GMAT Coordinate Geometry | Properties of Line | GMAT Sample Questions | GMAT 700 level Question
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- Опубліковано 19 вер 2024
- GMAT Coordinate Geometry | Properties of Line | GMAT Sample Questions | GMAT 700 level Question
This GMAT problem solving question is a part of the free GMAT online prep questions by Wizako. This question tests the understanding of equation and properties of a line and number theory.
Question:
Set S contains points whose x and y coordinates are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (8, 0) and the point (0, 12) is the lowest among all elements in set S. How many such points P exist in set S?
A. 1
B. 5
C. 11
D. 8
E. 3
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The question is asking for a point P that has sum of the distances to be lowest AMONG all elements in set S. Then why would it necessarily be on the line segment? If all points in s are outside the line segment, then p can be a point lying outside the line segment with the lowest sum of distances right?
Oh is it supposed to be assumed that S is not a limited set of points but the set of all points where x & y are natural numbers? But the question says S is "contains points" not "contains all points"
Why the point ( 8 0) and ( 0 12) don't count. These two point also on this line, and no where mentioned exclude these two point, thank you
Per the question, the x and y coordinates should be natural numbers. 0 is not a natural number. So, the two end points are not included.
Cheers
@@ksaravanabaskar5690 oh..yeah, thanks a lot Mr. Baskar.. your quick reply really solved my confusion.
Amazing Description sir 😍👌
Thanks for your feedback. The 4th and 5th question in this playlist are really interesting questions. Pls try them. ua-cam.com/play/PL3JsYBL14ZlvQM-tIQCTlwaog3hPMRYiV.html
The question doesn't ask x and y to be integers. It says they should be natural numbers. Therefore it can include fractions or decimals too. which makes the 2nd half of the answer irrelevant to me. don't you think so sir? It will be great if you clear my doubt.
Natural numbers do not include decimals or fractions. Natural numbers are positive integers starting from one. I hope that this clears your doubt. Best wishes for your GMAT preparation!
Can we also solve this question using distance formulae? If yes, could anyone please provide the solution. I started with the similar concept but used distance formulae to calculate the points instead of Intercept form. But I am stuck at the last.
Hello Tanya,
It is not advisable to solve this question via the distance formula as that approach will render a quadratic equations with two variables and 3 roots with no basis on what the variables might be as there are squares under roots involved. It is always better to use the two point formula or its successor, the intercept formula to solve this question. Please reply to this comment for any further queries. Best wishes for your GMAT Preparation!!!
how do we solve all of this in 3 minutes?
The GMAT is an adaptive test. So, it will have a mix of easy to difficult questions. The easier questions usually take much lesser than the average time of 2 minutes per question. So, the time saved there can be used for the tougher and time consuming questions