Please help to solve this problem ?

[Baskaranselva]

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

[erjamit]

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....

[shuklat]

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!

[Baskaranselva]

Thanks for the responses.

Baskaran

[gabriel]

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

[Baskaranselva]

Can you please send me the link.

Thanks

[dubeystuts]

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

[DanaJ]

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.

[dubeystuts]

Makes sense. Thank you very much.

[rbansal]

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