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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]

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01 Oct 2012, 05:11
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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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Question: 55
Page: 159
Difficulty: 600

[Reveal] Spoiler:
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Table.png [ 40.01 KiB | Viewed 10729 times ]
[Reveal] Spoiler: OA

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Re: In the table above, what is the number of green marbles in J [#permalink]

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01 Oct 2012, 05:11
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SOLUTION

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 $$80+z=180$$ --> $$z=100$$.

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Re: In the table above, what is the number of green marbles in J [#permalink]

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01 Oct 2012, 05:19
2
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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.

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Re: In the table above, what is the number of green marbles in J [#permalink]

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01 Oct 2012, 20:22
1
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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
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Re: In the table above, what is the number of green marbles in J [#permalink]

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04 Oct 2012, 00:41
1
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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]

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04 Oct 2012, 14:20
2
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Expert's post
SOLUTION

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 $$80+z=180$$ --> $$z=100$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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05 Oct 2012, 03:19
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]

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10 Dec 2012, 04:43
$$x + y = 80$$ 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:

$$80 + z = 180 --> z = 100$$

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Re: In the table above, what is the number of green marbles in J [#permalink]

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13 Apr 2014, 08:52
Bunuel wrote:
SOLUTION

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 $$80+z=180$$ --> $$z=100$$.

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]

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13 Apr 2014, 21:16
X+Y =80 --------- (1)

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

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

Subtract (3) -(1)

we get

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

Z=100;

Hence D.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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14 Apr 2014, 01:30
russ9 wrote:
Bunuel wrote:
SOLUTION

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 $$80+z=180$$ --> $$z=100$$.

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.

Hope this helps.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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28 Apr 2014, 21:27
Bunuel wrote:
russ9 wrote:
Bunuel wrote:
SOLUTION

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 $$80+z=180$$ --> $$z=100$$.

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.

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]

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29 Apr 2014, 00:58
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.

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.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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29 Apr 2014, 07:47
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]

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29 May 2014, 09:03
1
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official answer is not registered for this question.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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29 May 2014, 09:04
b2bt wrote:
official answer is not registered for this question.

______________
Edited. Thank you.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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20 Aug 2014, 23:47
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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Re: In the table above, what is the number of green marbles in J [#permalink]

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09 Sep 2014, 22:05
The table provided in this question was a boon for me. See how below.....
Attachment:

Table.png [ 45.65 KiB | Viewed 6276 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

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Re: In the table above, what is the number of green marbles in J [#permalink]

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21 Nov 2014, 03:28
From the given table we could make equations like
Equation 1. Given x+y=80 ----> x=80-y
Equation2. Given y+z=120
Equation3. Given x+z = 160
Substituting the value of x in Equation 3 from Equation 1
Equation 4. (80-y)+z=160 ----> -y+z = 80
Adding Equation 2 and Equation 4
2z=200 ---> Z=100.
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Re: In the table above, what is the number of green marbles in J [#permalink]

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22 Jul 2015, 09:52
just substract from the first equation the 2nd and the 3rd you'll get --> x+y-y-z-x-z = -200 ->x,y cancel out and Z=100 (D)
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Re: In the table above, what is the number of green marbles in J   [#permalink] 22 Jul 2015, 09:52

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