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In the table above, what is the number of green marbles in J

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In the table above, what is the number of green marbles in J [#permalink] New post 01 Oct 2012, 04:11
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In the table above, what is the number of green marbles in Jar R ?

(A) 70
(B) 80
(C) 90
(D) 100
(E) 110

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Re: In the table above, what is the number of green marbles in J [#permalink] New post 01 Oct 2012, 04:11
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SOLUTION

Image
In the table above, what is the number of green marbles in Jar R ?

(A) 70
(B) 80
(C) 90
(D) 100
(E) 110

We need to find the value of z, while given that:

x+y=80;
y+z=120;
x+z=160.

Sum these 3 equations: 2x+2y+2z=360 --> reduce by 2: x+y+z=180 --> since we know that x+y=80, then 80+z=180 --> z=100.

Answer: D.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the table above, what is the number of green marbles in J [#permalink] New post 01 Oct 2012, 04:19
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To solve, I took the sum of the expressions as seen below:


X + Y = 80
Y + Z = 120
X + Z = 160
2X + 2Y + 2Z = 360

Dividing by 2 we get X + Y + Z = 180.

Since we know X + Y = 80 from Jar P, we can deduce that Z = 100. Since Z is the number of green marbles in Jar R we have our solution.

[Reveal] Spoiler:
Answer is D, 100

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Re: In the table above, what is the number of green marbles in J [#permalink] New post 01 Oct 2012, 19:22
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x+y = 80 ---(1)
x+z = 160---(2)
z+y= 120---(3)
Subtract equation 1 from 2 & we get--> z-y = 80----(4)
Add equation (4) & (3) we get--> 2z= 200
z=100
Answer D
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 03 Oct 2012, 23:41
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x + y = 80 ......(1)
y + z = 120 .....(2)
x + z = 160 ......(3)

From (2) above, z=160-y .....Substitute value of z in (3)

==> x-y = 40 ....(4)

Solve (1) and (4), to get x = 60
==> y = 20
==> z = 100

Thus, number of green marbles in Jar R = 100 (Ans = D)
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 04 Oct 2012, 13:20
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SOLUTION

Image
In the table above, what is the number of green marbles in Jar R ?

(A) 70
(B) 80
(C) 90
(D) 100
(E) 110

We need to find the value of z, while given that:

x+y=80;
y+z=120;
x+z=160.

Sum these 3 equations: 2x+2y+2z=360 --> reduce by 2: x+y+z=180 --> since we know that x+y=80, then 80+z=180 --> z=100.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the table above, what is the number of green marbles in J [#permalink] New post 05 Oct 2012, 02:19
x+y=80...(1)
y+z=120 ==> z=120-y
x+z=160 ==> z=120-x...(3)

120-x=160-y
==> x-y=40...(2)

sloving (1) & (2) we get x=60
put value of x=60 in eqn (3),

60+z=160
=> z=100 Ans
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 10 Dec 2012, 03:43
x + y = 80 eq 1
y + z = 120 eq 2
x + z = 160 eq 3
______________
2x + 2y + 2z = 360 --> x + y+ z = 180 eq 4

Combine eq 4 and eq 1:

80 + z = 180 --> z = 100

Answer: D
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 13 Apr 2014, 07:52
Bunuel wrote:
SOLUTION

Image
In the table above, what is the number of green marbles in Jar R ?

(A) 70
(B) 80
(C) 90
(D) 100
(E) 110

We need to find the value of z, while given that:

x+y=80;
y+z=120;
x+z=160.

Sum these 3 equations: 2x+2y+2z=360 --> reduce by 2: x+y+z=180 --> since we know that x+y=80, then 80+z=180 --> z=100.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.


Are we always allowed to sum the 3 equations? Do we need to have some commonalities to be able to sum the equations?
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 13 Apr 2014, 20:16
X+Y =80 --------- (1)

Y+Z =120 -------- (2)

X+Z =160 -------- (3)

Subtract (3) -(1)

we get

Z - Y = 80 -----------(4)

ADD (4) and (2) equations,
Z=100;

Hence D.
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 14 Apr 2014, 00:30
Expert's post
russ9 wrote:
Bunuel wrote:
SOLUTION

Image
In the table above, what is the number of green marbles in Jar R ?

(A) 70
(B) 80
(C) 90
(D) 100
(E) 110

We need to find the value of z, while given that:

x+y=80;
y+z=120;
x+z=160.

Sum these 3 equations: 2x+2y+2z=360 --> reduce by 2: x+y+z=180 --> since we know that x+y=80, then 80+z=180 --> z=100.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.


Are we always allowed to sum the 3 equations? Do we need to have some commonalities to be able to sum the equations?


Yes, we can sum/subtract/multiply equations. I think you are mixing equations with inequalities, for which there are specific rules.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html

Hope this helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the table above, what is the number of green marbles in J [#permalink] New post 28 Apr 2014, 20:27
Bunuel wrote:
russ9 wrote:
Bunuel wrote:
SOLUTION

Image
In the table above, what is the number of green marbles in Jar R ?

(A) 70
(B) 80
(C) 90
(D) 100
(E) 110

We need to find the value of z, while given that:

x+y=80;
y+z=120;
x+z=160.

Sum these 3 equations: 2x+2y+2z=360 --> reduce by 2: x+y+z=180 --> since we know that x+y=80, then 80+z=180 --> z=100.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.


Are we always allowed to sum the 3 equations? Do we need to have some commonalities to be able to sum the equations?


Yes, we can sum/subtract/multiply equations. I think you are mixing equations with inequalities, for which there are specific rules.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html

Hope this helps.


Thanks for clarifying.

Just to confirm one of your comments above -- "Yes, we can sum/subtract/multiply equations." -- would this be valid for the problem even if one of the equations didn't have any common variables. What I mean is, if the equations read:

x+y=80;
a+b=120;
x+z=160.

Can we still add the 3?
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 28 Apr 2014, 23:58
Expert's post
russ9 wrote:
Bunuel wrote:
russ9 wrote:
Are we always allowed to sum the 3 equations? Do we need to have some commonalities to be able to sum the equations?


Yes, we can sum/subtract/multiply equations. I think you are mixing equations with inequalities, for which there are specific rules.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html

Hope this helps.


Thanks for clarifying.

Just to confirm one of your comments above -- "Yes, we can sum/subtract/multiply equations." -- would this be valid for the problem even if one of the equations didn't have any common variables. What I mean is, if the equations read:

x+y=80;
a+b=120;
x+z=160.

Can we still add the 3?

_______________________
Yes.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the table above, what is the number of green marbles in J [#permalink] New post 29 Apr 2014, 06:47
Bunuel wrote:
russ wrote:

Can we still add the 3?

_______________________
Yes.


Thanks -- that clarifies a lot!
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 29 May 2014, 08:03
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 29 May 2014, 08:04
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Re: In the table above, what is the number of green marbles in J [#permalink] New post 20 Aug 2014, 22:47
Another approach can be back solving by taking a value from choices for z and finding x and y to see if they make sense per the table.
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In the table above, what is the number of green marbles in J [#permalink] New post 09 Sep 2014, 21:05
The table provided in this question was a boon for me. See how below.....
Attachment:
Table.png
Table.png [ 45.65 KiB | Viewed 87 times ]


1. Replaced y with (80-x). The equation remains intact on "Jar P" row

2. Copied (80-x) in "Jar Q" row.

These 2 steps directly eliminates x & y

3. Adding rows "Jar Q" & "Jar R"

2z+80 = 280

z = 100

Answer = D
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In the table above, what is the number of green marbles in J   [#permalink] 09 Sep 2014, 21:05
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