M4maths Previous Puzzles

27 Mar 2015 Two digit numbers

A two digit number is such that its 7 multiple is a perfect square. Sum of all such possible two digit numbers will be

OPtion

1) 85
2) 91
3) 95
4) 100
5) 109
6) 112
7) 113
8) 121
9) 125
10)131

Solution

Since 7 multiple of the number is a perfect square so no will have a factor 7 and other factor will be definitely be a perfect square possibilities for the other factor are 1, 4, 9, 16 ....
7*1 = 7 digit
7*4 = 28 digit
7*9 = 63 digit
7*16 = 112 digit
So sum = 63 + 28 = 91

Option 2)

Correct Option: 2 Best Solution (26)

Surit Datta   10 years AGO

Two such numbers are possible
this are,
28 and 63
28*7 = 196
63*7 = 441
so summation of 28 and 63 is 91
so option 2
that's it.

Like? Yes (26) | No (4)  

Sanu Panji   10 years AGO

7*99= 693. so squre will bw less then 693 and number will be less then |sqrt(693)|=26
also the squre will have 7^2 as a factor. there are two of this kind.
14^2=196
21^2=441

so two number is 196/7=28 and 441/7=63
sum= 28+63 =91

Like? Yes (4) | No   

MRITUNJAY   10 years AGO

number will be 28 and 63.
when multiply by 7.
28*7=196=14^2
63*7=441=21^2
sum will be=63+28=91

Like? Yes (2) | No   

Yathiraj   10 years AGO

2 digit numbers whose multiple of 7 is a perfect square are 28 & 63.
Hence, 28+63 = 91

Option 2.


PL/SQL program
===============
declare
v_sum number := 0;
v_sqrt_val number;
begin
for i in 10..99
loop
v_sqrt_val := sqrt(i*7);

if v_sqrt_val = trunc(v_sqrt_val) then
v_sum := v_sum + i;
dbms_output.put_line('i: ' || i);
end if;
end loop;

dbms_output.put_line('sum of all such 2 digit numbers ' || v_sum);
end;
/

Like? Yes (2) | No   

Meenakshi   10 years AGO

The only possible two digit combinations whose 7 multiple is perfect squares are:63 and 28
The sum of digits are:63+28=>91

Like? Yes (2) | No   

Prithwijit Ghosh   10 years AGO

1*1*7=7 its 1 digiys
2*2*7=28
3*3*7=63
4*4*7=113 its 3 digits
So answer will be 28+63=91

Like? Yes (2) | No   

prem kishor   10 years AGO

these numbers are 28 and 63.
because 7*_*_
for perfect square one 7 should be and second banks can be 1,4,9.but if we put 1,then7*1 is single digit.
so, 7*4, and 7*9 two digit numbers are possible.

Like? Yes (2) | No   

anureet   10 years AGO

when 7{4+9+16+.........) is such sum
when 7{13}=91
7{4+9+16}=203

Like? Yes (2) | No   

Pragati Rode   10 years AGO

Find the 2 digit number which is multiple of 7...
14, 21,28 ...98
but there are two numbers i.e. 28 n 63
multiplying by 7 to these numbers we get perfect square.
addition of these two numbers is 91

Like? Yes (2) | No   

sravani   10 years AGO

7*4*7 so num is 28
7*9*7 so sum is 63
7*16 is 3digit
so sumof these two is 91

Like? Yes (1) | No   

GIRISH TYAGI   10 years AGO

7*4*7=28*7=196 AND 7*9*7=63*7=441

Like? Yes (1) | No   

Devendra Marghade   10 years AGO

28 & 63 are such a two numbers which results into squares, when multiplied by 7
28*7=196 and
63*7=441
So Sum 28+63=91
Ans: 2)

Like? Yes (1) | No   

Jaspalsingh Parmar   10 years AGO

28 and 63

Like? Yes (1) | No   

Jay parmar   10 years AGO

Optn 2

Like? Yes (1) | No   

aman aditya   10 years AGO

two nember are 28,63
so
28+63=91

Like? Yes (1) | No   

rakesh   10 years AGO

28,63
28+63=91

Like? Yes (1) | No   

Srinivas   10 years AGO

7*28=196
7*63=441
so 63+28 = 91

Like? Yes (1) | No   

SUSHANT KUMAR   10 years AGO

two digit no whose 7 multiple is a perfect square are 28 and 63
28*7=196 which is a perfect square
63*7=441 which is a perfect square
hence the sum is 28+63=91.

Like? Yes (1) | No   

pasupuleti pranavasree   10 years AGO

28*7=196. 196=14^2
63*7=441. 441=21^2
and 28+63=91

Like? Yes (1) | No   

kranthi kanchanapally   10 years AGO

from 11 to 99 the numbers 28 and 63 will give the perfect square when multiply with 7
so the sum=28+63=91

Like? Yes (1) | No   

sompon temtheerakij   10 years AGO

two numbers are 4*7 = 28 and 9*7 = 63
sum = 28+63 = 91

Like? Yes (1) | No   

mukund   10 years AGO

28&63 are two digit number
So sum is 91

Like? Yes (1) | No   

vivek   10 years AGO

only two such number are possible i.e 28 and 63.
28+63=91

Like? Yes (1) | No   

Madhumoy Gope   10 years AGO

The general no. is- N=(n^2)*7,such that (9

Like? Yes (1) | No   

Aritra Chongdar   10 years AGO

91/7=13
two digits are 1 and 3
1+3=4 ; 4 is a perfect square of 2

Like? Yes (1) | No   

Ritesh   10 years AGO

7*28=14*14
7*63=21*21
Therefore 63+28=91

Like? Yes (1) | No