Elitmus
Exam
Numerical Ability
Number System
How many possible combination of four consecutive numbers between 1to 1000 whose sum is divisible by 10.ex;-16+17+18+19=70
Read Solution (Total 14)
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- it is possible for all the numbers having unit digit as
(1,2,3,4) and (6,7,8,9)
so, b/n 1 to 10 difference there are two possibility (i,e, 1-10,11-20,21-30,etc)
so total possibility
= 1000*2/10
= 200
200 is the answer - 10 years agoHelpfull: Yes(60) No(21)
- ans is 199
2 possibles for every 10
20 possibles for every 100
200 possibles for 1000
but we will not consider 1(1,2,3,4 this not possible)
so 200-1=199
- 10 years agoHelpfull: Yes(43) No(10)
- 11+12+13+14=50 which is divisible by 10 and
16+17+18+19=70 which is divisible by 10.
So for 10 to 20 there is two possibilities, hence for 20 to 30 there will be two possibilities .
so in order to count how many possibilities for 10 to 1000, let
10,20,30,.....1000, we want to find no. of terms
last term=a+(n-1)d
1000=10+(n-1)10
=>100=1+n-1
=> n=100
so there will be 100*2 chances
=200
- 10 years agoHelpfull: Yes(15) No(2)
- ans-198 bcz 1 & 1000 not include it is given in question b/w 1 to 1000.
- 10 years agoHelpfull: Yes(3) No(10)
- let numbers be x,x+1,x+2,x+3
sum=4x+6=2(2x+3)
now for x=1,6,11.........996 it gives the multiple of 10.
so total no. is 996=1+(n-1)5
n=200 - 9 years agoHelpfull: Yes(3) No(0)
- ans is 199
2 possibles for every 10
20 possibles for every 100
200 possibles for 1000
but we will not consider 1(1,2,3,4 this not possible)
so 200-1=199
becoz between we will not consider
- 9 years agoHelpfull: Yes(2) No(1)
- ans is 33
- 10 years agoHelpfull: Yes(1) No(11)
- ans is 200
11+12+13+14=50 ( divisible by 10 )
16+17+18+19=70 ( divisible by 10)
from 10 to 20 there is two possibilities
for 20 to 30 there will be two possibilities .
so in order to count how many possibilities for 10 to 1000, let us assume that the nos. are in AP
10,20,30,.....1000
l=a+(n-1)d
1000=10+(n-1)10
=>100=1+n-1
=> n=100
so 100*2 combinations are possible.
- 10 years agoHelpfull: Yes(1) No(1)
- there are total of 200 combination of number between 1 to 1000
since in each 1 to 10 , 11 to 20 , 21 to 30 ...............991 to 1000 there are only two combination of four consecutive numbers whose sum is divisible by 10. - 10 years agoHelpfull: Yes(0) No(0)
- four consecutive numbers : a+b+c+d=10k;
1+2+3+4=10;
6+7+8+9=30;
11+12+13+14=50;
now give a look ,here among the possible combination there is pattern followed
1+5=6
2+5=7
3+5=8
4+5=9
similarly all combinations follow same pattern.
now find last combination consecutive digit :
will come from 1+(n-1)*5;
take n=200;
then 1+(200-1)*5=996;
so last consecutive combination :996+997+998+999=3990
so total number of such combinations are: (996-1/5)+1=200 - 9 years agoHelpfull: Yes(0) No(0)
- 1 to 10 = (1+2+3+4 , 6+7+8+9)=2 combinations
2 to 20=(11+12+13+14 , 16+17+18+19)=2 combinations
so total combinations between 1 and 100=10*2=20
like this total combinations 1 to 1000=20*2=200 - 9 years agoHelpfull: Yes(0) No(1)
- (x+(x+1)+(x+2)+(x+3))/10=(4x+6)/10=(2x+3)/5
(2x+3)/5=399
x=996
- 9 years agoHelpfull: Yes(0) No(1)
- 10-2p,
1000-200
ans-200-1=199 - 9 years agoHelpfull: Yes(0) No(0)
- 1+2+3+4=10
6+7+8+9=20
11+12+13+14=50
16+17+18+19=60
as show on
for ever 10 (like 1-10,11-20,21-30....)number we get 2 set of consecutive number
so,
possible combination is=(1000/10)*2=200 - 9 years agoHelpfull: Yes(0) No(0)
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