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Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2922 , given: 394

3a + 2b = 20 and 2a + 3b = 5 [#permalink]
Expert's post 00:00

Question Stats: 66% (01:04) correct 33% (00:56) wrong based on 59 sessions
3a + 2b = 20 and 2a + 3b = 5

 Quantity A Quantity B a+b a

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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Sandy
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Manager Joined: 26 Jan 2018
Posts: 189
GRE 1: Q165 V156 Followers: 1

Kudos [?]: 132 , given: 3

Re: 3a + 2b = 20 and 2a + 3b = 5 [#permalink]

5(a+b) = 25
a+b = 5 (eq1)
3a + 2b = 20

Multiplying eq1 with 2
2a+2b = 10
3a + 2b = 20

Substracting eq 2 from 1, a = 10

Hence B
GRE Instructor Joined: 10 Apr 2015
Posts: 3838
Followers: 148

Kudos [?]: 4496 , given: 69

Re: 3a + 2b = 20 and 2a + 3b = 5 [#permalink]
Expert's post
sandy wrote:
3a + 2b = 20 and 2a + 3b = 5

 Quantity A Quantity B a+b a

There are two primary ways to solve systems of equations

1) Substitution method
2) Elimination method

And most cases (and especially in this case), the elimination method will be faster.

Take:
3a + 2b = 20
2a + 3b = 5
Add the equations to get: 5a + 5b = 25
Divide both sides by 5 to get: a + b = 5

Now take:
3a + 2b = 20
2a + 3b = 5

Multiply both sides of the TOP equation by 3, and multiply both sides of the BOTTOM equation by 2 to get:
9a + 6b = 60
4a + 6b = 10

Subtract the bottom equation from the top equation to get: 5a = 50, which means a = 10

We now have:
QUANTITY A: 5
QUANTITY B: 10

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Manager Joined: 02 Sep 2019
Posts: 69
Concentration: Finance
GRE 1: Q151 V148 GPA: 3.14
Followers: 1

Kudos [?]: 39 , given: 21

Re: 3a + 2b = 20 and 2a + 3b = 5 [#permalink]
here we 2 equations.
1- 3a +2b=20
2- 2a +3b=5
Subtract both
a-b=15.
Ok we have
QA a+B QB a
subtract a from both to get
QA B
QB 0
and we know that a-b=15 and a here must be greater than b to get positive number.
any suggestion for my approach will be appreciated Re: 3a + 2b = 20 and 2a + 3b = 5   [#permalink] 22 Jun 2020, 22:05
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