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(#M40010586) ELITMUS Numerical Ability question NumberTheory Keep an EYE

you are given a number Q < 200. you have to calculate sum of All Q such that when Q divided by 5 or 7 gives remainder 2?

Asked In Elitmus sandeep pandey (12 years ago)

Solved Arneet Read Solution (14)

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Read Solution (14) :

shekhar pankaj  (12 years ago)

for 5
7 12 17.........197....39 terms sum=3978
for 7
9 16 23 30.......198...28 terms sum =2848
but some terms are counted more than 1 ..ie which are common in 5 and 7
eg 37 72 107 142 177..sum=535
so 6876-535=6341

Is this solution Helpfull? Yes (61) | No (16)  

ankur trivedi  (12 years ago)

first of all take LCM of 5 and 7 that will be 35 .since both give a remainder 2.then first value will be 35*1+2=37,second will be 35*2+2=72,third will be 35*3=107,and so on 142,177.and the sum of all these number is =37+72+107+142+177=535.

Is this solution Helpfull? Yes (22) | No (19)  

Arneet  (12 years ago)

@ Ankur,
Is there any reason for not considering Q=2 ?

In that case , sum of All Q such that when Q divided by 5 or 7 gives remainder 2 = 2+37+72+107+142+177=537

Is this solution Helpfull? Yes (17) | No (14)  

prayas goel  (11 years ago)

In question Q must be divided by "5 or 7" not "5 and 7"...and gives remainder 2
Let see first case when Q is divided by 5 and leaves remainder 2
in that case series
S1 will be 2,7,12,17,22....197= 40 terms
and sum will be
S1= 3980

In second Case when Q divided by 7 and leaves remainder 2
Series will be S2= 2,9,16,23...198= 29 terms
And sum will be S2= 2900

Total Sum will be 3980+2900=6880
But some terms are in common
which are 2, 37, 72,107, 142,177
Total= 537
So finally 6880-537=6343 will bw sum of all Q divided by 5 or 7 gives remainder 2..
Yes answer will be 537 if Q divided by "5 and 7"

Is this solution Helpfull? Yes (14) | No (1)  

ankur trivedi  (12 years ago)

hi SDeep Bhattacharya ,sorry for ignore number 2.answer will be 537.you are right .

Is this solution Helpfull? Yes (7) | No (7)  

Jay  (12 years ago)

6351
because the sum means on dividing by 5 like no 7 ,12 ,17.......197 =39 terms in AP with difference 5
=3978
now no. divided by 7 like 9 ,15, ...................198= 28 terms in AP with difference d=7 so =2898
now some terms like 37,72,107,142,177 are common in both series
so=3978+2898=6876 and subtracting 535=
6341 is correct ans my dear friend

Is this solution Helpfull? Yes (7) | No (8)  

vignesh  (12 years ago)

they given 5 or 7 it means they can be 7,9,12,16..............
so the answer is 6876

Is this solution Helpfull? Yes (6) | No (3)  

Swaraj Behera  (12 years ago)

6351
because the sum means on dividing by 5 like no 7 ,12 ,17.......197 =39 terms in AP with difference 5
=3978
now no. divided by 7 like 9 ,15, ...................198= 28 terms in AP with difference d=7 so =2898
now some terms like 37,72,107,142,177 are common in both series
so=3978+2898=6876 and subtracting 535=
6341 is correct ans

Is this solution Helpfull? Yes (5) | No   

deepika  (12 years ago)

how can u take 2...

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

Satyendra Singh  (11 years ago)

37, 72,107,142,177 non other than these no.s will be counted when diveide by 5 or 7 it will give 2 as common reminder.

Is this solution Helpfull? Yes (1) | No   

Vikas  (10 years ago)

for 5
7 12 17.........197....39 terms sum=3978
for 7
9 16 23 30.......198...28 terms sum =2848
but some terms are counted more than 1 ..ie which are common in 5 and 7
eg 37 72 107 142 177..sum=535
so 6876-535=6341
But we have to add 2 also...so 6341+2=6343 answer

Is this solution Helpfull? Yes (1) | No   

mayur   (12 years ago)

1186 ///////

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kratika jain  (11 years ago)

lcm 5&7=3
no . will be 37 72 107 142 177 (35*1+2....35*5+2)...
these no are in ap... sum is 535
thus 535

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ANKUR  (10 years ago)

6343 is correct

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