Elitmus
Exam
Numerical Ability
Number System
E=4*4! + 5*5! + 6*6! ........19*19!
Remainder when E is divided by 64
a)0 b)58 c)others
Read Solution (Total 13)
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- ans: rem = 40
E = 4*4! + 5*5! + 6*6! ........19*19!
E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
E = (20!-4!)
E/64 = (20!-4!)/64
=> rem = 0-24/64 = -24/64
=> rem = -24+64 = 40 - 10 years agoHelpfull: Yes(81) No(3)
- ans: rem = 40
(4*4!+5*5!+6*6!+7*7!)/64 other terms contain 64 as a multiple in it, therefore they give 0 as a rem.
(96+600+4320+35280)/64=40296/64=40 as rem.
- 10 years agoHelpfull: Yes(11) No(1)
- sry,ans = 40.. (96+600+4320+35280)/64 = 40 as rem
- 10 years agoHelpfull: Yes(2) No(1)
- (5*5!+6*6!+7*7!)/64 as other term will contain 64 as a multiple in it.
(120*5+6*720*7*5040)/64
(24+32+16)/64
72/64
hence 6 will be the remainder....
- 10 years agoHelpfull: Yes(1) No(4)
- (4*4!+5*5!+6*6!+7*7!)/64 other term will contain 64 as a multiple in it.
(120+600+4320+35280)/64 = 0 as rem - 10 years agoHelpfull: Yes(1) No(4)
E = 4*4! + 5*5! + 6*6! ........19*19!
E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
E = (20!-4!)
E/64 = (20!-4!)/64
=> rem = 0-24/64 = -24/64
=> rem = -24+64 = 40- 10 years agoHelpfull: Yes(1) No(3)
- C other
E can be written as(1!+2*2!+3*3!+4*4!......19*19!)-1+2*2!+3*3!
20!-1-23
20!*(-24)%64=-24=40
Answer 40 - 10 years agoHelpfull: Yes(0) No(6)
- Sry mistake 20!-24%64=-24...so remainder=40
- 10 years agoHelpfull: Yes(0) No(3)
- E = 4*4! + 5*5! + 6*6! ........19*19!
E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
E=5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20
Sn=n*(n+1)/2
E=20*21/2-(4+3+2+1)
E=200/64
REM=8 - 10 years agoHelpfull: Yes(0) No(9)
- 4!*(4+5*5+6*6*5+...)/64 i.e now took only 4!/64 which is 1/8
hence (4+5*5+....)/8 i.e remainder not greater than 8 - 7 years agoHelpfull: Yes(0) No(0)
- Could anyone explain me how this is possible ?
E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
E = (20!-4!)
since 5!-4!=5 similarly for all ..so shouldn't it be 5+6+7+8+..+20=200 ?
200%64=40? - 6 years agoHelpfull: Yes(0) No(0)
- Remainder is 40
- 3 years agoHelpfull: Yes(0) No(0)
- remainder is 40
- 3 years agoHelpfull: Yes(0) No(0)
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