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twice as many mice ran out

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by sanju09 » Tue May 27, 2014 1:30 am
There were m mice roaming in a room on one Sunday. A cat entered the room on that Sunday and ate one mouse and consequently x of the mice ran out of the room. The cat continued to enter the room on all of the following days to eat one mouse and consequently twice as many mice ran out of the room as on the previous day. If there was exactly one mouse remained in the room after the fourth visit of the cat to the room, which of the following cannot be a value of m?
A. 20
B. 35
C. 50
D. 65
E. 75



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by theCodeToGMAT » Tue May 27, 2014 1:47 am
1 = m - (1+x) - (1+2x) - (1+4x) - (1+8x)

1 = m - 4 - 15x
m - 15x = 5
m = 15x + 5

So, answer must be multiple of 15 plus 5

{A} YES
{B} YES
{C} YES
{D} YES
{E} NO

[spoiler]{E}?[/spoiler]
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by sanju09 » Tue May 27, 2014 3:17 am
theCodeToGMAT wrote:1 = m - (1+x) - (1+2x) - (1+4x) - (1+8x)

1 = m - 4 - 15x
m - 15x = 5
m = 15x + 5

So, answer must be multiple of 15 plus 5

{A} YES
{B} YES
{C} YES
{D} YES
{E} NO

[spoiler]{E}?[/spoiler]
Nice approach, Rahul!
The mind is everything. What you think you become. -Lord Buddha



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