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A positive integer, N, is the largest 2-digit integer that leaves the

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A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 11 May 2019, 00:59
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A positive integer, N, is the largest 2-digit integer that leaves the remainder 1 when it is divided by either 4 or 5. What is the maximum 2-digit integer that should be subtracted from N to get a positive integer divisible by 7?


A. 0
B. 4
C. 21
D. 74
E. 181
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Re: A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 11 May 2019, 02:15
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mangamma wrote:
A positive integer, N, is the largest 2-digit integer that leaves the remainder 1 when it is divided by either 4 or 5. What is the maximum 2-digit integer that should be subtracted from N to get a positive integer divisible by 7?


A. 0
B. 4
C. 21
D. 74
E. 181


Numbers that are div by 5 or 4 without remainder =20x, so we chech numbers 20x+1 and max number is 81. The smallest integer that div by 7 is 7 so 81-1 = 74
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Re: A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 13 Feb 2020, 03:58
Im confused by the wording "EITHER , OR ". If the no. is divisible by any one of them also valid? Because in that case we can have 86,91,96 too
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Re: A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 03 Apr 2020, 10:15
stormer07 wrote:
Im confused by the wording "EITHER , OR ". If the no. is divisible by any one of them also valid? Because in that case we can have 86,91,96 too
]


Remember the concept from probability: "the probability of getting a head or a tail" equals to P(H) + P(T).
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Re: A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 04 Apr 2020, 13:30
1
n = 4k+1
n = 5k+1
n-x=7

LCM(5,4) = 20
20,40,60,80,100

81-80 = 1 --> 81 is n

81-x=7
x = 81-7 = 74
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Re: A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 04 Apr 2020, 14:46
fireagablast wrote:
n = 4k+1
n = 5k+1
n-x=7

LCM(5,4) = 20
20,40,60,80,100

81-80 = 1 --> 81 is n

81-x=7
x = 81-7 = 74


I didn't understand why did you subtract 7 from 81
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A positive integer, N, is the largest 2-digit integer that leaves the  [#permalink]

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New post 05 Apr 2020, 08:19
ammuseeru wrote:
fireagablast wrote:
n = 4k+1
n = 5k+1
n-x=7

LCM(5,4) = 20
20,40,60,80,100

81-80 = 1 --> 81 is n

81-x=7
x = 81-7 = 74


I didn't understand why did you subtract 7 from 81


I assume you understand where the number 81 comes from.

So, in order to get a number that is divisible by 7 from subtracting from 81, lets check out the following numbers:

81 - 4 = 77
81 - 11 = 70
81 - 18 = 63
81 - 25 = 56
.
.
.
81- 67 = 14
81 - 74 = 7
81 - 81 = 0

Now you can see those numbers are 4, 11, 18,..., 67,74,81.

What is the question asking? The greatest 2-digit number that is subtracted from 81 is divisible by 7. From the list above, It must be 81; however, 81 is not in the answer choice, the next one is 74. Hope this will help.

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A positive integer, N, is the largest 2-digit integer that leaves the   [#permalink] 05 Apr 2020, 08:19

A positive integer, N, is the largest 2-digit integer that leaves the

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