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What is the least number which when divided by 5, 6, 7 and 8 leaves a

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What is the least number which when divided by 5, 6, 7 and 8 leaves a  [#permalink]

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New post 17 Jul 2017, 13:38
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:54) correct 30% (01:46) wrong based on 53 sessions

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What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108
B. 1683
C. 2007
D. 3363
E. 3339

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Re: What is the least number which when divided by 5, 6, 7 and 8 leaves a  [#permalink]

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New post 17 Jul 2017, 13:51
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What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108
B. 1683
C. 2007
D. 3363
E. 3339

As per the question , number must be divisible by 9

So only B , C and E remains - out of these only B when divided by 5 leaves 3 as remainder
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Re: What is the least number which when divided by 5, 6, 7 and 8 leaves a  [#permalink]

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New post 17 Jul 2017, 14:15
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GTExl wrote:
What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108
B. 1683
C. 2007
D. 3363
E. 3339

Kudo please if you liked the question.


The biggest tip here is that the number is divisible by 9.
IMPORTANT: if a number is divisible by 9, the sum of its digits is divisible by 9.
Check the answer choices....

A. 1108 sum of digits = 10 - not divisible by 9 - ELIMINATE
B. 1683 sum of digits = 18 - divisible by 9 - KEEP
C. 2007 sum of digits = 9 - divisible by 9 - KEEP
D. 3363 sum of digits = 15 - not divisible by 9 - ELIMINATE
E. 3339 sum of digits = 18 - divisible by 9 - KEEP

We're left with B, C and E

Next important tip: the number, when divided by 5 leaves a remainder 3
Some numbers that work are: 3, 8, 13, 18, 23, 28, 33, ...
So, the number in question must have either 3 or 8 as its units digit.

Check the remaining answer choices....
B. 1683 KEEP
C. 2007 ELIMINATE
E. 3339 ELIMINATE

Answer: B

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What is the least number which when divided by 5, 6, 7 and 8 leaves a  [#permalink]

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New post 17 Jul 2017, 15:43
GTExl wrote:
What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108
B. 1683
C. 2007
D. 3363
E. 3339


5*6*7*8=1680
(1680+3)/9=187
1683
B
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Re: What is the least number which when divided by 5, 6, 7 and 8 leaves a  [#permalink]

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New post 19 Apr 2019, 09:15
GTExl wrote:
What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108
B. 1683
C. 2007
D. 3363
E. 3339


for a number to be divisible by 9 , sum of no digits should be = 9
in this case option B is best match since it gives remainder of 3 also upon division with 5..
IMO B
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Re: What is the least number which when divided by 5, 6, 7 and 8 leaves a  [#permalink]

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New post 19 Apr 2019, 10:18
gracie wrote:
GTExl wrote:
What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108
B. 1683
C. 2007
D. 3363
E. 3339


5*6*7*8=1680
(1680+3)/9=187
1683
B


1680 is not the least number which is divisible by 5, 6, 7 & 8. The least number will be LCM of 5, 6 , 7 & 8 which is 840.
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Re: What is the least number which when divided by 5, 6, 7 and 8 leaves a   [#permalink] 19 Apr 2019, 10:18
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