Latest CDS Aptitude Question SOLUTION: Consider the numbers between 300 and 400 such that when each number is divided by 6,9 and 12, it leaves 4 as remainder in each case. What is the SUM of the numbers?

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(#M40003237) CDS question Elementary Mathematics Keep an EYE

Consider the numbers between 300 and 400 such that when each number is divided by 6,9 and 12, it leaves 4 as remainder in each case. What is the SUM of the numbers?

Solution

Numbers satisfying the condition that it leaves 4 as remainder when divided by 6 are 310,316,322,328,334,340,346,352,358,364,370,376,382,388,394
Numbers satisfying the condition that it leaves 4 as remainder when divided by 9 are 310,319,328,337,346,355,364,373,382,391
Numbers satisfying the condition that it leaves 4 as remainder when divided by 12 are 316,328,340,352,364,376,388
common numbers are 328,364 so sum = 692

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Asked In CDS CHANDAN KR SINGH (13 years ago)

Solved Read Solution (2)

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Dr.Dipin Singh  (13 years ago)

Consider the numbers such that when each number is divided by 6,9 and 12, it leaves 4 as remainder in each case.

LCM of 6,9,12 is 36.
The reqd numbers are 4+36*n where n=1,2,3,..... and nos are between 300 and 400.
so possible values of n are 9 and 10 .( if 400 is not considered)
Numbers are 328 and 364.
sum = 692

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pritha chaki  (13 years ago)

6p+4=9q+4
p/q=3/2...... 9q+4=12r+4... q/r=4/3
so p:q:r=6:4:3
now the no are in bet 300 and 400
so if we put mulpiple of 6 are 6, 12,....48,54,60...
so..6*48=288,6*54=324,6*60=360,6*66=396....
so the nor are 324,360...total=328+364=692

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