find if x on modulus is smaller than given number

Question

Let's say I have integers from 1 to 1000 (MOD 1000), let's also say that I know that somewhere between 1 and 1000 is the number I'm looking for it can be any number. Is there any way to compute if that number is or is not between two given points? Like point A = 700 and point B = 800, I'm trying to find out if point X is between those two points. I can add any number of points to the point X or I can negate point X (if it is 120, I can negate it to 780) but I never know the start point X. Does this problem have a solution or not? I can not divide and subtract (but I can add negated point to point X) Does this problem have a solution? So let's say that A = 700, B = 800 and I'm looking for point X which is 120 but I do not know it is 120, but if I add 100 to the point X I will have 130 (but I do not know it is 130, I would have to check that somehow computationally.

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mikemcgarry · Answer

Dear paulkol , I'm happy to respond.

With all due respect my friend, this problem is not clear, not well explained. It's very clear that you are gifted in math, but you have not succeed in making your meaning perfectly clear. In particular, it's quite unclear what the student would know--what information the student would get and what they would have to figure out. I'll point out that even though I understand modular arithmetic, this is a topic 100% not on the GMAT, so it's really not particularly relevant. Furthermore, the question you are asking is not at all in GMAT form. Nevertheless, it's fine to talk about some extraneous hard math here, but at least the question should be precisely stated and clear. The student knows that 0 < X < 1000. We are given points A = 700 and B = 800, which presumably the student would know. The student doesn't know the value of X, so doesn't know the value of (X + 100), but we certainly could return a T/F reading about whether, say, (X + 100) is between A & B. What do you think about this somewhat related question, in the form of a GMAT Data Sufficiency Question? X is a positive multiple of 10, and X < 200 What is the value of X? Statement #1 : there is only one multiple of X greater than 400 and less than 500 Statement #2 : there are no multiples of X greater than 500 and less than 600 Answer = (E) Mike

paulkol · Answer

Thank you for your answer. I will certainly check the links. And I apologize if I was not being clear, it was kind of hard to explain. Me personally after lot of thinking don't believe there is solution for the problem (I mean the X can not be found, because it can be anywhere and any proves I can think of can point to any point on the 1000 modulus.

Thank you very much for your answer again.

find if x on modulus is smaller than given number

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