A bag contains r red, g green, and w white marbles, where r, g and w

Question

A bag contains r red, g green, and w white marbles, where r, g and w are all positive integers. If one marble is picked randomly, is the probability that the marble is red higher than the probability that the marble is either green or white?

(1) The probability of selecting a green marble is 4/9

(2) The total number of marbles in the bag is less than 15.

(1) The probability of selecting a green marble is 4/9

(2) The total number of marbles in the bag is less than 15.

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nick1816 · Answer

Is r>g+w

Statement 1 - Total= 9x and Green= 4x

Case 1  - G=4; W=1; Total =9 (NO)

Case 2  - G=12; W=1; Total= 27 (Yes)

Insufficient

Statement 2- 
 Case 1-  R= 1; Total= 14 (NO)

Case 2-  R= 8; Total= 14 (Yes)

Insufficient

Combining both statement

Since Total number of balls is a multiple of 9 and is less than 15, Total number of balls must be 9; hence, number of green balls = 4.

Number of white balls is greater than or equal to 1; hence 1 ≤ r ≤ 4 < g+w

Sufficient

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • r, g, and w are positive integer. • If one marble is picked randomly, o Probability that picked marble is red = \frac{r}{r + g + w} o Probability that picked marble is either green or white = \frac{g}{r + g + w} + \frac{w}{r + g + w } = \frac{g+ w}{r + g + w} • We need to find out if \frac{r}{r + g + w }> \frac{g+ w}{r + g + w} o Or, we need to find out if r > g + w Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: The probability of selecting a green marble is 4/9 • According to this statement, \frac{g}{r + g + w} = \frac{4}{9} • From this statement, all we can know is that g is a positive multiple of 4 and r + g + w is a positive multiple of 9. • However, we don’t know the exact value of r, g, and w. Therefore, we cannot say whether r > g + w or not. Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D. Statement 2 : The total number of marbles in the bag is less than 15. • r + g + w < 15 o So, r + g + w can be 3 ,4, 5, ……14. • Now, let us consider two cases. o Case 1: If r = 2 , g = 3, and w = 4  In this case, r +g +w = 9 < 15 and r < g + w o Case 2: If r = 6, g = 3 and w = 2  In this case, r +g +w = 11< 15 and r > g + w • We are getting contradictory results. Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B. Step 3: Analyse Statements by combining. • From statement 1: g is a positive multiple of 4 and r + g+ w is a positive multiple of 9. • From statement 2: r + g+ w < 15 • On combining the two statements we get, o r + g+ w = 9 (only positive multiple of 9 < 15 ) o and g = 4 ( g cannot be 8 since in that case one of r and w has to zero)  Therefore, r + w = 9 – g = 5  Now, minimum value of w can be 1 • Maximum value of r = 4 < g + w = 5 • Thus, r < g + w Thus, the correct answer is Option C.

RS81 · Answer

Question is asking if
P(R )>P(G) or P(w)

So if you get the relation between the number of red marbles to green or white we'll be good.
 Statement 1: 
(easy trap)
Total number of marbles is 9x and green marbles =4x
So if you assume x = 1 then you have the answer => r = 4, g+w =5 and its given that g & w cannot be zero so max value one of them can take is 4. So you'll get the answer as sufficient.
But if you take x >2 any integer the answer is insufficient.
Lets take x = 4
r=16 & g + w = 20 so both can be 10 & 11 or one can be more than 16 i.e 17 and other can be 3

So this statement is insufficient.

Statement 2:  r + g + w <15
Alone this statement does not have much info so this is insufficient

Combine both 
r+g+w =9x & less than 15 then x can max be 1
Which give r = 4 g=w = 5.
So the  answer is C

GMATGuruNY · Answer

Question stem, rephrased:
Is  r > g+w?

Clearly, each statement on its own is insufficient to determine whether r > g+w.

Statements combined:
Since  P(g) = \frac{4}{9}  and  r+g+w < 15 , the total number of marbles must be A MULTIPLE OF 9 LESS THAN 15.
Thus:
There must be exactly 9 marbles, with the result that  g = \frac{4}{9}*9 = 4 .
Since r and w must be positive integers, the greatest possible value for  r=4 , with the result that  w=1 .
Since the greatest possible value for r is NOT greater than g+w, the answer to the rephrased question stem is NO.

C

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A bag contains r red, g green, and w white marbles, where r, g and w

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A bag contains r red, g green, and w white marbles, where r, g and w

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