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An ant started walking eastwards at a speed of 2 metres per minute. If 21 Jun 2019, 18:30
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55% (hard)

Question Stats:

69% (02:38) correct 31% (02:49) wrong based on 331 sessions

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An ant started walking eastwards at a speed of 2 meters per minute. If after every 4 minutes the ant reverses direction and halves its speed, how far would the ant be from the starting point after 5 hours?

A. 1/3 meters
B. 2/3 meters
C. 4/3 meters
D. 8/3 meters
E. 16/3 meters
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E
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An ant started walking eastwards at a speed of 2 metres per minute. If 22 Jun 2019, 12:39
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Lets say the ant walks 8 meters (distance covered in 4 minutes) eastwards from point A and turns at point B, then walks 4 meters westwards and turns at point C which should be 4 meters from starting point A, and then walks 2 meters eastwards and turns at point D and then 1 meter westwards and turns at point E and so on.

From this pattern we can observe that the ant never walks back west of point C which is 4 meters from A.

Therefore the answer must be the answer choice which is greater than 4

Only E fits

Answer is (E)

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An ant started walking eastwards at a speed of 2 metres per minute. If 22 Jun 2019, 11:40
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nick1816
An ant started walking eastwards at a speed of 2 meters per minute. If after every 4 minutes the ant reverses direction and halves its speed, how far would the ant be from the starting point after 5 hours?

A. 1/3 meters
B. 2/3 meters
C. 4/3 meters
D. 8/3 meters
E. 16/3 meters
Show more

1st 4 min, distance covered = 2*4 = 8 meters forward
2nd 4 min, distance covered is half in reverse direction (since spied is halved for same time) = -4 meters
3rd 4 min = +2 meters

So, series would look like 8, -4, 2, -1, 1/2, . . . Upto 60 terms
—> The above is a GP series with ratio, r = -1/2, 1st term a = 8

Sum of 60 terms = a(1 - r^(60))/(1 - r)

IMPORTANT to assume r^60 = (-1/2)^60 as 0!!

—> Sum = 8*(1 - 0)/(1 - (-1/2))
= 8/(3/2)
= 16/3 meters

IMO Option E

Pls Hit kudos if you like the solution

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An ant started walking eastwards at a speed of 2 metres per minute. If 24 Oct 2019, 06:54
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Dillesh4096
nick1816
An ant started walking eastwards at a speed of 2 meters per minute. If after every 4 minutes the ant reverses direction and halves its speed, how far would the ant be from the starting point after 5 hours?

A. 1/3 meters
B. 2/3 meters
C. 4/3 meters
D. 8/3 meters
E. 16/3 meters

1st 4 min, distance covered = 2*4 = 8 meters forward
2nd 4 min, distance covered is half in reverse direction (since spied is halved for same time) = -4 meters
3rd 4 min = +2 meters

So, series would look like 8, -4, 2, -1, 1/2, . . . Upto 60 terms
—> The above is a GP series with ratio, r = -1/2, 1st term a = 8

Sum of 60 terms = a(1 - r^(60))/(1 - r)

IMPORTANT to assume r^60 = (-1/2)^60 as 0!!

—> Sum = 8*(1 - 0)/(1 - (-1/2))
= 8/(3/2)
= 16/3 meters

IMO Option E

Pls Hit kudos if you like the solution

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I think your solution is brilliant but I am yet to understand how you determined that there are 60 terms in the series. I will be very grateful if you could help. Thanks in advance.
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An ant started walking eastwards at a speed of 2 metres per minute. If 24 Oct 2019, 07:09
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Dillesh4096
nick1816
An ant started walking eastwards at a speed of 2 meters per minute. If after every 4 minutes the ant reverses direction and halves its speed, how far would the ant be from the starting point after 5 hours?

A. 1/3 meters
B. 2/3 meters
C. 4/3 meters
D. 8/3 meters
E. 16/3 meters

1st 4 min, distance covered = 2*4 = 8 meters forward
2nd 4 min, distance covered is half in reverse direction (since spied is halved for same time) = -4 meters
3rd 4 min = +2 meters

So, series would look like 8, -4, 2, -1, 1/2, . . . Upto 60 terms
—> The above is a GP series with ratio, r = -1/2, 1st term a = 8

Sum of 60 terms = a(1 - r^(60))/(1 - r)

IMPORTANT to assume r^60 = (-1/2)^60 as 0!!

—> Sum = 8*(1 - 0)/(1 - (-1/2))
= 8/(3/2)
= 16/3 meters

IMO Option E

Pls Hit kudos if you like the solution

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Hi there, I am following up on my last question. After a careful review, I realised that there should be 75 terms instead of 60. There are a total of 5 hours. Each hour has 60 minutes which makes a total of 300 minutes. Divide this by 4 to get the number of terms as 75. The answer will of course remain the same but I think it is good to just clarify things.
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An ant started walking eastwards at a speed of 2 metres per minute. If 24 Oct 2019, 11:10
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coylahood
Dillesh4096
nick1816
An ant started walking eastwards at a speed of 2 meters per minute. If after every 4 minutes the ant reverses direction and halves its speed, how far would the ant be from the starting point after 5 hours?

A. 1/3 meters
B. 2/3 meters
C. 4/3 meters
D. 8/3 meters
E. 16/3 meters

1st 4 min, distance covered = 2*4 = 8 meters forward
2nd 4 min, distance covered is half in reverse direction (since spied is halved for same time) = -4 meters
3rd 4 min = +2 meters

So, series would look like 8, -4, 2, -1, 1/2, . . . Upto 60 terms
—> The above is a GP series with ratio, r = -1/2, 1st term a = 8

Sum of 60 terms = a(1 - r^(60))/(1 - r)

IMPORTANT to assume r^60 = (-1/2)^60 as 0!!

—> Sum = 8*(1 - 0)/(1 - (-1/2))
= 8/(3/2)
= 16/3 meters

IMO Option E

Pls Hit kudos if you like the solution

Posted from my mobile device

Hi there, I am following up on my last question. After a careful review, I realised that there should be 75 terms instead of 60. There are a total of 5 hours. Each hour has 60 minutes which makes a total of 300 minutes. Divide this by 4 to get the number of terms as 75. The answer will of course remain the same but I think it is good to just clarify things.
Show more

Hi coylahood

Yes. It’s 75 in place of 60. Thanks for the correction.

Yes, the answer will remain the same.

Regards
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An ant started walking eastwards at a speed of 2 metres per minute. If 13 Jul 2025, 10:10
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