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27 Jul 2018, 22:32
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (01:43) correct
66%
(01:41)
wrong
based on 279
sessions
History
Date
Time
Result
Not Attempted Yet
A Square is to be drawn on the xy plane. If one vertex of the square needs to be at
the origin, sides of the square need to be 5 units each, and all coordinates of all
vertices need to be integers, how many different squares are possible?
A. 4
B. 6
C. 8
D. 12
E. 16
Source: Experts Global
the origin, sides of the square need to be 5 units each, and all coordinates of all
vertices need to be integers, how many different squares are possible?
A. 4
B. 6
C. 8
D. 12
E. 16
Source: Experts Global
27 Jul 2018, 23:42
Kudos
Bookmarks
Hi,
This is a very interesting question.
Easily someone could fall for the trap answer as 4 here.
If one visualize the squares only on the x and y axis, then they end up falling for the trap.
So the vertices need not be only on the x and y axis, they have mentioned all the vertices should be integers,
So, Let’s try to visualize it,
We can see that,
Co-ordinates (-4,3) forms a side length of the square as 5 from the origin (0,0), Because 3-4-5 are pythogorean triplets.
As shown in the figure(In the attachment), we can form four squares starting with point (-4,3).
So similarly starting with the point (-3,4), we can form 4 different squares.
Already on the x and y axis there are 4 different squares.
So totally, we can form 12 different squares with side length as 5 and one vertex at the origin. So the answer is D.
Most important factor of solving a co-ordinate geometry question is visualizing.
Hope this helps.
This is a very interesting question.
Easily someone could fall for the trap answer as 4 here.
If one visualize the squares only on the x and y axis, then they end up falling for the trap.
So the vertices need not be only on the x and y axis, they have mentioned all the vertices should be integers,
So, Let’s try to visualize it,
We can see that,
Co-ordinates (-4,3) forms a side length of the square as 5 from the origin (0,0), Because 3-4-5 are pythogorean triplets.
As shown in the figure(In the attachment), we can form four squares starting with point (-4,3).
So similarly starting with the point (-3,4), we can form 4 different squares.
Already on the x and y axis there are 4 different squares.
So totally, we can form 12 different squares with side length as 5 and one vertex at the origin. So the answer is D.
Most important factor of solving a co-ordinate geometry question is visualizing.
Hope this helps.
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PS - GMAT thread.png [ 24.51 KiB | Viewed 15043 times ]
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