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A certain number of marbles are to be removed from a box con

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A certain number of marbles are to be removed from a box con  [#permalink]

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New post Updated on: 31 Jul 2014, 23:46
3
41
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C
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Question Stats:

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A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.


Searched for this question but could not find it.
If same question is already available then kindly delete it.

Originally posted by chetan86 on 31 Jul 2014, 20:48.
Last edited by chetan86 on 31 Jul 2014, 23:46, edited 2 times in total.
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Re: A certain number of marbles are to be removed from a box con  [#permalink]

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New post 01 Aug 2014, 11:58
10
3
WoundedTiger wrote:
chetan86 wrote:
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.


Searched for this question but could not find it.
If same question is already available then kindly delete it.

OA later.



Let there be R,Y and B red,yellow and blue balls be there initially. We need to find out Y-R = ?

St 1 basically says that B+Y=14 ( many combinations possible )
B : Y
1:13
2:12
3:11
4:10....

Not sufficient

St 2 says R+B=8

R: B
1:7
2:6
3:5
4:4
5:3...

Combining we see that Blue balls cannot be more than 7, So if

B=7, R=1 and Y=7 Y-R=6
B=6,R=2, and Y=8 then 8-2=6

If B=4,R=4, then Y=10 Y-R=6..

For all values Y-R=6...

Ans is C


Little correction: it should be Y + B = 13 and R + B = 7.

A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

We need to find Y - R.

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

This implies that Y + B = 13 because only if there are total of 13 blue and yellow marbles, removing 14 marbles guarantees getting a red one: you should pick all blue and yellow and the next one for sure will be red. But knowing that B + Y = 13 is not enough to get Y - R. Not sufficient.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

The same ways as above this means that R + B = 7. Not sufficient.

(1)+(2) Subtract R + B = 7 from Y + B = 13: (Y + B) - (R + B) = 13 - 7 --> Y - R = 6. Sufficient.

Answer: C.
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Re: A certain number of marbles are to be removed from a box con  [#permalink]

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New post 01 Aug 2014, 11:59
1
Bunuel wrote:
WoundedTiger wrote:
chetan86 wrote:
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.


Searched for this question but could not find it.
If same question is already available then kindly delete it.

OA later.



Let there be R,Y and B red,yellow and blue balls be there initially. We need to find out Y-R = ?

St 1 basically says that B+Y=14 ( many combinations possible )
B : Y
1:13
2:12
3:11
4:10....

Not sufficient

St 2 says R+B=8

R: B
1:7
2:6
3:5
4:4
5:3...

Combining we see that Blue balls cannot be more than 7, So if

B=7, R=1 and Y=7 Y-R=6
B=6,R=2, and Y=8 then 8-2=6

If B=4,R=4, then Y=10 Y-R=6..

For all values Y-R=6...

Ans is C


Little correction: it should be Y + B = 13 and R + B = 7.

A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

We need to find Y - R.

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

This implies that Y + B = 13 because only if there are total of 13 blue and yellow marbles, removing 14 marbles guarantees getting a red one: you should pick all blue and yellow and the next one for sure will be red. But knowing that B + Y = 13 is not enough to get Y - R. Not sufficient.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

The same ways as above this means that R + B = 7. Not sufficient.

(1)+(2) Subtract R + B = 7 from Y + B = 13: (Y + B) - (R + B) = 13 - 7 --> Y - R = 6. Sufficient.

Answer: C.


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Re: A certain number of marbles are to be removed from a box con  [#permalink]

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New post 31 Jul 2014, 23:40
1
chetan86 wrote:
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.


Searched for this question but could not find it.
If same question is already available then kindly delete it.

OA later.



Let there be R,Y and B red,yellow and blue balls be there initially. We need to find out Y-R = ?

St 1 basically says that B+Y=14 ( many combinations possible )
B : Y
1:13
2:12
3:11
4:10....

Not sufficient

St 2 says R+B=8

R: B
1:7
2:6
3:5
4:4
5:3...

Combining we see that Blue balls cannot be more than 7, So if

B=7, R=1 and Y=7 Y-R=6
B=6,R=2, and Y=8 then 8-2=6

If B=4,R=4, then Y=10 Y-R=6..

For all values Y-R=6...

Ans is C
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A certain number of marbles are to be removed from a box con  [#permalink]

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New post 12 Apr 2017, 08:03
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

Y + B = 14

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

B + R = 8


Combined-
Y - R = 6
C.
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Re: A certain number of marbles are to be removed from a box con  [#permalink]

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New post 28 Jan 2019, 05:01
chetan86 wrote:
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

\(? = Y - R\,\,\,\,\,\left( {{\text{yellow,}}\,{\text{red and}}\,\,{\text{blue}}\,\,{\text{marbles}}\,\,{\text{only}}} \right)\)

\(\left( 1 \right)\,\,Y + B = 13\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {Y,R,B} \right) = \left( {12,1,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 11 \hfill \cr
\,{\rm{Take}}\,\,\left( {Y,R,B} \right) = \left( {12,2,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 10 \hfill \cr} \right.\)

\(\left( 2 \right)\,\,R + B = 7\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {Y,R,B} \right) = \left( {12,6,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 6 \hfill \cr
\,{\rm{Take}}\,\,\left( {Y,R,B} \right) = \left( {13,6,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 7 \hfill \cr} \right.\)

\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,Y + B = 13 \hfill \cr
\,R + B = 7 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\,? = Y - R = 13 - 7\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.\)


We follow the notations and rationale taught in the GMATH method.

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Re: A certain number of marbles are to be removed from a box con  [#permalink]

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New post 21 Mar 2020, 10:22
it's an interesting exercise reviewing the error log. when I could not figure out how to evaluate both statements, I blindly assumed the answer is E, which is wrong. my rationale now that led to the right answer.

when we pick marbles from a box, as long as there is at least one marble of a color, there is a chance of picking up that marble. the only way we can guarantee a marble of a specific color being picked up is when all other colors have already been picked.

(1) if a minimum of 14 marbles have to be picked to guarantee a red marble, then yellow + blue = 14
(2) if a minimum of 8 marbles have to be picked to guarantee a yellow marble, then blue + red = 8.

since the question is asking for how many more yellow than red, you can find the answer by subtracting the equations (1) and (2) which gives yellow - red = 6. there are six more yellow marbles than red.

Answer is C.

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Re: A certain number of marbles are to be removed from a box con  [#permalink]

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New post 09 May 2020, 03:57
I have have done the following based on my understanding of the Question

From Statement 1: R+Y+B=14
R=1, as per the statement
Eq 1: So, Y+B=13. Therefore not sufficient
From Statement 2: R+Y+B=8
Y=1, as per statement 2
Eq 2: So, R+B=7. Therefore not sufficient

From Both (1) & (2) R+Y+B=14
From (2) R+B=7
So, Y=7
So, from Eq 1 & Eq 2: R+Y+2B=20
We know Y=7 & R+B=7

So, 7+7+B=20
B= 6
Finally, R=1
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Re: A certain number of marbles are to be removed from a box con   [#permalink] 09 May 2020, 03:57

A certain number of marbles are to be removed from a box con

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