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A bug is traveling between 2 points so that the distance it travels

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A bug is traveling between 2 points so that the distance it travels [#permalink]

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New post 30 Dec 2016, 04:49
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A bug is traveling between 2 points so that the distance it travels every day is half of the distance it traveled the day before. If the distance between the two points is 14 units, how much should it travel on the first day in order to reach its destination in 3 days?

A. 4
B. 14/3
C. 6
D. 7
E. 8

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Re: A bug is traveling between 2 points so that the distance it travels [#permalink]

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New post 30 Dec 2016, 07:04
2
Say the distance travelled on day 1 is x.
Total distance in 3 days x + x/2 + x/4 =14
x=8
E

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Re: A bug is traveling between 2 points so that the distance it travels [#permalink]

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New post 30 Dec 2016, 23:49
Bunuel wrote:
A bug is traveling between 2 points so that the distance it travels every day is half of the distance it traveled the day before. If the distance between the two points is 14 units, how much should it travel on the first day in order to reach its destination in 3 days?

A. 4
B. 14/3
C. 6
D. 7
E. 8



Solution

Given :

    1. The total distance between the two points is 14 units.
    2. The bug needs to reach the destination in 3 days.
    3. The distance traveled by the bug every day is half of the distance traveled the day before.

Find :

    What is the distance which he needs to travel on the first day.

Working Out :
    Using the information given, we can write :

    \(x + \frac{x}{2} + \frac{x}{2^2} = 14\)
    where x is the distance traveled on the first day.

    Instead of solving the equation, if we just observe it and use the answer options, we can infer, that we need to find such a value of x which gives an integer when it is divided by \(2\) and \(2^2\).

    So the answer could be either 4 or 8. Plugging in the values in equation 1, we get -

    when x = 4,
      4+ 2+ 1 = 7

    when x = 8
      8 + 4 + 2 = 14

Therefore, we can see clearly that x = 8 ensures that the bug covers 14 units in 3 days, hence that is our answer.

Correct Answer: Option E

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A bug is traveling between 2 points so that the distance it travels [#permalink]

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New post 31 Dec 2016, 00:09
Bunuel wrote:
A bug is traveling between 2 points so that the distance it travels every day is half of the distance it traveled the day before. If the distance between the two points is 14 units, how much should it travel on the first day in order to reach its destination in 3 days?

A. 4
B. 14/3
C. 6
D. 7
E. 8



Distance between two points is 14 units.

Say distance traveled on first, second,and third day =\(d\), \(\frac{d}{2}\), \(\frac{d}{4}\) respectively as given in question.

\(d\)\(+\) \(\frac{d}{2}\) \(+\) \(\frac{d}{4}\) \(= 14\)

d = 8

Hence, distance traveled on day first = 8 units (E)
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Re: A bug is traveling between 2 points so that the distance it travels [#permalink]

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New post 23 Mar 2017, 20:08
Bunuel wrote:
A bug is traveling between 2 points so that the distance it travels every day is half of the distance it traveled the day before. If the distance between the two points is 14 units, how much should it travel on the first day in order to reach its destination in 3 days?

A. 4
B. 14/3
C. 6
D. 7
E. 8


We can also back-solve the question using options.
8+8/2+8/4 = 8+4+2 = 12
Ans :E
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Re: A bug is traveling between 2 points so that the distance it travels [#permalink]

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New post 27 Mar 2017, 17:28
1
Bunuel wrote:
A bug is traveling between 2 points so that the distance it travels every day is half of the distance it traveled the day before. If the distance between the two points is 14 units, how much should it travel on the first day in order to reach its destination in 3 days?

A. 4
B. 14/3
C. 6
D. 7
E. 8


We can let x = the distance the bug travels on the first day.

Day 1 = x

Day 2 = (1/2)x

Day 3 = (1/4)x

We can create the following equation:

(x + (1/2)x + (1/4)x) = 14

Multiplying the entire equation by 4, we have:

4x + 2x + x = 56

7x = 56

x = 8

Answer: E
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Re: A bug is traveling between 2 points so that the distance it travels   [#permalink] 27 Mar 2017, 17:28
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