Marissa is responsible for watering 30 trees that have been planted in

Question

Marissa is responsible for watering 30 trees that have been planted in a circular pattern. Each day, she selects the first tree to water at random and then proceeds around the circle counter-clockwise, watering every \(n^{th}\) tree until all 30 trees have been watered. Which of the following is a possible value for n?

A. 3
B. 7
C. 9
D. 27
E. 28

A. 3
B. 7
C. 9
D. 27
E. 28

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nick1816 · Answer

IMO number, n, must be coprime to 30. Only option B, 7, is co-prime to 30.

GMATWhizTeam · Answer

Solution:  
To solve this question, we need to understand a basic thing; Marissa must water each plant only once, otherwise, she will end up watering the same plants again and again. Let’s take an example and understand
 • Let's assume there are 6 plants,
 o If she waters every second plant, then she will water plant in the sequence of 1, 3, 5, 1, 3, 5…, she will keep watering the same 3 plants again and again.
o If she waters every 3rd plant, then she will water plants in the sequence of 1, 4, 1, 4…, she will keep watering plane 1 and 4 again and again
o If she waters every 4th plant, then she will water plants in the sequence of 1, 5, 3, 1, 5, 3…, she will keep watering plane 1, 5 and 3 again and again.
o If she waters every 5th plant, then she will water plants in the sequence of 1, 6, 5, 4, 3, 2…, she will water each plant once.
o If she waters every 6th plant, then she will keep watering plant 1 again and again. 
• In the above case, only 5 is the case where she can water each plant and 5 is co-prime to 6.
 o We can extend this result in general; it means n must be co-prime to 30.
o Only 7 among the options is coprime to 30  
Hence, the correct answer is Option B

TestPrepUnlimited · Answer

We want to be able to water all trees, this means we want to create a loop that will water all 30 trees.

Take the choice A for example, we will water the  3rd, 6th, 9th ... 30th , and back to  3rd  tree so this creates a loop involving only 10 trees.

We would like a number x that cannot create a multiple of 30 by multiplying itself, until we reached x times 30.

Hence we need x to have no common factors with 30, this makes their LCM = x*30 and we would loop all trees.

The only number in the choices that has no common factor with 30 is choice B, 7.

Ans: B

ScottTargetTestPrep · Answer

Solution:

The short way of solving this problem is to determine the number that is relatively prime to 30. Recall that relatively prime numbers share no common factor besides 1. We see that only 7 is relatively prime to 30, so 7 must be the correct answer.

Alternate Solution:

We can number the trees from 1 to 30 and check each given answer choice:

A. 3

If n = 3, the trees watered are (the list below is the tree number and when a number is going be more than 30, it will be reduced by 30):
 
1, 4, 7, 10, 13, 16, 19, 22, 25, 28 | 1, 4, …

We see that not all the trees are watered since after the first round (note: one round means going around the circle once) of 10 trees are watered, the next round of trees are exactly the same 10 trees.

B. 7

If n = 7, by using the same concept in A, the trees watered are:

1, 8, 15, 22, 29 | 6, 13, 20, 2 | 4, 11, 18, 25 | 2, 9, 16, 23, 30 | 7, 14, 21, 28 | 5 12, 19, 26 | 3, 10, 17, 24 | 1, 8, ...

We see that after 7 rounds of watering, the trees repeat themselves. However, in the first 7 rounds, all 30 trees are watered (notice that 5 + 4 + 4 + 5 + 4 + 4 + 4 = 30).

Answer: B

Kinshook · Answer

Given: Marissa is responsible for watering 30 trees that have been planted in a circular pattern. Each day, she selects the first tree to water at random and then proceeds around the circle counter-clockwise, watering every  n^{th}  tree until all 30 trees have been watered.

Asked: Which of the following is a possible value for n?

A. 3: 3,6,9,12,15,18,21,24,27,30,.... : All 30 trees have not been watered.
B. 7: 7,14,21,28,5,12,19,26,3,10,17,24,1,8,15,22,29,6,13,20,27,4,11,18,25,2,9,16,23,30: All 30 trees have been watered.
C. 9: 9,18,27,6,15,24,3,12,21,30.....: All 30 trees have not been watered.
D. 27: 27,24,21,18,15,12,9,6,3,30....: All 30 trees have not been watered.
E. 28: 28,26,24,22,20,18,16,14,12,10,8,6,4,2,30.....: All 30 trees have not been watered.

IMO B

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Marissa is responsible for watering 30 trees that have been planted in

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