Latest Elitmus Aptitude Question SOLUTION: Y=(X^4)+4 Where X is a 4 digit number. What is the probability that Y is divided by 5 a)1/5 b)2/5 c)4/5 d)1 This is asked in today's(9/2/14) exam

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(#M40032745) ELITMUS Numerical Ability question aps Keep an EYE

Y=(X^4)+4
Where X is a 4 digit number. What is the probability that Y is divided by 5
a)1/5
b)2/5
c)4/5
d)1

This is asked in today's(9/2/14) exam

Asked In Elitmus Praveen kumar (10 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

Vicky singh  (10 years ago)

here is the silution .

when the last digit of x is 1 , last digit of y=(x^4)+4 is 5( as last digit of x^4 is 1 and 1+4=5 last digit of y)

similarly for 2 ..last digit of y is 0 (div by 5)
for 3.................y is 5 (div by 5)
for 4.................y is 0 (div by 5)
for 5.................y is 9 (not div by 5 )
for 6.................y is 0 (div by 5)
for 7.................y is 5 (div by 5)
for 8.................y is 0 (div by 5)
for 9.................y is 5 (div by 5)
for 0.................y is 4 (not div by 5)

hence probality = 8/10
= 4/5......is the answer.. :)

Is this solution Helpfull? Yes (35) | No (5)  

RAKESH  (10 years ago)

Y=(X^4)+4
y is divisible by 5 only if unit digit of y is 0 or 5

unit digit of x=0 => last digit of y = 4
unit digit of x=1 => last digit of y = 5
unit digit of x=2 => last digit of y = 0
unit digit of x=3 => last digit of y = 5
unit digit of x=4 => last digit of y = 0
unit digit of x=5 => last digit of y = 9
unit digit of x=6 => last digit of y = 0
unit digit of x=7 => last digit of y = 5
unit digit of x=8 => last digit of y = 0
unit digit of x=9 => last digit of y = 5

i.e when unit digit of x is 0 & 5 then y is not divisible by 5

x= total 4 digit no. = 9*10*10*10 = 9000
y=(x^4+4),divided by 5= 9000-9*10*10-9*10*10 = 7200

so p= y/x = 7200/9000 = 72/90 = 4/5

Is this solution Helpfull? Yes (31) | No (1)  

vipin kumar  (10 years ago)

y is divisible by 5 only if y has its last digit as "0" or "5"
;;;
x may has its last digit 0-9.
so to make y divisible by 5 we need last digit of x^4 as 1 or 6 so that
y=x^ + 4= (...1)+4=...5 or
y=x^ + 4= (...6)+4=...0

so we have only 8 cases where we get y divisible by 5
if last digit of x is 1,2,3,4,6,7,8,9
u can get this from cyclicity
1-> 1,1,1,1
2-> 2,4,8,6
3-> 3,9,7,1
4-> 4,6,4,6
6-> 6,6,6,6
7-> 7,9,3,1
8-> 8,4,2,6
9-> 9,1,9,1
so out of 10 we have 8 chances where y is divisible by 5 so probability is
= 8/10 =4/5 ( option c)

Is this solution Helpfull? Yes (3) | No   

deepak kumar  (10 years ago)

x is 4 digit no. if unit digit of(x^4) is 1 or 6 then it is divisible by 5.
if unit place of 4 digit is 1,2,3,4,6,7,8,9 then we get output of unit place is 1 or 6.
total 4 digit no is 9*10*10*10
and divisible no is 9*10*10*8,
hence probablity is 9*10*10*8/9*10*10*10= 72/90=4/5

Is this solution Helpfull? Yes (2) | No   

gagandeep singh  (10 years ago)

since X is a 4 digit no.
i.e. let X = xxxx where x= 0 to 9,

now ,to make y divisible by 5,
which is possible if only last term of (x^4) is '1' or '6', in that case.

=> y = (xxx1)+ 4 = xxx5; or
=> y = (xxx6)+ 4 = xxx0

therefore, to get last term as 5 or 0, last digit can only be substituted by '1'
or '6'.
it can be done in two (1,6) out of ten ways(0,1,2,3,4,5,6,7,8,9).
so , prob. =2/10 or 1/5...

1/5 is the answer.

Is this solution Helpfull? Yes (2) | No (1)  

nitesh kumar sharma  (10 years ago)

Last digit of X can be 1,2,3,4,6,7,8,9 (total 8 digits) so that expression(X^4 + 4) would return 0 or 5 as last digit (to be divisible by 5)
we have total no of 4 digit numbers = 9000
& no of 4 digit numbers having last digit among (1,2,3,4,6,7,8,9) is = 8*900
probablity = 8*900/9000 = 4/5

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shubham ghule  (9 years ago)

c)4/5
as no should be divisible by 5 addition of (X^4)+4 should have units place as 0 or 5
so nos will be 1,3,7,9,2,4,6,8
so probability is 8/10=4/5

Is this solution Helpfull? Yes (1) | No   

Abhishek Shrivastava  (10 years ago)

possibility of 4 digit no's
For unit place possible digits are 1,9,4,6
For 10th place possible digits are 0 to 9
For 100th place possible digits are 0 to 9
For 1000th place possible digits are 1 to 9
Hence, possible 4 digit nos = 9*10*10*4=3600
total possible 4 digit nos = 9*10*10*10=9000
Hence, Probability = 3600/9000=2/5.

Is this solution Helpfull? Yes | No (6)  

shree  (10 years ago)

b) 2/5 because in the table of 4 only 20 40 is divided by 5 so it will come 2 times

Is this solution Helpfull? Yes | No (7)  

Sangita Sarkar  (10 years ago)

ans is c) 4/5

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priyanka  (9 years ago)

@rakesh u r taking repition while takin total cases n non repeat while taking favorabl cases??

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Tushar jain  (9 years ago)

for (x4 + 1) to be divisible by 5, than it should have 0 or 5 as the last digits.

unit place of x^4 will be any of these

0^4=0;1^4=1;2^4=6;3^4=1;4^4=6;5^4=5;6^4=6;7^4=1;8^4=6;9^4=1
hence if we replace X by any of d no: from 0 to 9, non of d no: contain last digit 0 or 5.
hence probability is 0.

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