Latest Elitmus Aptitude Question SOLUTION: Find the number of zeros in the product: 1^1*2*2*3^3*4^4............98^98*99^99*100^100 A)1200 B)1300 C)1050 D)None of these

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(#M40018520) ELITMUS Logical Reasoning question Number Systems Keep an EYE

Find the number of zeros in the product:
1^1*2*2*3^3*4^4............98^98*99^99*100^100
A)1200
B)1300
C)1050
D)None of these

Asked In Elitmus Sumit Rawal (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

Arpit Jaiswal  (10 years ago)

B) 1300
Number of zeroes will depend on number of multiplication by 10 in the given expression
Also, 10=2*5
Obviously there will be more 2's than 5's in the expression
So we have to only fint the number of 5 in the given expression which if given by the numbers whose last digit it either 0 or 5:
like 5^5 contains 5 '5's
10^10 contains 10 '5's

hence:
5^5 - 05
10^10 - 10
15^15 - 15
20^20 - 20
25^25 - 2*25=50 (as 25=5*5 contains two 5's)
30^30 - 30
35^35 - 35
40^40 - 40
45^45 - 45
50^50 - 100 (50=5*5*2)
55^55 - 55
60^60 - 60
65^65 - 65
70^70 - 70
75^75 - 150 (75=5*5*3)
80^80 - 80
85^85 - 85
90^90 - 90
95^95 - 95
100^100 - 200 (100=5*5*4)
Hence total number of 5's= 5+10+15+20+50+30+35+40+45+100+55+60+65+70+150+80+85+90+95+200=1300

Is this solution Helpfull? Yes (38) | No (1)  

Prakash Gupta  (10 years ago)

calculate powers of 5 & multiple of 5...
5+10+15+.......+100= 1050
since in 25,50,75&100 contains 5^2
so their respective powers should be added one more time
25+50+75+100=250
total=1050+250=1300 ans.

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rajat chabria  (10 years ago)

is ter anyone here who can help me out in elitmus test i've my test on this sunday... 7th of july...

Is this solution Helpfull? Yes (7) | No   

Sumit Rawal  (10 years ago)

the answer 1300 seems to be correct.If so, the answer given in book arun sharma i.e. 1050 is wrong

Is this solution Helpfull? Yes (4) | No   

Jitha Mitra Harivanam  (10 years ago)

me too friends aravind.mitra6@gmail.com send me all types of meterial u have abt Elitmus Questions

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sushmita nigam  (10 years ago)

the answer 1300 is correct and the answer given in arun sharma is also 1300

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RAHUL BANSAL  (10 years ago)

the smallest no. that contains 0 is 10
10=5*2 so just calculate no of 5 in the given expression
the no that contain 5 are {5,10,15,20......}
so taking this no only we have 5^5*10^10*.....100^100= ( 5^5*5^10*5^15....)=5^1050

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Sumit Rawal  (10 years ago)

The answer is 1050

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shweta sharma  (10 years ago)

mr.sumit pls expln d answer?

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shweta sharma  (10 years ago)

I m having elitmus exam on nxt sunday...plz mail me all questions at shwetashrm.991@gmail.com

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Rahul kumar  (10 years ago)

plz mail me elitmus question or any study material to my email i:rahul260191@gmail.com.

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neetigupta  (10 years ago)

I m having elitmus exam on nxt sunday...plz mail me all questions and any study material at neetigupta.bu@gmail.com............plz plz its urgent........

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SAMBIT KUMAR GHOSH  (10 years ago)

@arpit pls explain me the details abt '25^25'-50 ...pls pls...

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prayas goel  (10 years ago)

Answer will be 1050..
since we need to count only nos of 5
so count no. of 5 is 5^5+10^10+15^15+20^20.....100^100
that will be 5+10+15+20+25+30......100 = 1050

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