Latest Elitmus Aptitude Question SOLUTION: Find the total no of 3 digits number such that if one of the digit is 3 then it must be followed by 7.

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(#M40033161) ELITMUS Numerical Ability question Elitmus 23rd feb14 Keep an EYE

Find the total no of 3 digits number such that if one of the digit is 3 then it must be followed by 7.

Asked In Elitmus Vivek Jain (10 years ago)

Unsolved Read Solution (17)

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Read Solution (17) :

RAKESH  (10 years ago)

two forms is possible
_37 or 37_

_37 => _ can be 1,2,4,5,6,8 9 => 7 no.s

37_ => _ can be 0,1,2,4,5,6,8,9 => 8 no.s

total= 7+8 =15

Is this solution Helpfull? Yes (40) | No (9)  

Vivek Jain  (10 years ago)

@rakesh question says "if" what about the other cases where the digit 3 is not present. I think we have to consider them also. because from what i remember 15 was not among the options . and yea repetitions are not allowed which u already assumed

Is this solution Helpfull? Yes (10) | No   

SRISHTI VISHNOI  (10 years ago)

Two possibilities _37 or 37_
_37=> 8 ways
37_=> 9 ways

the numbers that don't have 3 as a digit must also be considered.
8*9*9 => 648 numbers that don't have 3 as a digit.

So total numbers are 648+8+9= 665.

Is this solution Helpfull? Yes (9) | No (3)  

shailaja  (10 years ago)

i think 19 =>137,237,337,437,537,637,737,837,937 total 9
and 370,371,372,373,374,375,376,377,378,379 =>10
10+9=19

Is this solution Helpfull? Yes (4) | No (12)  

jaswinder  (10 years ago)

if 3 is not present
then, 8*8*7=448
and if 3 is present
then, 6*1*1=6
or 1*1*8=8
so total=448+6+8=462

Is this solution Helpfull? Yes (2) | No (1)  

Harshit Chauhan  (9 years ago)

total no. of 3 digit no.having each digit distinct are
8*8*7=468
and now
3 digit no.'s having one of d digit 3 and followed by 7=15 where each digit is distinct.
so total no. of such type of no.'s are =468+15=483

Is this solution Helpfull? Yes (2) | No   

Sourav Chandra  (10 years ago)

i think the answer is 15 as if first position is 3 then 2nd is 7 and third can be filled in 8 ways excluding 3&7. and in case 2,2nd and 3rd position is 3&7 and first position can be filled in 7 ways excluding 0,3&7. so total ways=8+7=15

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Sujoy Das  (10 years ago)

If it is said that Repetition is not allowed then there are two cases 1st) When 3 is at the beginning,2nd)When 3 is at the middle
For 1st case 3_ _ there are 8 possible ways
For 2nd case _3_ there are 7 possible ways
Therefore total there are 15 ways

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manivikas  (10 years ago)

i think we should consider the numbers also like 731.. bcaz the question is not bounded to 7 followed by 3

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NAGESWARARAO  (10 years ago)

ans:27
137,237,337,437,537,637,737,837,937 total 9
370,371,372,373,374,375,376,377,378,379 =>10
and we can consider 3_7 also bcoz here not mentioned immideatly followed so
i think we can consider 307,317,327,337,347,357,367,387,397 total=8
totaal=27

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Pooja Chandrakar  (10 years ago)

3 must be followed by 7 but 7 can be followed by any no. except 3
possibility _37 or 37_
137, 237, 437, 537, 637, 737, 837, 937 = 8
370, 371, 372, 374, 375, 376, 377, 378, 379 = 9
total= 8+9 =17
not possible cases are 037,337, 373

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shilpa  (10 years ago)

rakesh wat abt 3rd possibility 73_ it wont be occur r else wat

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komal pandhariwal  (10 years ago)

2 forms possible :
_37 and 37_
1st case _37, 1,2,4,5,6,7,8,9 can come as 3 is folled by 7 but evry 7 doesnt follow 3 so 7 will b considered.i.e. 8 possibilities
2nd case also 37_ 0,1,2,4,5,6,7,8,9 9 possibilities
so..8+9=17

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Ankur Mehay  (10 years ago)

To fill first position of 3 digit number we have eight possibility i.e 8ways
2nd position fill with 7 ways
3rd position with 6 ways

Now next condition if 3 occur in number then 7 is also came in that no. So at end we have 7 ways
To fill last position.
(8×7×6)+7=343.

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hp maity  (10 years ago)

(9p3-8p2)(for the case not having 3)+8( for 37_)+7(for _37)=463

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Abhishek Jha  (10 years ago)

We need to consider two cases:
i> when 3 is there in the no., then rules follow
ii> when 3 is not there, we use simple permutation rules for counting.
Ans. will ne result of & .

Moreover, question is not clear whether we need to count the number where 3 is at the units place.

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abhishek maini  (9 years ago)

not an elitmus level question...

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