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.
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)
Desh deepak gupta said:
6 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)
Sagar HR said:
6 years ago
Or we can solve using the formula a^2+b^2=[a+b]^2- 2ab.
(107+93)^2 - 2(107*93) = 20098.
(107+93)^2 - 2(107*93) = 20098.
(2)
Sgyanaranjan said:
6 years ago
100+100=200.
7.7+7.7=98,
So the answer is 20098.
7.7+7.7=98,
So the answer is 20098.
(1)
GYANARANJAN SAHOO said:
6 years ago
Thanks @Anjali.
Anjali said:
6 years ago
(100+7)(100+7)+(100-7)(100-7).
= 10000+700+700 + 49 + 10000-700-700 + 49.
= 20000+98 = 20098.
= 10000+700+700 + 49 + 10000-700-700 + 49.
= 20000+98 = 20098.
(5)
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.
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)
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.
Sia said:
7 years ago
@Jonavin, @Hari.
We can't use (a+b) (a-b) because there is (a^2+b^2).
Instead of (a^2-b^2).
We can't use (a+b) (a-b) because there is (a^2+b^2).
Instead of (a^2-b^2).
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers