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

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Joined: 17 Oct 2012
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Location: India
Concentration: Strategy, Finance
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A certain number of marbles are to be removed from a box con  [#permalink]

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Updated on: 01 Aug 2014, 00:46
2
33
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:35) correct 21% (01:44) wrong based on 729 sessions

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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, 21:48.
Last edited by chetan86 on 01 Aug 2014, 00:46, edited 2 times in total.
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Joined: 02 Sep 2009
Posts: 58434
Re: A certain number of marbles are to be removed from a box con  [#permalink]

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01 Aug 2014, 12:58
6
2
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.

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

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01 Aug 2014, 00:40
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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Joined: 02 Sep 2009
Posts: 58434
Re: A certain number of marbles are to be removed from a box con  [#permalink]

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01 Aug 2014, 12:59
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.

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

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12 Apr 2017, 09:03
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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28 Jan 2019, 06:01
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.

Regards,
Fabio.
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Re: A certain number of marbles are to be removed from a box con   [#permalink] 28 Jan 2019, 06:01
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