Latest Elitmus Aptitude Question SOLUTION: even no.from 1 to 23 & odd no.from 25 to 100 are multiplied & added. What's the no. of '0'(zero) in sum options 1,2,7,8

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(#M40030508) ELITMUS Logical Reasoning question Keep an EYE

even no.from 1 to 23 & odd no.from 25 to 100 are multiplied & added. What's the no. of '0'(zero) in sum options 1,2,7,8

Asked In Elitmus manjunath b p (10 years ago)

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komal  (10 years ago)

the question was like this in set c..
even no from 1 to 23 and odd no from 25 to 100 was multiplied,what is the no of 0s in the product
options were
a)9 b)10 c)11 d)12
ans would be 12 as odd no between 25 to 95 have 10 times 5,and 1 to 23 contains 17 times 2 along with 0s in 10 and 20 shown as follows:
2,4,6,8,10,12,14,16,18,20,22
=2,2*2,2*3,2*2*2,10,2*2*3,2*7,2*2*2*2,2*9,2*10,2*11
no of 2s from above=17
25,35,45,55,65,75,85,95
=5*5,5*7,9*5,5*11,5*13,5*5*3,5*17,5*19
no of 5s from above=10
each 5 and 2 gives 10 and thud accounts for 1 no of 0s in the product
so the product will have 12 0s in total(including 2 no of 10s)

Is this solution Helpfull? Yes (28) | No (4)  

RAKESH  (10 years ago)

even no.from 1 to 23 are=2,4,6,8,10,12,14,16,18,20,22
odd no.from 25 to 100 are=25,27,29,31,33,35,37,...,97,99
now consider
x=2*4*6*8*10*12*14*16*18*20*22=2^11*11!,contains 2 zeroes at end
and
y=25*27*29*31*33*35*37...*97*99 doesnt't contains any even no. , so there is no factor of 2 in product,however lots of factors of 5,so this product will not give any zeroes at end
so (x+y) willnot give any zeroes in sum


if x & y are multiplied then
x contains a factor 2^19*5^2
y contains terms 25*35*45*55*65*75*85*95,which gives a factor 5^10
x*y will give 12 zeroes in end

Is this solution Helpfull? Yes (23) | No (1)  

abc  (10 years ago)

2 zero(only from even numbers)
multiplication of odd no's from 25 to 95 have 10 times '5' but not a single '2'.so there is no zero from here

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abc  (10 years ago)

ya if they are multiplied answr is 12.
but if they are added as the question above( "" even no.from 1 to 23 & odd no.from 25 to 100 are multiplied & added.what's the no. of '0'(zero) in sum "")

then answr is 2 only

Is this solution Helpfull? Yes (3) | No (4)  

RAKESH  (10 years ago)

even no.from 1 to 23 are=2,4,6,8,10,12,14,16,18,20,22
odd no.from 25 to 100 are=25,27,29,31,33,35,37,...,97,99
now consider
x=2*4*6*8*10*12*14*16*18*20*22=2^11*11!,contains 2 zeroes at end
and
y=25*27*29*31*33*35*37...*97*99 doesnt't contains any even no. , so there is no factor of 2 in product,however lots of factors of 5,so this product will not give any zeroes at end
so (x+y) willnot give any zeroes in sum


if x & y are multiplied then
x contains a factor 2^18*5^2
y contains terms 25*35*45*55*65*75*85*95,which gives a factor 5^10
x*y will give 12 zeroes in end

Is this solution Helpfull? Yes (3) | No   

Priyabrat  (10 years ago)

Ye two no of tens finally kahan se aagaya bhai??

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animesh jian  (10 years ago)

@KOMAL when we multiplied 1-to-23 we get 2 or 3 zeros but no any zeros are in 25 to 100.and then we add these multiplication then we got no any zeroes....
so plz explain.

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Shaibal Dutta  (10 years ago)

HEY RAKES THERE IS 9 5 IN ODD NO. THN Y U GUISE TAKNG 12 ??

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vinod  (10 years ago)

hey@saibal
In case of even no 10 and 20 having one 5 with each


'in case of odd no we get 10 and from even no we get 2 so totally 12 5's

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Prashant Kumar  (9 years ago)

9 zeros................

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Ehtesham  (9 years ago)

here ,number of 0 is asked:
so to find number of 0,we have to find number of(5*2)

in 2,4,6,8,10,...22 there are two 5. and about eighteen 2.
so in this case number of 0 will be decided by the number which is less .i.e 5.

so there will be two 0.
in 25,27,29,..95
number of 5 is 10

so after multiplication total number of zero will be 10+2=12

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