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06 Aug 2024, 21:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
51% (03:16) correct
49%
(02:37)
wrong
based on 43
sessions
History
Date
Time
Result
Not Attempted Yet
Find the sum of all the 3-digit positive integers which are divisible by 3, but not by 19.
A. 156,372
B. 155,517
C. 156,486
D. 155,487
E. 156,283
A. 156,372
B. 155,517
C. 156,486
D. 155,487
E. 156,283
10 Aug 2024, 12:42
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Bunuel
1st \(3\) digit divisible by \(3 =3*34 = 102\)
Last \(3\) digit divisible by \(3 =3*333= 999\)
\(333-34+1 = 300 \)= Total number of three digit numbers divisible by three.
Hence sum of all three-digit positive integers which are divisible by \(3\)
\(\frac{300}{2} (102+999 )= 165,150\) : using sum of \(n\) terms in AP \(= \frac{n}{2}\)( 1st term + last term )
Number of terms divisible by \(57 \)( Terms need to be divisible by both \(19\) and \(3\) hence \(19*3 =57\) )
1st three digit number divisible by \(57 =57*2= 114\)
Last three digit number divisible by \(57 =57*17= 969\)
\(17-2+1 = 16 \): Total number of three digit numbers divisible by \(57\)
Hence sum of all three-digit positive integers which are divisible by \(57\)
\(\frac{16}{2} (114+969)= 8664\)
Therefore sum of all the 3-digit positive integers which are divisible by \(3\), but not by \(19.\)
\(165,150 - 8664 = 156,486\)
Ans C
Hope it helped.
09 Oct 2025, 07:47
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