-3 then

(-5, -3) and (3, -5) are different quadrants. Not possible in our question.

If a=-5 and b=-3

(5, -3) and (3, -5) then both in quadrant 4.

If a=-5 and b=3 then

(5, 3) and (-3, 5) are different quadrants. **Not possible in our question.**

Conclusion – if the points are in the same quadrant, that quadrant can either be quadrant 2 or quadrant 4.

The question we are asked is whether point (-x, y) is in that same quadrant as where the common quadrant is (which is 2 or 4)

Without any additional information, point (-x, y) can be any quadrant since there is no limitation on x and y yet. So we do not have sufficient information to answer the question just yet. Let’s take the (1) and (2) we are given:

(1) tells us that x and y are the same sign. Either both positive or both negative

(2) tells us that both a and x are the same sign. Either both positive or both negative

From (1) we see that (-x, y) is going to be in quadrants 2 and 4.

If x and y are both positive, the point is in quadrant 2.

If x and y are both negative, the point is in quadrant 4.

We can’t be 100% sure that this information answers our question. Originally point (-x, y) can be any quadrant – since there is no restriction on x or y.

With (1) we know they are both the same sign, and this limits the quadrants to 2 and 4. We still dont’ know which one exactly it’s going to be.

From (2), we see that a and x are the same sign. However, this does not help us limit what quadrants (-x, y) are NOR does it help us limit what quadrants (-a, b) and (-b, a) are.

However, if we combine (1) and (2), we can use transitive property and say that x, y and a all have the same sign.

x = y

y = z

x = y = z

Same concept.

x same sign as y

y same sign as z

x same sign as y same sign as z

Now we know that if x is positive, then a must also be positive and so points (-a, b) and (-b, a) are in quadrant 2. At the same time, point (-x, y) is ALSO quadrant 2. We know definitively that quadrant 2 is the common quadrant here.

If x is negative, then a must also be negative. From above, the only possibility is for b to be negative. And so points (-a, b) and (-b, a) are in quadrant 4.

At the same time, point (-x, y) is ALSO quadrant 4. (both x and y are negative).

Combining (1) and (2) we can get a definitive answer so (C) is the answer.

You might ask, how do I answer this question in real-time during the actual exam.

This question is about signs. Quickly draw that (1) gives us that x and y are the same sign. If they are the same sign, do I have enough info to answer the question? That question being that (-x, y) is in the same quadrant as the original condition proposed in the question. It doesn’t seem like the information helps us narrow down so (1) is insufficient.

Quickly draw from (2) that a and x are the same sign. This also doesn’t narrow down the quadrants for us.

Combine (1) and (2) – notice the overlap is in x. Draw that a, x, and y all are the same sign.

THen run scenarios where a,x, and y are positive =>quardrant 2

THen run scenarios where a,x, and y are negative => quadrant 4.

We got definitive answers so (C) helps us get there.

Question 2:

Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each.

If Juan bought more than 10 paper books, how many hardcover books did he buy?

Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each.

If Juan bought more than 10 paper books, how many hardcover books did he buy?

(1) total cost of hardcover books that Juan bought was at least $150

(2) total cost of the books that Juan bought was less than $260

8x + 25y

x >10

(1) Total cost of harder was at least $150. That means he bought at least 6 hardcover books at $25 each. We don’t know how many hardcover books he bought exactly, just that it was more than 6.

(2) Well, if he spent at least 10*$8 = $80 on paperbacks – the remainder goes to hardcover books. At most, $260 – $80 = $180 was spent on hardcovers. This could have been 1 hardcover – 2, 3, 4, 5, 6, or 7 hardcovers. We don’t have the definitive answer.

What if we combined (1) and (2).

More than 6 hardcovers…the only option is 7 hardcovers for $175. It’s a definitive answer.

Does this meet requirements for (1) and (2)? It does. Answer (C)

Click here for more GMAT Practice Test questions to aid you in your GMAT preparation process and study plan.

Table of Contents | See Pricing

Verbal Questions: Sentence Correction | Critical Reasoning | Reading Comprehension

Quant Videos: Problem Solving | Data Sufficiency

## Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

`<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>`