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MathRevolution
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154 candies are distributed to children with the same number. What can Updated on: 13 Jan 2016, 02:30
Originally posted by MathRevolution on 10 Jan 2016, 06:39.
Last edited by Bunuel on 13 Jan 2016, 02:30, edited 2 times in total.
Edited the question.
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65% (01:38) correct 35% (01:15) wrong based on 118 sessions

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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



* A solution is going to be uploaded in two days.
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D
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154 candies are distributed to children with the same number. What can 10 Jan 2016, 06:51
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MathRevolution
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



* A solution is going to be uploaded in two days.
Show more

hi,
the coloured portion is not very clear. whose range are we looking for?
Irrespective of the range of children or candies, the answer would depend on the factors of 154..
154=1*154
154=2*77
154=7*22
154=11*14...


A. 1~10 - 1,2,7
B. 10~20 -11,14
C. 20~30 -22
D. 40~50 ----
E. 70~80 -77


now all ranges mentioned are covered except 40-50
ans D
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154 candies are distributed to children with the same number. What can 10 Jan 2016, 07:28
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chetan2u
MathRevolution
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



* A solution is going to be uploaded in two days.

hi,
the coloured portion is not very clear. whose range are we looking for?
Irrespective of the range of children or candies, the answer would depend on the factors of 154..
154=1*154
154=2*77
154=7*22
154=11*14...


A. 1~10 - 1,2,7
B. 10~20 -11,14
C. 20~30 -22
D. 40~50 ----
E. 70~80 -77


now all ranges mentioned are covered except 40-50
ans D
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If 154 candies distributed to same candidates so 154 divisible by 154 must be 1?
What am I doing wrong?
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154 candies are distributed to children with the same number. What can 12 Jan 2016, 02:32
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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
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154 candies are distributed to children with the same number. What can 12 Jan 2016, 14:46
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MathRevolution
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

Show more


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,
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154 candies are distributed to children with the same number. What can 12 Jan 2016, 18:48
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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.
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