Sat Question HELP!?

Question

If p-q=4 and r is the number of integers less than p and greater than q, then which of the following could be true?

I. r=3
II. r=4
III. r=5


(A) I only
(B) II only
(C) III only
(D) I and II
(E) I,II, and III


the correct answer is (D) but the book doesn't provide any explanation. Can someone really smart please explain this step by step(i'm retarded-->lol). I would be so grateful. I don't even know where to start. I stink at SAT Math. Thank you!

Answer 1

the reason its ii and ii is this

say you look and say hey!


7-3 is 4

Since r is the number of integers between both numbers (7 and 3) you look at them. 6,5 and 4 are between those two numbers so in this cast r is three.

what about 7.5- 3.5= 4

the numbers 7,6,5, and 4 are integers between these numbers so there are four.

there are no other combinations that can produce more than that so three and four are both correct answers and thats why the answer that says that both 3 and four are correct answers is true.

please vote me best answer =)

Answer 2

The answer is (D), because...

p - q = 4

The equation tells you that p is 4 more than q.

So now we can say that:

q+1, q+2, q+3 are values less than p and greater than q.

That only applies for when q is an integer.

What if q weren't an integer?

p = q + 4

q = .5

q+.5 ,q+1.5, q+2.5, q+3.5 are possible integers.

I'll now explain why not (lll)

It can't be (lll) because p = q + 4

There can't be 5 integers in between a distance of 4.

Answer 3

putting some examples will help in problems like these. let us say p=5, and q=1 (to make p-q=4), then the integer has to be between 1 and 5, but >1 and <5, so possible values for integers are {2,3,4}, making r=3.

I can not think of any combination of p and q where r can be 4. My answer is (A). The book must be wrong.

I stand corrected (see Jawad's answer) - the problem did not say p and q are integers.

Answer 4

p-q = 4. Nothing is said about restricting the integers to just positive , or just negative or both positive and negative and including 0. Thus this is a very poor question.
Let's assume p= 3 and q =0.
Then the number of integers r < 3 is 3 (2,1,0) and the the number of digits greater than 0 is 3(1,2,3).
Now suppose that p= 4 and q = 0
In this case, there are 4 integers <4 (0,1,2,3) and there are 4 digits > 0 (1,2,3,4).
So in these special cases r could be 3 or 4.

But I think the problem very poorly worded and open to different interpretations.

Answer 5

You're looking for the total number of integers between p and q. If p-q=4, then you CAN'T have more than 4 because you wouldn't be able to get four then-you'd have p-q=5. That leaves III out. I'm not sure why I is included except that it says "could be" true, so while you'll have four integers between the numbers, you will also have three.

I hope that makes sense...