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Glass of water

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Glass of water

by gmatrant » Fri Oct 19, 2007 9:49 am
I couldnt understand this problem.. how to solve it.

An ice cube is floating in a glass of water with between 1/6 and 1/7 of its mass above water and the rest submerged below the water's surface. The ratio of the part of the mass above water to the part of the mass below water is between
(A) 1/5 and 1/6
(B) 1/6 and 1/7
(C) 5/6 and 5/7
(D) 6 and 7
(E) 6/7 and 7/6

Ans : A
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by Prasanna » Fri Oct 19, 2007 10:15 am
When 1/6 of the ice cube is above water then 5/6 is below it. The ratio of ice cube above water to below water is 1/5

When 1/7 of the ice cube is above water then 6/7 is below it. The ratio of ice cube above water to below water is 1/6

Hence option A
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by mschling52 » Fri Oct 19, 2007 10:17 am
I think this one is A.

Let x be the fraction of the ice cube above the water. We are told that

1/7 < x < 1/6

Then for the lower bound of this range, the ratio of the mass above the water to the mass below is

(1/7)/(6/7) (1/7 above compared to 6/7 below)

=(1/7)*(7/6) = 1/6.

And, for the upper bound of the range, the ratio of the mass above the water to the mass below is

(1/6)/(5/6)

=(1/6)*(6/5) = 1/5.

So, we know the ratio of the mass above to the mass below will be between 1/6 and 1/5.
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by beatthegmat » Fri Oct 19, 2007 7:01 pm
Moved this post to the PS area.
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