Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 29)
29.
107 x 107 + 93 x 93 = ?
Answer: Option
Explanation:
| 107 x 107 + 93 x 93 | = (107)2 + (93)2 |
| = (100 + 7)2 + (100 - 7)2 | |
| = 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] | |
| = 20098 |
Discussion:
20 comments Page 1 of 2.
Shreya said:
7 years ago
Simplest way.
(107)^2+(97)^2.
To find 107 square.
Take 1 as it is.
After that add 07+07= 14.
Next step is taken a square of 7 is 49.
Write as 11449.
Note: This method is applicable for the number in between 100 to 109 only.
For number 70 to 100 is,
Subtract 93 from 100.
We get 7. Take a square of 7 is 49.
Next step is to subtract 7 from 93 we get 86.
Write it as 8649.
Then perform addition.
i.e. 11449+8649 = 20098.
(107)^2+(97)^2.
To find 107 square.
Take 1 as it is.
After that add 07+07= 14.
Next step is taken a square of 7 is 49.
Write as 11449.
Note: This method is applicable for the number in between 100 to 109 only.
For number 70 to 100 is,
Subtract 93 from 100.
We get 7. Take a square of 7 is 49.
Next step is to subtract 7 from 93 we get 86.
Write it as 8649.
Then perform addition.
i.e. 11449+8649 = 20098.
Milind Hanchate said:
1 decade ago
Simplest way.
(107)^2+(97)^2.
To find 107 square.
Take 1 as it is.
After that add 07+07= 14.
Next step is take square of 7 is 49.
Write as 11449.
Note: This method is applicable for number in between 100 to 125.
For number 75 to 100 is,
Subtract 93 from 100.
We get 7. Take square of 7 is 49.
Next step is subtract 7 from 93 we get 86.
Write it as 8649.
Then perform addition.
i.e. 11449+8649 = 20098.
(107)^2+(97)^2.
To find 107 square.
Take 1 as it is.
After that add 07+07= 14.
Next step is take square of 7 is 49.
Write as 11449.
Note: This method is applicable for number in between 100 to 125.
For number 75 to 100 is,
Subtract 93 from 100.
We get 7. Take square of 7 is 49.
Next step is subtract 7 from 93 we get 86.
Write it as 8649.
Then perform addition.
i.e. 11449+8649 = 20098.
Manoj said:
1 decade ago
We can solve this by using digital sum method:
=(1+0+7)*(1+0+7)+(1+2)*(1+2)
=(8*8)+(3*3)
=64+9
=(6+4)+9
=10+9
=19
=1+9
=10
=1+0
=1
Then check the answers in the same way. If we get 1 for option A it is the answer. For looking it is difficulty but if you practice once its going to simple believe me friends.
=(1+0+7)*(1+0+7)+(1+2)*(1+2)
=(8*8)+(3*3)
=64+9
=(6+4)+9
=10+9
=19
=1+9
=10
=1+0
=1
Then check the answers in the same way. If we get 1 for option A it is the answer. For looking it is difficulty but if you practice once its going to simple believe me friends.
M S Husain said:
10 years ago
Note--Digital sum is only eliminate method not sure give to correct answer it's sure cancel all wrong answer.
Ajaz 110 and 125.
= (110)^2.
Break 110 as [1!10] = a^2 2*a*b b^2.
I take b as 10 that is 2 digit so we take only two digit if more than 2 carry forward.
1*1 2*1*10 100 == 12100.
Ajaz 110 and 125.
= (110)^2.
Break 110 as [1!10] = a^2 2*a*b b^2.
I take b as 10 that is 2 digit so we take only two digit if more than 2 carry forward.
1*1 2*1*10 100 == 12100.
Chitti said:
7 years ago
In simple way
107 * 107 + 93 * 93 = ?
First, add 107+93=200(first 3 numbers in option) when unit places sum is 10 it is possible not for all.
Consider that one is correct
For example:102*102+98 * 98 = 20008,
102+98=200.
107 * 107 + 93 * 93 = ?
First, add 107+93=200(first 3 numbers in option) when unit places sum is 10 it is possible not for all.
Consider that one is correct
For example:102*102+98 * 98 = 20008,
102+98=200.
Ajit Kumar said:
8 years ago
We can do in this way;
a^2+b^2=(a+b)^2-2ab;
107^2+93^2= (107+93)^2-2*107*93;
= 200^2-19902;
= 40000-19902;
= 20098.
a^2+b^2=(a+b)^2-2ab;
107^2+93^2= (107+93)^2-2*107*93;
= 200^2-19902;
= 40000-19902;
= 20098.
(1)
Desh deepak gupta said:
7 years ago
Simply;
107 * 107 + 93 * 93=
=(107-7) * (107-7)+(93+7) * (93+7).
=(100 * 100)+(-7 * - 7)+(100 * 100)+(7 * 7).
= 10000 + 10000 + 49 + 49,
= 20098.
107 * 107 + 93 * 93=
=(107-7) * (107-7)+(93+7) * (93+7).
=(100 * 100)+(-7 * - 7)+(100 * 100)+(7 * 7).
= 10000 + 10000 + 49 + 49,
= 20098.
(4)
S.abi said:
9 years ago
107 + 7 = 114.
7^2 = 49.
so 107^2 = 11449.
93^2 = 8649.
93-7 = 86.
7^2= 49.
Then add 111449 + 8649 = 20098.
7^2 = 49.
so 107^2 = 11449.
93^2 = 8649.
93-7 = 86.
7^2= 49.
Then add 111449 + 8649 = 20098.
Isha said:
4 years ago
107 * 107 + 93 * 93.
= 107^2 + 93^2.
= (100+7)^2 +(100-7)^2.
= 10000 + 49 + 1400 + 10000 + 49 - 1400.,
= 20098.
= 107^2 + 93^2.
= (100+7)^2 +(100-7)^2.
= 10000 + 49 + 1400 + 10000 + 49 - 1400.,
= 20098.
(2)
Sakthi said:
7 years ago
Take Number also Approximately number 110 * 110 = 12100,
90*90=8100,
12100+8100=20200(Approx).
90*90=8100,
12100+8100=20200(Approx).
(1)
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