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How many positive integers less than \(1000 \) have the property that the sum of the digits of each such number is divisible by \(7\) and the number itself is divisible by \(3\)?

Note by Vilakshan Gupta
2 months ago

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Hey , what does discounted actually refer to?

Toshit Jain - 1 month, 2 weeks ago

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27

Alex Roy - 1 week, 5 days ago

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its sum is divisibli by 21 using this you can solve

Suresh Kumar - 2 weeks, 1 day ago

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this question came in this year PRMO answer is 28

Suresh Kumar - 2 weeks, 1 day ago

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@Md Zuhair 8

Toshit Jain - 1 month, 2 weeks ago

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O i see....

Md Zuhair - 1 month, 2 weeks ago

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@Pokhraj Harshal Rajasthan region!

Toshit Jain - 1 month, 2 weeks ago

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And what about the other participants and their marks from your school. I mean the averages and the highest marks

Pokhraj Harshal - 1 month, 2 weeks ago

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Which region are u from??

Pokhraj Harshal - 1 month, 2 weeks ago

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WB rgion

Md Zuhair - 1 month, 2 weeks ago

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@Pokhraj Harshal Ok! Then I'm also getting the same...

Toshit Jain - 1 month, 2 weeks ago

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How much? Without the question?

Md Zuhair - 1 month, 2 weeks ago

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The questions will be cancelled

Pokhraj Harshal - 1 month, 2 weeks ago

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Are the marks gonna be added to everyone's total or the questions will be cancelled (lowering the cutoff)?

Toshit Jain - 1 month, 2 weeks ago

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They will be added to totsl

Alex Roy - 1 week, 5 days ago

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Hey I'm getting 8/27 from jharkhand as per the new answer key of hbcse.will I qualify???

Pokhraj Harshal - 1 month, 3 weeks ago

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Lets see....

Md Zuhair - 1 month, 3 weeks ago

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Hello, There are 28 postive integers left less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3 You can check out for more queries related to the JEE EXAMS from the following compilation
<a href="https://scoop.eduncle.com/jee-main-exam-date-notification">JEE MAIN Exam dates and Notification</a>

Rahul Sharma - 1 month, 3 weeks ago

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I believe the answer is 28 integers. The sum of these integers' digits must be divisible by 21, since a number divisible by 3 also has its sum of digits divisible by 3; in addition to the sum of digits divisible by 7. None of the digits can be less 3 since the sum of digits would be less than 21. Possible combinations = 7+6+5+4+3+2+1 = (7+1)+(6+2)+(5+3)+4=3*8+4=28.

Simon Dancose - 1 month, 4 weeks ago

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Ah - that's where the 28 comes from - much more mathematical than my just listing and counting them

Katherine Barker - 1 month, 3 weeks ago

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Exactly

Vilakshan Gupta - 1 month, 3 weeks ago

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I agree with all that, and I got the same answer, but if I give you 4 digits at random (say 3, 4, 5 and 6) and ask how many numbers you can make out of them, the answer is 432*1 = 24, not 4+3+2+1 = 10. What am I missing?

Katherine Barker - 1 month, 2 weeks ago

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@Vilakshan Gupta Ok!

Toshit Jain - 2 months ago

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Yup.I think so.

Vilakshan Gupta - 2 months ago

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@Md Zuhair @Vilakshan Gupta I haven't attempted one of the bonus question. Will I still get marks for it?

Toshit Jain - 2 months ago

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I think the question can be cancelled as how can a person attempt to decinal answers and i had attempted ine. So i dunno.

Md Zuhair - 2 months ago

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yeah hundreds digit cant be 1,2

Shreyan Chakraborty - 2 months ago

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@Shreyan Chakraborty The Hundreds digit can't be 1 or 2..

Toshit Jain - 2 months ago

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ANSWER IS 28....HAS A BIJECTION WITH a+b+c=21 WHERE 0<a,b,c<=9........

Shreyan Chakraborty - 2 months ago

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Are na na.... I am not telling that. How much are you getting?

Md Zuhair - 2 months ago

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@Shreyan Chakraborty .. How much?

Md Zuhair - 2 months ago

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JANI NA BAJE HOYECHE

Shreyan Chakraborty - 2 months ago

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LetTheFateDecide !!Bye

Toshit Jain - 2 months ago

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which class are u in toshit?

Vilakshan Gupta - 2 months ago

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It's 11 in Rajasthan ! 😅😒

Toshit Jain - 2 months ago

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According to Resonance , cutoff in Chandigarh is just 4(questions)

Toshit Jain - 2 months ago

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i don't think it will be so low

Vilakshan Gupta - 2 months ago

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If that isnt, then wb will be higher and i will surely not qualify

Md Zuhair - 2 months ago

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Ya. Thats ridiculous. WB region has always got a higher cutoff...

Md Zuhair - 2 months ago

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Coz as per cutoff(s) uploaded by Resonance , cutoff in Chandigarh is lower than others ( Rajasthan , Maharashtra , UP , etc) ... That's why!

Toshit Jain - 2 months ago

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So , you are already selected..Great 👍

Toshit Jain - 2 months ago

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How already selected?

Md Zuhair - 2 months ago

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oh

Vilakshan Gupta - 2 months ago

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Rajasthan..U?

Toshit Jain - 2 months ago

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oh...btw,where do u live (i mean which region)

Vilakshan Gupta - 2 months ago

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Geometry was quite tough and lengthy! Excluding bonus , I'm getting 8

Toshit Jain - 2 months ago

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Sir😅 I am getting 10 along with bonus!

Toshit Jain - 2 months ago

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Oh. U mean 8/28 u r getting?

Md Zuhair - 2 months ago

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well, if it is bonus that means 2 questions marks are given extra.If it was been written question deleted then scores would be evaluated out of 28

Vilakshan Gupta - 2 months ago

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unfortunately, i will get only 10 questions correct. I did very silly mistakes

Vilakshan Gupta - 2 months ago

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@Md Zuhair Is the paper for 9,10,11 and 12 same?

Toshit Jain - 2 months ago

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Yes Sir!

Md Zuhair - 2 months ago

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How mañy have you got right in PRMO - 17?

Toshit Jain - 2 months ago

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Answer is 28

Toshit Jain - 2 months ago

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we just need to find the numbers which add upto 21

Vilakshan Gupta - 2 months ago

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28

Vilakshan Gupta - 2 months ago

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25 is the answer as per me

Pokhraj Harshal - 2 months ago

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No - I get 28 too - I constructed a 0 - 9 by 0 -9 addition table in excel, and then started adding a 3rd digit to any number whose 2 digits had added to 12 or more - though now I think about it, I could just as easiky have srated my list with 399 and continued from there. And it has to be 28 cos it's one starting with3, 2 starting with 4, 3 starting with 5 etc, and 1+2+3+4+5+6+7 = 28

Katherine Barker - 2 months ago

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What ans did you get?

Aaron Jerry Ninan - 2 months ago

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Hey Aaron. How much are u getting with bonus? With bonus i am getting 12.

Md Zuhair - 2 months ago

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zuhair tui ki amk jiggesh korchish??

Shreyan Chakraborty - 2 months ago

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Accha.. nijer whatsapp number ta de... whatsapp e kotha bolchi

Md Zuhair - 2 months ago

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