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# What is the sum of the two digit numbers that leave a remainder of 1

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What is the sum of the two digit numbers that leave a remainder of 1  [#permalink]

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11 Nov 2018, 08:53
4
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Difficulty:

55% (hard)

Question Stats:

63% (02:03) correct 37% (02:07) wrong based on 54 sessions

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What is the sum of the two digit numbers that leave a remainder of 1 when divided by both 3 & 4
A)430
B)440
C)450
D)460
E)470

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Re: What is the sum of the two digit numbers that leave a remainder of 1  [#permalink]

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11 Nov 2018, 23:18
3
Abhi077 wrote:
What is the sum of the two digit numbers that leave a remainder of 1 when divided by both 3 & 4
A)430
B)440
C)450
D)460
E)470

When the number is divided by 3 or by 4, the remainder is 1.
This means the number is of the form

N = 12a + 1
Since 12 is the LCM of 3 and 4.

All such 2 digit numbers are 12*1 + 1, 12*2 + 1, .... 12*8+1

This is an arithmetic progression of 8 terms with first term as 13 and last term as 97.

Sum = n*(First term + Last term)/2 = 8*(13 + 97)/2 = 440

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What is the sum of the two digit numbers that leave a remainder of 1  [#permalink]

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Updated on: 24 Nov 2018, 13:19
Abhi077 wrote:
What is the sum of the two digit numbers that leave a remainder of 1 when divided by both 3 & 4
A)430
B)440
C)450
D)460
E)470

least two digit number is 3*4+1=13
greatest two digit number is 13+7*12=97
total two digit numbers=7+1=8
13+97=110
110/2=55 mean
55*8=440 sum
B

Originally posted by gracie on 11 Nov 2018, 19:22.
Last edited by gracie on 24 Nov 2018, 13:19, edited 1 time in total.
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Re: What is the sum of the two digit numbers that leave a remainder of 1  [#permalink]

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24 Nov 2018, 09:42
Abhi077 wrote:
What is the sum of the two digit numbers that leave a remainder of 1 when divided by both 3 & 4
A)430
B)440
C)450
D)460
E)470

Two consecutive numbers never share a common factor other than 1.

Therefore we need LCM of 3 and 4 to find a common number which can be divided by 3 and 4 evenly.

LCM of 3 and 4 = 4*3 = 12

Now, numbers divided by 12 leaving a remainder of 1 are ;

13, 25, 37, 49, 61, 73, 85, 97

Sum (13 + 97) + (25 + 85) + (37 + 73) + (49 + 61)

110 + 110 + 110 + 110 = 440 (B)

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Re: What is the sum of the two digit numbers that leave a remainder of 1  [#permalink]

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27 Jan 2020, 18:18
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Re: What is the sum of the two digit numbers that leave a remainder of 1   [#permalink] 27 Jan 2020, 18:18