Problem Solving

a. Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 ?

1. 5^6
2. 13^5
3.2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5

Ans : 2^6 + 3^6


b. The value of 10^8 - 10^2 /10^7- 10^3, is the closed to which of the following ?

1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4

Ans : 10

1)
2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 =

2^5(1 + 1) + 3^5(1+1+1) =

2^5(2) + 3^5(3) = the desired answer....

b. The value of 10^8 - 10^2 /10^7- 10^3, is the closed to which of the following ?

1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4

Ans : 10[/quote]

sOLUTION:

10^8 - 10^2/10^7- 10^3

= 10^2 (10^6-1)/ 10^3(10^4 - 1)
= 10^6-1 / 10 (10^4-1)

nOW 10^6-1 IS APPROX EQUAL TO 10^6 AND 10^4-1 IS APPROX EQUAL TO 10^4

hENCE
= 10^6/ (10 *10^4)
= 10^6/10^5
=10 WHICH IS THE ANSWER!

Thanks for the responses.

Baskaran

This should be in the problem solving section and also please follow the rule of one question per thread.

Can you please send me the link.

Thanks

I am sorry but I don't understand how we can get the answer 2^6 + 3^6 for question 1 in the thread. Can someone please explain??

Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 ?

1. 5^6
2. 13^5
3.2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5

Ans : 2^6 + 3^6

Many Thanks

I think you will agree with me that 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 is two times 2^5 plus three times 3^5. Now let's write that down:
2*2^5 + 3*3^5 = (2^1)*(2^5) + (3^1)(3^5). When multiplying powers of the same number, just add the exponents! So you get that 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 = 2^6 + 3^6.

Makes sense. Thank you very much.

shuklat wrote:b. The value of 10^8 - 10^2 /10^7- 10^3, is the closed to which of the following ?

1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4

Ans : 10

sOLUTION:

10^8 - 10^2/10^7- 10^3

= 10^2 (10^6-1)/ 10^3(10^4 - 1)
= 10^6-1 / 10 (10^4-1)

nOW 10^6-1 IS APPROX EQUAL TO 10^6 AND 10^4-1 IS APPROX EQUAL TO 10^4

hENCE
= 10^6/ (10 *10^4)
= 10^6/10^5
=10 WHICH IS THE ANSWER![/quote]


Can you please explain this step by step I still find it very confusing