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compare quanities

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compare quanities [#permalink] New post 25 Aug 2018, 15:01
Expert's post
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Question Stats:

83% (00:31) correct 16% (00:19) wrong based on 106 sessions
Quantity A
Quantity B
\(10^6+10^5\)
\(10^7+10^4\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: compare quanities [#permalink] New post 15 Nov 2018, 12:19
Expert's post
sandy wrote:
Quantity A
Quantity B
\(10^6+10^5\)
\(10^7+10^4\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


One approach is to evaluate each part....

Given:
Quantity A: 10^6 + 10^5
Quantity B: 10^7 + 10^4

Evaluate to get:
Quantity A: 1,000,000 + 100,000
Quantity B: 10,000,000 + 10,000

Evaluate to get:
Quantity A: 1,100,0000
Quantity B: 10,010,000

Answer: B

Cheers,
Brent
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Re: compare quanities [#permalink] New post 19 Nov 2018, 16:08
10^4 (10^3 + 1) << quantity B

10^4 (10^2 + 10) << quantity A

B is the answer choice
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Re: compare quanities [#permalink] New post 25 Nov 2018, 14:52
Answer: B
The best approach for this question is to make them somehow seem look like each other and write them in form of multiplication thus we can simplify them easily.
Here the minimum multiply factor of both can be 10^4 :

A: 10^6 + 10^5 = 10^4 * (10^2 + 10^1)
B: 10^7 + 10^4 = 10^4 * (10^3+ 1)

10^4 is the same between both of them, so we compare (10^2 + 10^1)=110 and (10^3+ 1)=1001 which (10^3+ 1) is bigger and B is bigger than A
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Re: compare quanities [#permalink] New post 26 Nov 2018, 06:09
Expert's post
sandy wrote:
Quantity A
Quantity B
\(10^6+10^5\)
\(10^7+10^4\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



If you realize that \(10^7\) is 10 times \(10^6\), you will immediately choose the quantity with \(10^7\).

\(10^7=10*10^6=10^6+10^6+10^6+10^6+10^6+10^6+10^6+10^6+10^6+10^6\), thi swill surely be greater than \(10^6+10^5\)
so B>A
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: compare quanities   [#permalink] 26 Nov 2018, 06:09
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