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A ten headed demon

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by sanju09 » Sun Oct 20, 2013 5:18 am
A ten headed demon has its sixth head 40 percent heavier than its second head, counting left to right. His each head from second to fifth is x pounds heavier than the previous one, and his each head from sixth to tenth is x pounds lighter than the previous one. If his first head weighs 4 pounds, then what is the value of x?
A. ½
B. 1
C. 1½
D. 2
E. 2½



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by theCodeToGMAT » Sun Oct 20, 2013 5:31 am
L TO R : 6th Head = 1.4 (2nd)

1st = H
2nd = H + x
3rd = H + 2x
4th = H + 3x
5th = H + 4x
6th = H + 3x
7th = H + 2x
8th = H + x
9th = H
10th= H - x

H = 4

H + 3x = 1.4 (H + x)
4 + 3x = 1.4*4 + 1.4X

1.6x = 1.6
x = 1

is it {B}?

btw, belated Happy Dussehra :)
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by mevicks » Sun Oct 20, 2013 6:24 am
Original situation: 4_ a_ __ __ __ 1.4a __ __ __ __

Directly test the answer values, starting with C:

x = 1.5
Add 1.5 from 2nd to fifth, Inclusive. Reduce 1.5 from 6th onwards...
4_ 6.5 8_ 9.5 11 9.5 __ __ __ __
But 6.5*1.4 = 9.1 ≠ 9.5
Since the answer is greater test the next lower value

x = 1
Add 1 from 2nd to fifth, Inclusive. Reduce 1 from 6th onwards...
4_ 5_ 6_ 7_ 8_ 7_ __ __ __ __
5*1.4 = 7

Thus the answer seems to be B
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by ganeshrkamath » Sun Oct 20, 2013 6:53 am
sanju09 wrote:A ten headed demon has its sixth head 40 percent heavier than its second head, counting left to right. His each head from second to fifth is x pounds heavier than the previous one, and his each head from sixth to tenth is x pounds lighter than the previous one. If his first head weighs 4 pounds, then what is the value of x?
A. ½
B. 1
C. 1½
D. 2
E. 2½



Made up
W6 = 1.4W2
W6 = W5 - x
= (W4 + x) - x
= (W3 + 2x) - x
= (W2 + 3x) - x
= W2 + 2x

1.4W2 = W2 + 2x
0.4W2 = 2x
x = 0.2W2
x = 0.2(W1 + x)
x = 0.2W1 + 0.2x
0.8x = 0.2W1
x = W1/4 = 4/4 = 1

Choose B

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by sanju09 » Mon Oct 21, 2013 11:06 pm
theCodeToGMAT wrote:L TO R : 6th Head = 1.4 (2nd)

1st = H
2nd = H + x
3rd = H + 2x
4th = H + 3x
5th = H + 4x
6th = H + 3x
7th = H + 2x
8th = H + x
9th = H
10th= H - x

H = 4

H + 3x = 1.4 (H + x)
4 + 3x = 1.4*4 + 1.4X

1.6x = 1.6
x = 1

is it {B}?

btw, belated Happy Dussehra :)
Yes, it's (B)! Plugging in the answers would have been a far faster approach for this kind of a question; as adopted by mevicks.

[spoiler]Same to you for the greetings, Rahul![/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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