A teacher organized a field trip for a group of children, with the

Question

A teacher organized a field trip for a group of children, with the total number of children between 58 and 62, inclusive. If each child must be assigned to exactly one group, can the teacher divide all the children equally into groups?

(1) The number of groups is greater than 6 but fewer than 9.

(2) The total number of children is not divisible by 5.

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Bunuel · Accepted Answer

Official Solution:

A teacher organized a field trip for a group of children, with the total number of children between 58 and 62, inclusive. If each child must be assigned to exactly one group, can the teacher divide all the children equally into groups? 
 
We are asked whether all the children can be divided  equally  into groups, which means (the number of children)/(the number of groups) is an integer.
 
(1) The number of groups is greater than 6 but fewer than 9.
 
So the number of groups is either 7 or 8. From the stem, the number of children is 58, 59, 60, 61, or 62. None of these is divisible by either 7 or 8. So it does not matter how many children there are. In every case, equal division into either 7 or 8 groups is not possible. Sufficient.
 
(2) The total number of children is not divisible by 5.
 
This removes 60 from consideration, leaving 58, 59, 61, and 62. If the number of children is 58 and there are 2 groups, the answer is Yes. But if the number of groups is 4, the answer is No. Not sufficient.

Answer: A

Dereno · Answer

The teacher organised the field trip for a group of students , total number of students between 58 and 62 inclusive.

Number of students = { 58, 59, 60, 61, 62}

The question mentions, each child has be to be in a group, and  CAN  the teacher divide the group equally ?

The question CAN has two outcomes - yes / no.

If we are able to get a conclusive yes or no, it’s sufficient else not sufficient.

Statement 1:

(1) The number of groups is greater than 6 but fewer than 9.

Group size = (7,8).

As none of the numbers { 58, 59, 60, 61, 62} are divisible fully by either 7 or 8 or LCM of (7,8). We can definitely say that group of equal numbers cannot be formed. Hence,  Sufficient.

Statement 2:

(2) The total number of children is not divisible by 5.

The total number of children is not divisible by 5 = { 58, 59, 61, 62} remains.

Among the numbers, 59 and 61 are prime numbers. So only factor other than the number is 1.

For numbers, 58 and 62, we have

58 = 2*29 
62 = 2*31

So, it can be either groups of 2,31 or 29. 
or cannot be separated as a group = 59,61.

Hence, we cannot conclusively say a group can be created. So  Insufficient

Option A

gmatophobia · Answer

The number of children in the group can be 58, 59, 60, 61, and 62

Statement 1
  
 (1) The number of groups is greater than 6 but fewer than 9.

The number of groups can either be 7 or can be 8.

The possible values of the number of students in the group is neither a multiple of 7 or is a multiple of 8. Hence, we can conclude that the teacher cannot divide all children equally into groups.

The information provided in the statement alone is sufficient to answer the question asked.

Statement 2
  
 (2) The total number of children is not divisible by 5.

From the information provided in Statement 2, we can conclude that the number of students in the group is not equal to 60. However, we can't say conclusively whether the teacher could divide all the children equally into groups. For example,

if the number of students is 62, and the number of groups = 2 → the teacher can divide the students equally into groups

if the number of students is 62, and the number of groups = 3 → the teacher cannot divide the students equally into groups

Statement 2 alone is not sufficient to answer the question asked.

Option A

A teacher organized a field trip for a group of children, with the

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