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TAGS: GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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GRE Math Challenge #71- (a/b) or (a+3)/(b+3) [#permalink]
1
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Expert's post 00:00

Question Stats: 73% (00:37) correct 26% (00:23) wrong based on 71 sessions

a and b are positive integers.

 Quantity A Quantity B $$\frac{a}{b}$$ $$\frac{a+3}{b+3}$$

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

Kudos to the right solution and explanation
[Reveal] Spoiler: OA

_________________

Sandy
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Re: GRE Math Challenge #71 [#permalink]
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Expert's post
sandy wrote:
a and b are positive integers.

Quantity A: $$a/b$$

Quantity B: $$\frac{(a+3)}{(b+3)}$$

One of my favorite QC strategies is called "Looking for Equality" (free video on this topic here: http://www.greenlighttestprep.com/modul ... on?id=1099).
In this strategy, I first look for values of x such that the two quantities are equal. This often involves checking some easy numbers like 0, 1, -1 etc.

Consider these two cases:
Case #2: a = 1 and b = 1
Quantity A: a/b = 1/1 = 1
Quantity B: (a+3)/(b+3) = (1+3)/(1+3) = 4/4 = 1
Since the two quantities are EQUAL, the correct answer is either C or D

Now try some other values of a and b:
Case #2: a = 1 and b = 2
Quantity A: a/b = 1/2
Quantity B: (a+3)/(b+3) = (1+3)/(2+3) = 4/5
Since the two quantities are NOT EQUAL, the correct answer is D

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Last edited by GreenlightTestPrep on 18 May 2015, 11:25, edited 1 time in total.
Manager Joined: 17 Feb 2015
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Re: GRE Math Challenge #71 [#permalink]
#Sandy this is not a challenge, it can be a practice question..... GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 122

Kudos [?]: 1958  , given: 397

Re: a and b are positive integers [#permalink]
3
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Expert's post
Explanation

The best strategy here is to assume values of a and b.

Let a = 1 and b =2 .

Quantity A: $$\frac{1}{2}$$
Quantity B: $$\frac{1+3}{2+3}=\frac{4}{5}$$

Quantity B is greater.

Let a = 6 and b=3
Quantity A: $$\frac{6}{3}=2$$
Quantity B: $$\frac{6+3}{3+3}=\frac{3}{2}$$

Quantity A is greater.

Hence a relationship cannot be determined. Thus option D is correct.
_________________

Sandy
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Re: a and b are positive integers [#permalink]
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sandy wrote:
Explanation

The best strategy here is to assume values of a and b.

Let a = 0 and b =1 .

Quantity A: $$\frac{0}{1}=0$$
Quantity B: $$\frac{0+3}{1+3}=\frac{3}{4}$$

Quantity B is greater.

Let a = 6 and b=3
Quantity A: $$\frac{6}{3}=2$$
Quantity B: $$\frac{6+3}{3+3}=\frac{3}{2}$$

Quantity A is greater.

Hence a relationship cannot be determined. Thus option D is correct.

Just wanted to say that 0 is not a positive integer. 0 is neither positive nor negative, GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 122

Kudos [?]: 1958  , given: 397

Re: a and b are positive integers [#permalink]
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Expert's post
You are right. Changed it!

Thanks
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Sandy
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Re: GRE Math Challenge #71- (a/b) or (a+3)/(b+3) [#permalink]
since there is no restriction for a / b (i mean like a>1 b>a , this kind of restriction)
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Re: GRE Math Challenge #71- (a/b) or (a+3)/(b+3) [#permalink]
D
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Re: GRE Math Challenge #71- (a/b) or (a+3)/(b+3) [#permalink]
Why would you not assume different numbers for the variables a & b. If you assume a & b are the number 1, would they not be the same variable since they are the same number? GRE Instructor Joined: 10 Apr 2015
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Re: GRE Math Challenge #71- (a/b) or (a+3)/(b+3) [#permalink]
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Expert's post
PTDom wrote:
Why would you not assume different numbers for the variables a & b. If you assume a & b are the number 1, would they not be the same variable since they are the same number?

It's a common misconception that two different variables (e.g., x and y) must represent different values, but this is not the case.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: GRE Math Challenge #71- (a/b) or (a+3)/(b+3)   [#permalink] 25 May 2019, 09:25
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