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05 Nov 2022, 15:29
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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:
22% (02:02) correct
78%
(02:15)
wrong
based on 32
sessions
History
Date
Time
Result
Not Attempted Yet
A jogging track in a park is in the shape of a regular hexagon inscribed in an equilateral triangle such that PQR is an Equilateral triangle and UVWXYZ is a regular hexagon inscribed inside the equilateral triangle.
Points Y and Z lie on PQ, Points U and V lie on PR, and Points X and W lie on QR.
Two people M and N start jogging along this track along different paths. The speeds of M and N are in the ratio 1:2 and M can complete the distance PR in 9 minutes.
If both of them start jogging from Y and M follows the clockwise path around the hexagon while N follows the clockwise path around the equilateral triangle, where will they meet for the first time, and after how long?
A. At Y after 28 minutes
B. At X after 51 minutes
C. At U after 54 minutes
D. At W after 36 minutes
E. At V after 45 minutes
Points Y and Z lie on PQ, Points U and V lie on PR, and Points X and W lie on QR.
Two people M and N start jogging along this track along different paths. The speeds of M and N are in the ratio 1:2 and M can complete the distance PR in 9 minutes.
If both of them start jogging from Y and M follows the clockwise path around the hexagon while N follows the clockwise path around the equilateral triangle, where will they meet for the first time, and after how long?
A. At Y after 28 minutes
B. At X after 51 minutes
C. At U after 54 minutes
D. At W after 36 minutes
E. At V after 45 minutes
Archit3110
05 Nov 2022, 19:56
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a hexagonal figure has '6' equal equilateral ∆
given PQR is an equilateral ∆ and Points Y and Z lie on PQ, Points U and V lie on PR, and Points X and W lie on QR.
also
Sm/Sn = 1/2
for any side of ∆ the ratio of its side with a hexagon the sides will be in '3' equal parts
PR being same we can find time N takes to cover the distance
let PR be x
x/9 * ( Tn /x ) = 1/2
x = 4.5
Let PR be 6 units
Speed of M ; 6/9 ; 0.66 and Speed of N ; 1.33
since they are moving in opposite direction so relative speed
0.66+1.33 ; ~2
need to determine "where will they meet for the first time, and after how long"
use answer options to determine , the correct option should be a factor of '6'
Option A . At Y after 28 minutes , the distance covered would be 28*2 ; 56 ; which is not factor of 6 incorrect
Option B . At X after 51 minutes , the distance covered would be 51*2 ; 102 , which is factor of 6 ; correct
OPTION B is correct
aashishmittal63 whats the source of this question..?
given PQR is an equilateral ∆ and Points Y and Z lie on PQ, Points U and V lie on PR, and Points X and W lie on QR.
also
Sm/Sn = 1/2
for any side of ∆ the ratio of its side with a hexagon the sides will be in '3' equal parts
PR being same we can find time N takes to cover the distance
let PR be x
x/9 * ( Tn /x ) = 1/2
x = 4.5
Let PR be 6 units
Speed of M ; 6/9 ; 0.66 and Speed of N ; 1.33
since they are moving in opposite direction so relative speed
0.66+1.33 ; ~2
need to determine "where will they meet for the first time, and after how long"
use answer options to determine , the correct option should be a factor of '6'
Option A . At Y after 28 minutes , the distance covered would be 28*2 ; 56 ; which is not factor of 6 incorrect
Option B . At X after 51 minutes , the distance covered would be 51*2 ; 102 , which is factor of 6 ; correct
OPTION B is correct
aashishmittal63 whats the source of this question..?
aashishmittal63
06 Nov 2022, 02:55
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I have a doubt here.
Let's say that the side of the regular hexagon is x. We know that angles P,Q and R are all 60. All the smaller triangles formed(QYX, PZU, RVW) will also be equilateral triangles as all angles are 60(internal angles in a hexagon are 120 and all angles formed in the triangles are compliments of 120).
Then we know that YX=YQ=QX=x and side of PQR=3x
Now both M and N start at Y and move in the same direction with speed of M:N as 1:2. We also know that M covers 3x in 9 mins; so M will cover x in 3 mins and N will do so in 1.5 mins.
Now assuming both start at Y and move in clockwise direction. Snapshot after 3 mins: M will x units along YX and end up at X. N will cover 2x units from Y to Q(x)and then Q to X(x) and be at X.
Then isn't the answer X after 3 minutes.
Where am I wrong?
Let's say that the side of the regular hexagon is x. We know that angles P,Q and R are all 60. All the smaller triangles formed(QYX, PZU, RVW) will also be equilateral triangles as all angles are 60(internal angles in a hexagon are 120 and all angles formed in the triangles are compliments of 120).
Then we know that YX=YQ=QX=x and side of PQR=3x
Now both M and N start at Y and move in the same direction with speed of M:N as 1:2. We also know that M covers 3x in 9 mins; so M will cover x in 3 mins and N will do so in 1.5 mins.
Now assuming both start at Y and move in clockwise direction. Snapshot after 3 mins: M will x units along YX and end up at X. N will cover 2x units from Y to Q(x)and then Q to X(x) and be at X.
Then isn't the answer X after 3 minutes.
Where am I wrong?
