Quant Question Of The Day: 28
[latexpage]
Numbers
How many ordered integral pairs (x,y) satisfy the equation 3x2 – y2 = 1747 ?
A. 0
B. 1
C. 2
D. More than 2 pairs
Recent Forum Posts/Questions/Answers
Recent Blog Posts
Recent Blog Comments
- LouisHayes on Quant Question Of The Day: 275
- pankaj saket on GK Question of the day: 22
- sajal on Puzzle of The Day
- sajal on Puzzle of The Day
- Lalit Bansal on Quant Question Of The Day: 275
- Rajendra Kumar on Countdown to CAT 2020|DAY 87|LRDI
- Shruti Tiwari on GK Question of the day: 21
- Deepika on GK Question of the day: 21
- Deepika on Quant Question Of The Day: 275
- Anubhav Swaroop on Quant Question Of The Day: 269
Other websites
© 2007-2020 by TathaGat.
A. 0
Let’s look at this as 3x^2 = 1747 + y^2
Now, 1747 is of form 3k+1. Therefore, y^2 is of form 3k+2 for x^2 to be integral.
We know, square of any natural no. is of form 3k or 3k+1. Thus, no such solution possible.
No such pairs are possible.
Also ,is there any shortcut to ascertain which number is prime and which is not.Because my initial time got wasted in finding whether it is a prime number or not.
no such pair is possible as 1747 is a prime number (6K-1)
therefore answer A
Only one option is there i.e first find the square root then check with the prime no.below that square root ..if divided then it’s not else it is.
Only one option is there i.e first find the square root then check with the prime no.below that square root ..if divided then it’s not else it is……..and in this no such pair is possible
You find the square of the number closest to the given one; in this case 42 square = 1764.
Then you divide the given number i.e. 1747 with all the prime numbers below 42. If it is not divisible by any of these prime numbers, then the given number is also prime.
I use this method. If there is a shorter method than this then kindly share the same sir.
Sir please post the solution of this problem.
No pair possible