The cube of sum of a positive integer and its square is a five digit number. What will be the sum of

M4maths Previous Puzzles

13 Feb 2015 Possible value of integer

The cube of sum of a positive integer and its square is a five digit number. What will be the sum of cubes of sum of integer and its square for all possible value of integer.

OPtion

1) 96462
2) 101088
3) 108652
4) 113764
5) 119766
6) 124760
7) 128642
8) 132496
9) 136468
10)142444

Solution

Let the integer is x then according to given condition
(x+x^2)^3 = Five digit number
for x = 4; (x+x^2)^3 = Four digit number
for x = 7; (x+x^2)^3 = Six digit number
so x = 5 and 6
fox x = 5; (x+x^2)^3 = 27000
for x = 6; (x+x^2)^3 = 74088
Sum = 101088

Option 2)

Correct Option: 2 Best Solution (33)

Surit Datta   9 years AGO

let the integer be a
we have to calculate (a + a^2) such that it become a 5 digit number.
only possible for 5 and 6
(5 + 5^2) = 27000
(6 + 6^2) = 74088
so there sum is 27000 + 74088
which is 101088
so option 2
that's it.

Like? Yes (12) | No (5)  

Supriya Mondal   9 years AGO

Let the number is a
So,according to the question we can write that
(a+a^2)^3=5 digit number
After calculation we get that only 2 values satisfy this condition. They are 5 and 6
So ans will be=(5+5^2)^3+(6+6^2)^3
=(30)^3+(42)^3
=27000+74088
=101088
So,option 2)101088 is the right answer

Like? Yes (8) | No (3)  

g lokesh   9 years AGO

(x+x2)3=fivedigit number,
substituting x=1,2,3......
condition satisfies only for x=5,6
x=5,value is 27000
x=6,value is 74088
sum=101088

Like? Yes (1) | No   

praveen kumar   9 years AGO

5 and 6 are only two integers which fits under 1st condition of given problem.
accordind to Q
(5+25)^3+(6+36)^3=101088

Like? Yes (1) | No   

arush gupta   9 years AGO

ans 101088

Like? Yes (1) | No   

ADARSH GAURAV   9 years AGO

101088 is the answer

Like? Yes (1) | No   

madhu   9 years AGO

[x+x^2]^3=27000 for x=5
and [x+x^2]^3=74088 for x=6
so 101088 is the answer we get after adding both...

Like? Yes (1) | No   

Saurabh Kumar Gupta   9 years AGO

The minimum 5-digit perfect cube is: 22^3 = 10648
The maximum 5-digit perfect cube is: 46^3 = 97336
So out of numbers between 22-46, only 30(5+25) and 42(6+36) can be represented as sum of a +ve integer and its square.
So, the required answer is: 30^3 + 42^3 = 101088

Like? Yes (3) | No (3)  

Vibha   9 years AGO

(x+x^2)^3
by hit and trial
x= 5,6
hence
result = 27000 + 74088
= 101088 ans

Like? Yes (1) | No (1)  

shubham mishra   9 years AGO

there are two possible positive integer.
5,6
now
((5+5^2)^3) +((6+6^2)^3)=101088

Like? Yes (1) | No (1)  

MRITUNJAY   9 years AGO

(X+x^2)^3=five digit number

x= 5 and 6 satisfy the condition
(5+25)^3=27000
(6+36)^3=74088
sum of these two are 74088+27000
=101088

option 2.

Like? Yes (1) | No (1)  

RAHUL KUMAR   9 years AGO

5+5^2 = 30^3=27000
6+6^2=42^3=74088
27000+74088=101088
option 2 is r8.

Like? Yes (1) | No (1)  

Abhishek birkh   9 years AGO

(x+x^2)^3=5digit
22

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ABHINAV PUSHPAM   9 years AGO

Option 2 is answer

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Dharmraj Sharma   9 years AGO

for equation (x+x^2)^3=5 digit number
range of (x+x^2)
22

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Sanu Panji   9 years AGO

x=5, 6
(5+5^2)^3=27000
(6+6^2)^3=74088
sum= 101088

Like? Yes (1) | No (1)  

Jaspalsingh Parmar   9 years AGO

option 8 is correct

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Preethi   9 years AGO

5 and 6 are the numbers that satisfy given condition

Like? Yes (1) | No (1)  

Dimple Kundanani   9 years AGO

Ans is B)

Like? Yes (1) | No (1)  

JEETENDER KALACHAND KEWLANI   9 years AGO

acc to question
(x(1+x))^3=5 digit no.

if x=3......12^3=1628
if x=4....20^3=8000
if x=5....30^3=27000
if x=6....42^3=74088
if x=7....56^3=175616

hence we conclude that acc to ques x=5 and 6 are only valid candidates...hence sum of these will be
30^3 + 42^3=101088

Like? Yes (1) | No (1)  

A M ANKIT KALLURAYA   9 years AGO

(X+x^2)^3=five digit number

x= 5 and 6 satisfy the condition
(5+25)^3=27000
(6+36)^3=74088
sum of these two are 74088+27000
=101088

option 2.

Like? Yes (1) | No (1)  

Ajinkya Kulkarni   9 years AGO

(x+x^2)^3=5 digit no

so only numbers from 22 and 46 have cube in 5 digits ....
21 has cube of 4 digit and 47 has cube of 6 digit ...

(5+25)^3+(6+36)^3=101088

Like? Yes (4) | No (4)  

Sunil Chavan   9 years AGO

let the +ve integer is X and its square X^2.
according to problem defn i.e (X+X^2)^3 = (five digit number)
now go on put 1,2,3,4,5,6,7,......n in the above eqn
for X=5 we get 27000(five digit num).......(a)
and for X=6 we get 74088(five digit num).....(b)
ADD eqn (a) and (b)
we will get 101088 option(2)

Like? Yes (1) | No (1)  

RAKESH   9 years AGO

(x+x^2)^3= five digit no.

x=5 & 6
30^3 + 42^3 = 101088

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kaushik mishra   9 years AGO

Let the no be n
So according to given condition
(n+n^2)^3=five digit number
Number satisfying these conditions are n=5,6 as after 6 for eg 7 onwards will result into 6 digit number so putting n=5
(5+25)^3=27000
Putting n=6
(6+36)^3=74088
Adding these two results we get 27000+74088=101088
Which is the answer...

Like? Yes (1) | No (1)  

Budhaditya Bhattacharya   9 years AGO

(X+x^2)^3=five digit number

x= 5 and 6 satisfy the condition
(5+25)^3=27000
(6+36)^3=74088
sum of these two are 74088+27000
=101088

Like? Yes (1) | No (1)  

Paras Jain   9 years AGO

its 101088 Ans.
for x=5 and x=6 [(x+x^2)]^3

Like? Yes (1) | No (1)  

Jitendra Prasad   9 years AGO

(X+x^2)^3=five digit number

x= 5 and 6 satisfy the condition
(5+25)^3=27000
(6+36)^3=74088
sum of these two are 74088+27000
=101088

option 2.

Like? Yes (1) | No (1)  

Devendra Kumar   9 years AGO

(x+x^2)^3=five digit number

x= 5 and 6 satisfy the condition
(5+25)^3=27000
(6+36)^3=74088
sum of these two are 74088+27000
=101088

option 2 is correct

Like? Yes (1) | No (1)  

Abhik Das   9 years AGO

only The no 5 and 6 satisfies the condition.so the sum will be=[(5^2+5)^3+(6^2+6)^3]=[27000+74088]=101088

Like? Yes (1) | No (1)  

JANARTHANAN RAM   9 years AGO

possible cmntn is 5,6.
min 5 dgt no=10648 ....(22^3)
max 5 dgt no 97336.....(46^3)
sum of a positive integer and its square should be btwen 22 & 46
so we hve only 5+5^2=30...& 6+6^2=42;
so ans is 30^3+42^3=101088;

Like? Yes (2) | No (3)  

KUMAR HARSH   9 years AGO

here let integer is 5 and 6
then in first statement (n[i]+n[i]^2)3
for n[1]=5is 27000
for n[2]=6 is 74088
and in second statement [sum of [(n[i]+n[i]^2)3]]
these=27000+74088=101088

Like? Yes (1) | No (2)  

Alka Sinha   9 years AGO

only 5 and 6 falls in this category.
(5 + 5^2)^3 = 27000
(6 + 6^2)^3 = 74088

Sum = 101088

Like? Yes (1) | No (2)