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Ashley had a certain amount of money which was more than $1,000. If sh

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NoMat
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Ashley had a certain amount of money which was more than $1,000. If sh [#permalink] New post   11 May 2021, 14:39
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Ashley had a certain amount of money which was more than $1,000. If she were to equally distribute the money among 7 children, she would be left with $6; if she were to equally distribute the money among 6 children, she would be left with $5; if she were to equally distribute the money among 5 children, she would be left with $4. What is the smallest amount of money that she could have had?

A) 1149
B) 1109
C) 1099
D) 1049
E) 1009
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twobagels
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Re: Ashley had a certain amount of money which was more than $1,000. If sh [#permalink] New post   11 May 2021, 19:39
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Which is the smallest # which ...

# - 6 = 7*x
# - 5 = 6*y
# - 4 = 5*z

So, subtract each respective remainder and see if the first is a multiple of 7, next is a multiple of 6 and lastly a mult of 5.

1049 - 6 = 1043, which is a multiple of 7
1049 - 5 = 1044, which is a mult of 6
1049 - 4 = 1045, which is a mult of 5
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Re: Ashley had a certain amount of money which was more than $1,000. If sh [#permalink] New post   12 May 2021, 01:31
twobagels wrote:
Which is the smallest # which ...

# - 6 = 7*x
# - 5 = 6*y
# - 4 = 5*z

So, subtract each respective remainder and see if the first is a multiple of 7, next is a multiple of 6 and lastly a mult of 5.

1049 - 6 = 1043, which is a multiple of 7
1049 - 5 = 1044, which is a mult of 6
1049 - 4 = 1045, which is a mult of 5


Thanks a lot for the suggestion, but you took the solution, what about when you don't have it? This wouldn't work
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Ashley had a certain amount of money which was more than $1,000. If sh [#permalink] New post   Updated on: 05 Dec 2023, 00:21
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NoMat wrote:
Ashley had a certain amount of money which was more than $1,000. If she were to equally distribute the money among 7 children, she would be left with $6; if she were to equally distribute the money among 6 children, she would be left with $5; if she were to equally distribute the money among 5 children, she would be left with $4. What is the smallest amount of money that she could have had?

A) 1149
B) 1109
C) 1099
D) 1049
E) 1009


Say she had N dollars.

N = 7a + 6
N = 6b + 5
N = 5c + 4
Common remainder in each case is -1. So N will be of the form 7*6*5k - 1 = 210k - 1.

Since N is at least 1000, k must be at least 5 and hence N = 1049

Answer (D)

For the logic behind this, check:

Division:
https://youtu.be/A5abKfUBFSc
https://anaprep.com/number-properties-b ... isibility/

Remainders
https://anaprep.com/number-properties-b ... isibility/
https://anaprep.com/number-properties-m ... emainders/
https://anaprep.com/number-properties-a ... -shortcut/
https://anaprep.com/number-properties-t ... emainders/

Originally posted by KarishmaB on 12 May 2021, 02:05.
Last edited by KarishmaB on 05 Dec 2023, 00:21, edited 1 time in total.
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twobagels
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Re: Ashley had a certain amount of money which was more than $1,000. If sh [#permalink] New post   12 May 2021, 09:32
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NoMat wrote:
twobagels wrote:
Which is the smallest # which ...

# - 6 = 7*x
# - 5 = 6*y
# - 4 = 5*z

So, subtract each respective remainder and see if the first is a multiple of 7, next is a multiple of 6 and lastly a mult of 5.

1049 - 6 = 1043, which is a multiple of 7
1049 - 5 = 1044, which is a mult of 6
1049 - 4 = 1045, which is a mult of 5


Thanks a lot for the suggestion, but you took the solution, what about when you don't have it? This wouldn't work


I didn't look at the solution.
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Re: Ashley had a certain amount of money which was more than $1,000. If sh [#permalink]
12 May 2021, 09:32
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