154 candies are distributed to children with the same number. What can

D is the answer because range 40-50 does not have number divisible to 154.

All other ranges have divisible numbers:

(A) 1-10: 7
(B) 10-20: 14
(C) 20-30: 22
(D) no number of 40, 41, 42, 42, 44, 45, 46, 47, 48, 49, 50 is divisible by 154
(E) 70-80: 77

Hence: D

The wording of the question is certainly not clear. What it is trying to say is:
If 154 candies are distributed evenly to \(x\) number of children (so that each child receives the same number of candies), \(x\) could be in any of the following ranges except:


To answer this we need to know which numbers divide 154 evenly, i.e. we need to know all the factors of 154. 154 can be divided in the following ways:
1*154
2*77
7*22
11*14

So 154 has the following factors:
1, 2, 7, 11, 14, 22, 77, 154

We know these are all the factors of 154, because they are all the products of the prime factors of 154 - 2, 7, 11:

2
7
11
2*7 = 14
2*11 = 22
7*11 = 77
2*7*11 = 154
(and not forgetting 1)

Looking at the ranges provided in the answer choices, at least one factor of 154 appears in each of the ranges except D. 40 to 50.

Cheers,

154 candies are distributed to children with the same number. What can’t be the range including the number of children?
A. 1~10 B. 10~20 C. 20~30 D. 40~50 E. 70~80


-> In 154=1*154=2*77=7*22=11*14, you can come up with 4 cases. One is distributing 77 candies to 2 children each. Another is distributing 2 candies to 77 children each. Also, you can distribute 22 candies to 7 children. The other is distributing 7 candies to 22 children. Amongst these cases, what is not included is D. 40~50. Therefore, the answer is D.