If k, m, and p are integers, is k m p odd? (1) k and m are

Question

If k, m, and p are integers, is k – m – p odd? 
(1) k and m are even and p is odd. 
(2) k, m, and p are consecutive integers.

Here some views are there saying even and odd integers can be classified only in positive, some says it should also include negative.. Can someone tell what should we consider for GMAT purpose?

Bunuel · Answer

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. An even number is an integer of the form n=2k , where k is an integer. So for k<0 --> n=2*k<0 --> negative numbers could be even too. An odd number is an integer that is not evenly divisible by 2. An odd number is an integer of the form n=2k+1 , where k is an integer. So for k<0 --> n=2*k+1<0 --> negative numbers could be odd too. As for the question. Is k-m-p=odd ? (1) k and m are even and p is odd --> k-m-p=even-even-odd=odd . Sufficient. (2) k, m, and p are consecutive integers --> if k, m, and p are 1, 2, and 3 respectively then the answer is NO but if k, m, and p are 2, 3, and 4 respectively then the answer is YES. Two different answers, hence not sufficient. Answer: A. Though there is one thing wrong with this question: if (2) means that k, m, and p are consecutive integers in this order, then m=k+1 , so m is odd and k is even or vise-versa, but (1) say that both k and m are even, so statements contradict each other. But: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other . So not a good question. Hope it helps.

whiplash2411 · Answer

Basically rewrite this question in another form.

You are asked to evaluate if  k - m - p is odd. This basically asks if  k - (m+p) is odd.

Now, there are two cases that can possibly arise, since for the difference of two numbers to be odd, one is even and the other is odd.

Case 1

k = odd
 m + p  = even

Case 2

k  = even
 m+p = odd

Now let's look at the statements.

1. k and m are even and p is odd. This puts us under Case 2 since k is even. m is even and p is odd; this means that m+p is odd. So we have even - odd = odd. Sufficient.

This basically narrows down our answer choices to A and D.

2. k, m and p are consecutive integers. This breaks down into two further cases.

Case A: k = even.

k = even
m = odd
p = even

So we get k - (m+p) = even - (odd+even) = even - odd = odd

Case B: k = odd

k = odd
m = even
p = odd

So we get k - (m+p) = odd - (even + odd) = odd - odd = even

So this statement is inconclusive. Hence we can rule out D and the answer choice A is correct.

vigneshpandi · Answer

Case 1: Since K and M are even we get a straight answer which is even-even=even and then even-odd is odd.

Case 2: Assume k,m,p as 1,2,3 and 2,3,4. In first case k-m-p is even while in second case it is odd.

Hence answer is A

gulatin2 · Answer

Given that is statement 1 , k & m are given even where as p is given odd and we know as a fact that sum/subrtraction even +/- odd number is always odd. so statemtent 1 is sufficient to provide an answer to question asked.

Statement 2. provided three integers are consecutive integers, we can not know for sure if k-m-p will be even or odd as it does not lead to one conclusive answer.

Two statements combined do not provide sufficient answer. Hence A is the right answer

cano · Answer

Bunuel, are you certain about this? I thought that the 2nd statement could sometimes change the information provided. I got this from the book "GMAT Math workbook", Kaplan. Quoting chapter 4, Geometry:

"The diagrams on the GMAT  are  drawn to scale unless otherwise stated. You can estimate distances, angles and such from the diagram. Also note that the diagrams on Data Sufficiency questions can change if one of the statements introduces new information."

I inferred from that paragraph that if a diagram could change after the 2nd statement, then the 2 statements contradict each other. Well, they are not quite the opposite, but not the same either. I also inferred that if that could happen in DS geometry, the same could happen in any DS question.

Of course, then it wouldn't make sense to have option C, but I thought it's still possible that they target any other answer choice.

Can anyone share more light on this, please?

Bunuel · Answer

100%.

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other . Though I don't know what you mean by: "2nd statement could sometimes change the information provided."

As for the diagrams: I disagree with Kaplan on this one. I've seen several GMAT questions where diagrams were not drawn to scale. I asked the similar question to Ian Stewart (GMAT instructor) and he gave me the explanation about the "trust" of the diagrams in GMAT:

" In general, you should not trust the scale of GMAT diagrams, either in Problem Solving or Data Sufficiency.   It used to be true  that Problem Solving diagrams were drawn to scale unless mentioned otherwise, but I've seen recent questions where that is clearly not the case. So I'd only trust a diagram I'd drawn myself. ...

Here I'm referring only to the scale of diagrams; the relative lengths of line segments in a triangle, for example. ...  You can accept the relative ordering of points and their relative locations as given  (if the vertices of a pentagon are labeled ABCDE clockwise around the shape, then you can take it as given that AB, BC, CD, DE and EA are the edges of the pentagon;  if a line is labeled with four points in A, B, C, D in sequence, you can take it as given that AC is longer than both AB and BC;  if a point C is drawn inside a circle, unless the question tells you otherwise, you can assume that C is actually within the circle;  if what appears to be a straight line is labeled with three points A, B, C, you can assume the line is actually straight, and that B is a point on the line  -- the GMAT would never include as a trick the possibility that ABC actually form a 179 degree angle that is imperceptible to the eye, to give a few examples).

So don't trust the lengths of lines, but do trust the sequence of points on a line, or the location of points within or outside figures in a drawing.  "

Hope it helps.

KapTeacherEli · Answer

I was asked to respond to this problem, but it looks like I'm late to the party. Nonetheless, the answer seems clear here; negative numbers can, indeed, be even and odd.

IanStewart · Answer

I guess Bunuel has already quoted me on this subject above, but I'd just point out one obvious example of a diagram in a GMATPrep Problem Solving question which is not even close to being drawn to scale: plane-geometry-semicircle-from-gmatprep-85154.html Here the diagram makes the two points P and Q appear to be level (i.e., the diagram makes it appear that they have the same y coordinate) and that isn't close to being true. You should only trust diagrams in the PS section of the GMAT if you've drawn them yourself, and the prep company you quote above is wrong on that point. That is not what they mean to say, though I can understand why the text you quoted might create confusion - it's very badly worded. As Bunuel points out, the two statements can never contradict each other. However, in geometry, the amount of information you're given may determine how much 'freedom' you have to draw your diagram. For example, if you're asked the rather straightforward question: What is the perimeter of triangle ABC? 1. Triangle ABC is equilateral. 2. The length of side AB is 5 From Statement 1, we can draw all kinds of triangles - a triangle where each side is 2, or where each side is 5, or where each side is 1000. From Statement 2 alone, we can also draw all kinds of triangles - it could be a 3-4-5 triangle, or a 5-5-5 triangle, or a 5-12-13 triangle, or all kinds of other triangles. But when we combine the two statements, we must have a 5-5-5 triangle. So in this case, the more information we use, the more of our potential diagrams we can rule out. The point is (and I guess this is what they were trying to convey in the text you quoted above) that you might be able to draw a lot of different potentially correct diagrams using only one statement, but when you combine the two statements, that might rule out some or most (but never all) of the possibilities. So when they say "note that the diagrams on Data Sufficiency questions can change if one of the statements introduces new information", that's quite misleading, since your diagram can't 'change'; what they mean is that the new information in a statement might rule out certain possibilities.

cano · Answer

Bunuel and IanStewart,

Thanks for your detailed answers. I'm glad that I misunderstood that text, so it will be a little easier with well prepared questions. At least, as Ian said, I'll have more possibilities ruled out. I was thinking in a very easy example:

Find the measure of angle A (in the diagram will be shown which one is A, for the sake of example imagine anyone).

1. Triangle ABC is an isosceles right triangle.
2. Triangle ABC is equilateral.

In this case, there is no way we can choose option C since the 2 statements provide very different information. I originally understood that a question like that could appear and the diagram would have to be different after statement 2. But now I'm glad that I won't have to face these awkward situations.

Thanks again to both of you!

Bunuel · Answer

This question cannot appear on the GMAT because two statement clearly contradict each other: equilateral triangle cannot be right.

KarishmaB · Answer

Cano:
Data Sufficiency questions are like puzzles. 
I have a triangle in my hand and I ask you, what is the measure of angle A? (Question Stem)
You say that you do not know.
I give you a hint - ABC is a right isosceles triangle. (Statement I)
You analyze the hint and say that you still do not know.
I decide to give you another hint to solve the puzzle. ABC is an equilateral triangle. (Statement II)
This is incorrect, isn't it? It is the same triangle I am asking about. How can it be both 90-45-45 and 60-60-60. 
Since it is the same puzzle, my hints (i.e. the two statements) cannot contradict each other.

cano · Answer

Thanks Karishma for your explanation, you made your point very clear. Note that I inferred that from just a sentence that I read in a book at the beginning of my quant preparation. Now I understand the concept better and believe that the piece of information that I quoted is misleading. Probably that's why they give the book away for free...?

Two days ago I got registered for my Veritas Prep course (the prize I won on the 100k event), so now I have access to the On Demand materials. Last night I went to the lesson about DS. The recorded lesson goes for 76 minutes but before the 2:00 mark they already tell you this: "You can never assume that figures on Data Sufficiency questions are drawn to scale." I think this is much more serious, clear and straight forward than the quotation of my other previous post.

I now checked back the Kaplan book and read now in the DS section (chapter 6) to see what they say about it. I quote: "Diagrams accompanying problems agree with information given in the questions, but may not agree with additional information given in statements (1) and (2)." Well, I find this note as misleading as the note from the Geometry section, if not more.

So, guys, thanks to you now I don't have any more confusion about this issue.

PS: be careful which prep materials you use! If you are not sure about something, just ask the experts!

KarishmaB · Answer

I am glad it helped. And yes, never ever assume anything from your diagram in DS (its a good idea to not assume anything from the diagram in a PS question too but the silver lining there is that you can definitely find the answer so if the diagram is tempting you to assume something, analyze whether your assumption actually has merit. It can work as a clue sometimes.)
OG12 mentions in Data Sufficiency section "Be very careful not to make unwarranted assumptions based on the images represented."
I will wrap up this discussion with a quick problem to illustrate this point:

What is the length of side AB of parallelogram ABCD?

Attachment:

doc.jpg [ 6.03 KiB | Viewed 4428 times ]

I. AC = 8 cm
II. BD = 6 cm

I should not assume that the diagonals are perpendicular here. It is not essential that they will be since it is a parallelogram but the figure leads us to believe otherwise!
The answer here will be E, not C.

On the other hand, if I modify the question to say:
ABCD is a parallelogram such that its all four sides are equal, what is the length of the side AB if AC = 8 cm and BD = 6 cm?

Attachment:

doc.jpg [ 6.03 KiB | Viewed 4428 times ]

Now when I see the diagram, I should think, will diagonals be perpendicular? Then, hopefully it will strike that since all sides are equal, it becomes a rhombus and hence the diagonals will be perpendicular bisectors. Therefore, I can use Pythagorean theorem here. So I am not assuming anything from the figure here as well, but sometimes it can give us a clue to analyze and arrive at our own conclusion.

KapTeacherEli · Answer

Hi Bunuel,

At Kaplan, we do our best to get the most accurate information that we can, and in this case, we have it straight from the horses mouth. Page 150 of the 12th edition official guide says of problem solving that 'Figures are drawn as accurately as possible'. We're confident that the language is unambiguous, and that's what we tell our students.

That being said, I'll admit I'm puzzled by the link IanStewart provided. It's pretty clear that the diagram is way off scale on that one. We're looking into the specifics of that problem, and if it turns out there has been some sort of change in testing policy we will of course alter our teaching methods to suit. But Kaplan is the first to know about changes to standardized tests, and the GMAC has made no public announcements that would suggest that the text on page 150 no longer holds true.

Regardless, I think Ian and I can agree that even if the figures are accurate, relying on them should be reserved for confirmation of an answer gotten through mathematical strategy and reasoning. So if you polish your geometry skills, you'll be able to nail those points, and the answer to our debate will be moot!

If k, m, and p are integers, is k m p odd? (1) k and m are

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If k, m, and p are integers, is k m p odd? (1) k and m are

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