Possible values of X and Y for the problem

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In summary, X and Y are whole numbers where X+Y equals the square of a number, X-Y is a prime number, and X*Y is a twin number. To solve such problems, it is best to start with the condition that provides the most specific information and work from there. However, with these given conditions, the only possible solution is X=22 and Y=3. This method may seem ad hoc, but there are typically no equations for these types of problems.
  • #1
issac newton
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X and Y are whole nos
X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)
X/Y=irrational no.

how to solve such kind of problems apart from trial n error basis(ad hoc) ?
 
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  • #2
If x and y are whole numbers, then x/y can't be irrational.
 
  • #3
sorry abt the fourth condition. what if first 3 conditions are considered ??

X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)

what are the possible values of x and y. how to approach such a problem to narrow down our answers ??
 
  • #4
Issac Newton said:
sorry abt the fourth condition. what if first 3 conditions are considered ??

X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)

what are the possible values of x and y. how to approach such a problem to narrow down our answers ??
Start with the last condition. What does that allow you to say about X and Y? (either one of them is 1 or ...?)
 
  • #5
The value of x or y can be 1 or 11. but all values of x with y being 1,will not satisfy the other two conditions. like
99*1=99 but

99-1=98 not a prime.

so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

is there any equation solving method and also can this question have a solution if at all ??
 
  • #6
Issac Newton said:
The value of x or y can be 1 or 11. but all values of x with y being 1, will not satisfy the other two conditions. like
99*1=99 but

99-1=98 not a prime.

so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

is there any equation solving method and also can this question have a solution if at all ??

99 = 3 * 33, so 1 and 11 aren't the only values x or y can take.

There's 1 solution to your problem.

Don't be surprised that you're getting "ad hoc" methods, you've thrown together a few random arbitrary conditions, especially the "twin number" bit.
 
  • #7
thank u abacus.

i think the answer is 22 and 3.

22*3=66

22-3=19

22+3=25
 
  • #8
Ok, I misunderstood. I thought by "twin" number you meant a semiprime. You just mean two digits the same, right?
Typically there are no equations for these sorts of problems. The technique is to start with the pieces of information that narrow down the possibilities fastest.
Btw, for X*Y there are also possibilities like 3*22, etc.
 

1. What are possible values of X and Y for the problem?

The possible values of X and Y for a problem depend on the specific problem and its constraints. It is important to carefully analyze the problem and determine all possible values that X and Y could take on.

2. How do you determine the possible values of X and Y for a problem?

To determine the possible values of X and Y for a problem, you must first consider any given constraints or limitations. Then, you can use mathematical equations or logical reasoning to determine the range of values that X and Y can take on.

3. Can there be more than one set of possible values for X and Y for a problem?

Yes, there can be multiple sets of possible values for X and Y for a problem. This is especially true if there are no explicit constraints or if the problem is open-ended.

4. How do the possible values of X and Y affect the outcome of a problem?

The possible values of X and Y can greatly impact the outcome of a problem. They can determine the range of solutions or results that are possible and can help guide the problem-solving process.

5. Can the possible values of X and Y change during the problem-solving process?

Yes, the possible values of X and Y can change as you gather more information or make assumptions. It is important to continuously reassess and adjust the possible values as needed during the problem-solving process.

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