mec placement
I have learnt many good things about TCS from my seniors. Its training is more innovative and good. It has many awards like “Golden Peacock National Traning Award in 2006 ”, “National award for innovative learning practices” etc. Even it has many achievements like “First One to launch R&D in India”, “Indias largest ISP” and many more that I saw in its site. So I am passionate about TCS.
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16)Let x = the 1st digit on the first mile stone
Let y = the 2nd digit
Let s = speed of the car
"Then travels for 1 hour and sees the same 2 digits in reverse order."
10x + y + 1s = 10y + x
10x - x + s = 10y - y
9x + s = 9y
"1 hours later he sees that the milestone has the same 2 digits with a 0 between them."
10y + x + s = 100x + y
10y - y + s = 100x - x
9y + s = 99x
Rearrange the above two equations for elimination
9x - 9y + s = 0
-99x+9y + s = 0
----------------adding eliminates y
-90x + 2s = 0
2s = 90x
s = 45x
x has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added to
a two digit milestone, could not be at another two digit milestone.)
Find y
9x + s = 9y
9(1) + 45 = 9y
9 + 45 = 9y
simplify divide by 9
1 + 5 = y
y = 6
Speed is 45 mph
Try this:
1st milestone: 16
travel one hr +45
2nd milestone: 61
travel one hr:+45
3rd milestone:106
Let y = the 2nd digit
Let s = speed of the car
"Then travels for 1 hour and sees the same 2 digits in reverse order."
10x + y + 1s = 10y + x
10x - x + s = 10y - y
9x + s = 9y
"1 hours later he sees that the milestone has the same 2 digits with a 0 between them."
10y + x + s = 100x + y
10y - y + s = 100x - x
9y + s = 99x
Rearrange the above two equations for elimination
9x - 9y + s = 0
-99x+9y + s = 0
----------------adding eliminates y
-90x + 2s = 0
2s = 90x
s = 45x
x has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added to
a two digit milestone, could not be at another two digit milestone.)
Find y
9x + s = 9y
9(1) + 45 = 9y
9 + 45 = 9y
simplify divide by 9
1 + 5 = y
y = 6
Speed is 45 mph
Try this:
1st milestone: 16
travel one hr +45
2nd milestone: 61
travel one hr:+45
3rd milestone:106
4. Let O stand for an ordinary coin and G stand for the gold coin
Initially,
O1-O2-G-O3-O4-..-O20
Suppose Alice does the 1-move. Then,
O2-O1-G-O3-O4-..-O20
Then Bob can follow two paths
1. Bob does a 0-move
2. Bob does a 2-move or a higher move
1. If Bob does a 0-move, A cannot do a 1-move or 0-move. So, A would do a 2-move or a higher move. Then,
O1-G-O3-..-O20
Bob then cannot do a 0-move. So A wins
2. If Bob does a 2-move or higher, A would do a 0-move and win!
Radius of the extreme square be r , its diameter is equal to 1.4r +r. other 7 square will have diameter as 2r each.
so total 1.4r + r + 14r + 1.4r + r = 1.4 s
so ratio comes out to be 13.2 : 1
hence option 3 So, for A to win, 1-move is the best strategy!
Initially,
O1-O2-G-O3-O4-..-O20
Suppose Alice does the 1-move. Then,
O2-O1-G-O3-O4-..-O20
Then Bob can follow two paths
1. Bob does a 0-move
2. Bob does a 2-move or a higher move
1. If Bob does a 0-move, A cannot do a 1-move or 0-move. So, A would do a 2-move or a higher move. Then,
O1-G-O3-..-O20
Bob then cannot do a 0-move. So A wins
2. If Bob does a 2-move or higher, A would do a 0-move and win!
Radius of the extreme square be r , its diameter is equal to 1.4r +r. other 7 square will have diameter as 2r each.
so total 1.4r + r + 14r + 1.4r + r = 1.4 s
so ratio comes out to be 13.2 : 1
hence option 3 So, for A to win, 1-move is the best strategy!
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