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

Similar questions to practice:
12-easy-pieces-or-not-126366.html#p1033935
in-his-pocket-a-boy-has-3-red-marbles-4-blue-marbles-and-85216.html
of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html
in-a-deck-of-52-cards-each-card-is-one-of-4-different-color-83183.html
a-box-contains-10-red-pills-5-blue-pills-12-yellow-56779.html
each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html
a-student-is-asked-to-pick-marbles-from-a-bag-that-contains-72390.html
of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html
if-a-librarian-randomly-removes-science-books-from-a-library-93861.html
each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html
a-box-contains-10-tablets-of-medicine-a-and-15-tablets-157726.html
there-are-12-red-balls-10-blue-balls-15-red-balls-and-134437.html
in-a-jar-there-are-21-white-balls-24-green-balls-and-175461.html

Hope it helps.

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.

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

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

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

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


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

Regards,
Fabio.

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.

cheers.

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

Also i am confused if this question makes sense, these statements seems to be contradicting. 1st says that we need 14 for 1 red, 2nd say that we need 8 for one yellow - so basically in 2nd, if we take 7 then it will be having red and blue but then how is statement 1 holding true? if according to st.2 we can get red in 7 only then why st.1 says we will get red in 14.

There are several solutions above explaining this.

To understand the concept better, check other Worst Case Scenario Questions from our Special Questions Directory for additional practice.

Hope this helps.