Latest Athenahealth Aptitude Question SOLUTION: What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 Whe

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What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 When Divided By 10?

Asked In Athenahealth kiran (11 years ago)

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Ajeet  (11 years ago)

remainder of 1 when divided by 2: (2-1=1)
remainder of 2 when divided by 3: (3-2=1)
remainder of 3 when divided by 4: (4-3=1)
remainder of 9 when divided by 10: (2-1=1)

so N+1 should be divisible by 2,3,4,10

(where N is desired number)

L.C.M. of 2,3,4,10 = 60 (= N+1)

N = 59

PS: thanks to dinesh.
Previous solution is the answer when number is divided 'successively' but that's not written in the problem statement.

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dinesh  (11 years ago)

59 also a probable answer.you can verify it.

Is this solution Helpfull? Yes (3) | No   

Ajeet  (11 years ago)

2 | x
---------
3 | y - 1
---------
4 | z - 2
---------
10| u - 3
---------
| v - 9

for smallest +ve integer, v =1

u = 1*10+9 = 19
z = 19*4+3 = 79
y = 79*3+2 = 239
x = 239*2+1 = 479 [answer]

Is this solution Helpfull? Yes (1) | No (5)  

Nivethitha S  (9 years ago)

LCM of (2,3,4,10)=60;
LCM-1;
Ans:59

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Mahi  (10 years ago)

Ans: 59
59%10=9
59%4=3
59%3=2
59%2=1

Is this solution Helpfull? Yes | No (1)  

Muthuselvi  (10 years ago)

119 becaze 119/2 reminder 1 and 119/3 reminder 2 that way the ans is 119

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vinoth  (10 years ago)

Ans=59
59%10=9
59%4=3
59%3=2
59%2=1

Is this solution Helpfull? Yes | No (1)  

Sathish  (10 years ago)

is 59
divided by 2 remainder 1
divided by 3 remainder 2
divided by 4 remainder 3

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M Santhosh Kumar  (10 years ago)

Answer : 59
59 / 2 = 29 ;(58) remainder 1
59 / 3 = 19 ;(57) remainder 2
59 / 4 = 14 ;(56) remainder 3
59 / 10 = 5 ;(50) remainder 9

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