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30 Jul 2020, 08:28
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D
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Difficulty:
95%
(hard)
Question Stats:
45% (02:29) correct
56%
(02:43)
wrong
based on 200
sessions
History
Date
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Find the sum of all the digits '3', which we use while writing all distinct integers from 1 to 1000?
A) 300
B) 600
C) 813
D) 900
E) 930
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A) 300
B) 600
C) 813
D) 900
E) 930
Source: https://www.GMATinsight.com
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30 Jul 2020, 09:41
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Number of digit 3's which we use while writing all distinct integers from 000 to 999 is (3*1000)/10 = 300.
Their sum = 3*300=900
Their sum = 3*300=900
30 Jul 2020, 11:24
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target is to determine sum of total distinct integers from 1 to 1000; which have digits 3 in them
1-10 ; 1 ;
20-99; at tens place ; 1*9 and units place; 9*1 ;9 and 33 ; which 1
so from 1 to 99 ; 1+9+9+1 ; 20
from
100 to 199
at units place ; 1*10*1 ; 10 and tens place ; 1*1*10 ; 10
total 20 times
200 to 299 ; at units place ; 1*10*1 ; 10 and tens place ; 1*1*10 ; 10
total 20 times
similarly from 400 to 999 we will have
at tens place ; 6*1*10 ; 60
and units place; 6*10*1; 60
total 120
hence total from 0 to 299 and 400 to 999 ; 120+60 ; 180
from
300-399 ;
at hundereds place ; 100 times
and
at units place ; 1*10*1 ; 10 and tens place ; 1*1*10 ; 10
total 20 times
so total ; 120 times in 300 to 399
total ; 180+120 ; 300
so distinct integer numbers are 300 and sum of it would be ; 300*3 ; 900
OPTION D
1-10 ; 1 ;
20-99; at tens place ; 1*9 and units place; 9*1 ;9 and 33 ; which 1
so from 1 to 99 ; 1+9+9+1 ; 20
from
100 to 199
at units place ; 1*10*1 ; 10 and tens place ; 1*1*10 ; 10
total 20 times
200 to 299 ; at units place ; 1*10*1 ; 10 and tens place ; 1*1*10 ; 10
total 20 times
similarly from 400 to 999 we will have
at tens place ; 6*1*10 ; 60
and units place; 6*10*1; 60
total 120
hence total from 0 to 299 and 400 to 999 ; 120+60 ; 180
from
300-399 ;
at hundereds place ; 100 times
and
at units place ; 1*10*1 ; 10 and tens place ; 1*1*10 ; 10
total 20 times
so total ; 120 times in 300 to 399
total ; 180+120 ; 300
so distinct integer numbers are 300 and sum of it would be ; 300*3 ; 900
OPTION D
GMATinsight
Find the sum of all the digits '3', which we use while writing all distinct integers from 1 to 1000?
A) 300
B) 600
C) 813
D) 900
E) 930
A) 300
B) 600
C) 813
D) 900
E) 930
