Latest Elitmus Aptitude Question SOLUTION: how many numbers are there below 1000 which are neither perfect square nor perfect cube? A) 961 B)958 c)955 D) not remb

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(#M40152147) ELITMUS Numerical Ability question Keep an EYE

how many numbers are there below 1000 which are neither perfect square nor perfect cube?

A) 961
B)958
c)955
D) not remb

Asked In Elitmus snehitha gona (8 years ago)

Unsolved Read Solution (13)

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Read Solution (13) :

Soumen Maity  (8 years ago)

31^2= 961 and 32^2= 1024... so square of 1 to 31 is less than 1000.

Again 10^3= 1000.... so cube of 1-9 are below 1000.

So, total no. of perfect square and perfect cube is (31+9)-1 [as 1 is common for both].

So the ans is 1000-39= 961

Is this solution Helpfull? Yes (38) | No (16)  

himanshu awasthi  (8 years ago)

ans :962
for numbers 1 to 31 there are squares below 1000
for numbers 1 to 9 there are squares below 1000
square and cube of 1 is 1 , 4*4*4=64 and 8*8=64,9*9*9=729 and 27*27=729 so we have to consider it thrice
then 31+9=40-3=37
ans 962

Is this solution Helpfull? Yes (33) | No (5)  

abhilash chhipa  (8 years ago)

962 is the right answer
because there are 31 digits having square below 1000
and 9 digits having cubes below 1000
and 1,64,729 are counted twice so u have to subtact these choices

Is this solution Helpfull? Yes (10) | No   

vivek  (8 years ago)

Total no of squares of a number below 1000 are 31
Total no of cubes below 1000 are 9 in which 1 ,64, 729 already taken in squares.so required no = 999-31-6=962

Is this solution Helpfull? Yes (10) | No   

karnati.triveni  (8 years ago)

ans :961
for numbers 1 to 31 there are squares below 1000
for numbers 1 to 9 there are squares below 1000
square and cube of 1 is 1 so we have to consider only once
then 31+9=40-1=39
ans 961

Is this solution Helpfull? Yes (5) | No (6)  

shobhit chaudhary  (8 years ago)

cubes of no 1 to 9 less than 1000 = 9 nos
squares of no 1 to 31 less than 1000= 31 nos
the coinciding cubes and squares are ^ 6 therefore 1^6 ,2^6,3^6 =3 nos
total nos =31+9-3=37
nos below 1000 therefore from 999
999-37=962 ans

Is this solution Helpfull? Yes (5) | No   

vivek  (8 years ago)

@gona 962 is given in options.

Is this solution Helpfull? Yes (1) | No   

mohit  (8 years ago)

@SUDHEER KUMAR 'MORON' ques is below 1000 so ans will be 962 at least read ques properly before solving

Is this solution Helpfull? Yes (1) | No   

Rajeev kumar  (7 years ago)

We use the Inclusion-Exclusion Principle. There are 1000 integers from 1 to 1000;
among these numbers, 31 are perfect squares (indeed, 312 = 961 ≤ 1000, but 322 > 1000), 10 are perfect cubes (this is because 103 = 1000), and 3 are both squares and cubes (these three numbers are 16 = 1, 26 = 64, and 36 = 729). Thus, by the Inclusion-exclusion principle, there are
1000 − (31 + 10) + 3 = 962
numbers that are neither perfect squares nor perfect cubes.

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

snehitha gona  (8 years ago)

962 is not given in options surely..option d is either 956 or 949

Is this solution Helpfull? Yes | No (1)  

sudheer kumar  (8 years ago)

the ans is 958 bcoz we have 10 cubes below 1000 and square are 32 so from 1000 minus these number we get ens 1000-42=958

Is this solution Helpfull? Yes | No (2)  

Sonu kumar  (8 years ago)

1,2,4,8,9,16,25,27,36,49,64,81,100,121,125,144,169,196,216,225,256,289,324,343,361,400,441,484,512,529,576,625,676,729,784,841,900,961=== total 38 numbers...so anwwer is 962

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deepak kumar  (8 years ago)

1 and 64 are common for both square and cube.
so it should be 31(for square numbers)+9(for 1-9 cube numbers)-2=38
Is it correct?

Is this solution Helpfull? Yes | No (3)  

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