Quant#2
This topic has expert replies
- anirudhbhalotia
- Master | Next Rank: 500 Posts
- Posts: 123
- Joined: Tue Nov 23, 2010 7:18 pm
- Location: Mumbai, India
- Thanked: 5 times
- Followed by:4 members
-
- Master | Next Rank: 500 Posts
- Posts: 437
- Joined: Sat Nov 22, 2008 5:06 am
- Location: India
- Thanked: 50 times
- Followed by:1 members
- GMAT Score:580
10^2 (10^6 - 1)
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10
Hope is the dream of a man awake
- anirudhbhalotia
- Master | Next Rank: 500 Posts
- Posts: 123
- Joined: Tue Nov 23, 2010 7:18 pm
- Location: Mumbai, India
- Thanked: 5 times
- Followed by:4 members
beat_gmat_09 wrote:10^2 (10^6 - 1)
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10
Didn't get it.
How do you expand/solve 10^8 - 10^2? Isnt this = 10^6?
Similarily10^7 - 10^3 = 10^4?
-
- Master | Next Rank: 500 Posts
- Posts: 437
- Joined: Sat Nov 22, 2008 5:06 am
- Location: India
- Thanked: 50 times
- Followed by:1 members
- GMAT Score:580
No. 10^8 - 10^2 !=10^6 ; Is 10^2 - 10 = 10 ? No. 10^2 = 100 so 100-10 = 90anirudhbhalotia wrote:beat_gmat_09 wrote:10^2 (10^6 - 1)
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10
Didn't get it.
How do you expand/solve 10^8 - 10^2? Isnt this = 10^6?
Similarily10^7 - 10^3 = 10^4?
Check out indices rules, you'll need to use these rules.
If m and n are positive integers, and then
(i) a^m a^n = a^(m + n)
(ii) [Quotient Law]
(iii) (a^m)^n = a^(mn)
(iv) (ab)^m = a^m . b^m
(v) a^0= 1
(vi) a^(m/n) = (a^m)^1/n
10^8 is quite a huge figure and subtracting 100 is approximately the same value - 10^8
moreover the question asks you the closest value not the exact/accurate value, so you can use approximation.
Hope this helps.
Hope is the dream of a man awake
-
- Junior | Next Rank: 30 Posts
- Posts: 20
- Joined: Tue Aug 03, 2010 8:37 am
- Thanked: 1 times
To make it simple
10^2(10^6-1)
---------------
10^3(10^4-1)
(10^3*2-1^2)
------------------
10(10^2*2 -1^2)
use the formula (a^2-b^2)= (a-b)(a+b)
therefore numrator will be (10^3-1)(10^3+1)
and dr will be (10^2-1)(10^2+1)
so to simplify
round off 10^3-1 to 10^3 and so on
therefore we will get
(10^3-1)(10^3+1)
-------------------------
10(10^2-1)(10^2+1)
to make it approx round off +1 and -1
so we get 10^3*10^3
-------------------- = 10
10*10^2*10^2
hope this make sense
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10[/quote]
Didn't get it.
How do you expand/solve 10^8 - 10^2? Isnt this = 10^6?
Similarily10^7 - 10^3 = 10^4?[/quote]
10^2(10^6-1)
---------------
10^3(10^4-1)
(10^3*2-1^2)
------------------
10(10^2*2 -1^2)
use the formula (a^2-b^2)= (a-b)(a+b)
therefore numrator will be (10^3-1)(10^3+1)
and dr will be (10^2-1)(10^2+1)
so to simplify
round off 10^3-1 to 10^3 and so on
therefore we will get
(10^3-1)(10^3+1)
-------------------------
10(10^2-1)(10^2+1)
to make it approx round off +1 and -1
so we get 10^3*10^3
-------------------- = 10
10*10^2*10^2
hope this make sense
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10[/quote]
Didn't get it.
How do you expand/solve 10^8 - 10^2? Isnt this = 10^6?
Similarily10^7 - 10^3 = 10^4?[/quote]
-
- Junior | Next Rank: 30 Posts
- Posts: 20
- Joined: Tue Aug 03, 2010 8:37 am
- Thanked: 1 times
To make it simple
10^2(10^6-1)
---------------
10^3(10^4-1)
(10^3*2-1^2)
------------------
10(10^2*2 -1^2)
use the formula (a^2-b^2)= (a-b)(a+b)
therefore numrator will be (10^3-1)(10^3+1)
and dr will be (10^2-1)(10^2+1)
so to simplify
round off 10^3-1 to 10^3 and so on
therefore we will get
(10^3-1)(10^3+1)
-------------------------
10(10^2-1)(10^2+1)
to make it approx round off +1 and -1
so we get 10^3*10^3
-------------------- = 10
10*10^2*10^2
hope this make sense
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10[/quote]
Didn't get it.
How do you expand/solve 10^8 - 10^2? Isnt this = 10^6?
Similarily10^7 - 10^3 = 10^4?[/quote]
10^2(10^6-1)
---------------
10^3(10^4-1)
(10^3*2-1^2)
------------------
10(10^2*2 -1^2)
use the formula (a^2-b^2)= (a-b)(a+b)
therefore numrator will be (10^3-1)(10^3+1)
and dr will be (10^2-1)(10^2+1)
so to simplify
round off 10^3-1 to 10^3 and so on
therefore we will get
(10^3-1)(10^3+1)
-------------------------
10(10^2-1)(10^2+1)
to make it approx round off +1 and -1
so we get 10^3*10^3
-------------------- = 10
10*10^2*10^2
hope this make sense
_____________
10^3 (10^4 - 1)
10^6 - 1 approx = 10^6 same for 10^4
10^6
= _____
10^5
= 10[/quote]
Didn't get it.
How do you expand/solve 10^8 - 10^2? Isnt this = 10^6?
Similarily10^7 - 10^3 = 10^4?[/quote]
- goyalsau
- Legendary Member
- Posts: 866
- Joined: Mon Aug 02, 2010 6:46 pm
- Location: Gwalior, India
- Thanked: 31 times
To make it simple
10^2(10^6-1)
---------------
10^3(10^4-1)
10^6 = 100,00,00 ,,,,,,,,, 10^4 = 100,00
10^6 - 1 = 999,999 ,,,,,, 10^4 - 1 = 999,9
999,999
------------------ { Cancel by 9 }
10(999,9)
111,111
-------------
10 ( 111,1)
1111 * 100 = 111,100 ....... Numerator can be written as 1111 * 100 { i know 11 is left that is very small and we can neglect that as problem asks for the approximation }
1111 * 100
-------------
10 ( 111,1)
100
-----
10
Answer is 10........... ( )
Saurabh Goyal
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.