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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: 01 Aug 2014, 00:46
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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.
Spoiler: OA

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

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

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New post 01 Aug 2014, 12:58
4
1
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, 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.

Answer: C.


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Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
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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, 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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Re: A certain number of marbles are to be removed from a box con   [#permalink] 23 May 2018, 02:35
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