Troubling Tree

Algebra Level 2

Assume that there is a tree that grows in such a way that its height on a given day is twice what it was on the previous day. For example, the tree was 1 meter tall on first day, 2 meters tall on the second, 4 meters tall on the third day, and so on.

On the 50th day, it reached its full length. On which day it was just half the full length?


The answer is 49.

Varun Gupta by Varun Gupta , 23, India

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3 solutions

Uttam Verma
Jul 21, 2014

The tree doubles its length everyday.. so if the tree is at its full length on 50th day, it must be half its length on 49th day.. This is because on 50th day , its length will be twice its length on 49th day and ,we know, 2 times half(2*1/2) equals one whole..!! So its length will be just half of its full length on 49th day..!!

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Jeremy Bansil
Jul 13, 2014

The asked question would fool you if you don't read carefully. It is said that the tree grows twice as big as it was on the last day . So the answer's 49th day.

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Jalees Mughal
Jul 30, 2014

common factor is 2 so, 2 50 = 1.125 × 10 14 { 2 }^{ 50 }\quad =\quad 1.125\quad \times \quad { 10 }^{ 14\quad } = 1.125 × 10 14 2 = 5.629 × 10 14 =\quad \frac { 1.125\quad \times \quad { 10 }^{ 14\quad } }{ 2 } \quad =\quad 5.629\quad \times \quad { 10 }^{ 14 } and, = 2 49 = 5.629 × 10 14 =\quad { 2 }^{ 49 }\quad =\quad 5.629\quad \times \quad { 10 }^{ 14 } so correct ans is 49..

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