Jars A and B each contain a mix of red and blue pebbles. The ratio of

Solution:

We can let x and 4x be the number of red and blue pebbles in jar A, respectively. Since x = 120, then 4x = 480. That is, jar A has 120 red pebbles and 480 blue marbles. Now, let’s let 3y and 2y be the number of red and blue pebbles in jar B, respectively. We can create the equation:

(120 + 3y) / (480 + 2y) = 1/2

480 + 2y = 240 + 6y

240 = 4y

60 = y

Therefore, there are 2(60) = 120 blue pebbles in jar B. Since there are 480 blue pebbles in jar A, there are a total of 120 + 480 = 600 blue pebbles in the two jars combined.

Answer: D

Hi All,

We're told that Jars A and B each contain a mix of red and blue pebbles. The ratio of red and blue pebbles in jar A is 1:4 and the ratio of red and blue pebbles in jar B is 3:2. Furthermore, when the contents of the two jars are mixed, the ratio of red and blue pebbles turns out to be 1:2 and jar A has 120 red pebbles in it. We're asked for the TOTAL number of blue pebbles in the two jars combined. This question can be solved in a number of different ways, including by TESTing THE ANSWERS and doing a little Arithmetic.

To start, we know that Jar A has 120 red pebbles in it. Since the ratio in Jar A is red:blue = 1:4, then means that there are 4(120) = 480 blue pebbles in Jar A. By extension, the TOTAL number of blue pebbles must be GREATER than 480...so we can eliminate Answers A, B and C. Let's TEST Answer D....

Answer D: 600 blue pebbles.

Since there are 480 blue pebbles in Jar A, there would be 600 - 480 = 120 blue marbles in Jar B...

The ratio in Jar B is red:blue = 3:2.... so with 120 blue pebbles, there would be (3/2)(120) = 180 red pebbles in Jar B.

Total red pebbles = 120 + 180 = 300 red pebbles
Total blue pebbles = 480 + 120 = 600 blue pebbles
Total ratio red:blue = 300:600 = 1:2
This is an exact match for what we were told, so this MUST be the answer!

Final Answer:

GMAT assassins aren't born, they're made,
Rich

In this, we use the concept of compound mixtures.

By the theory of compound mixtures, when V1 Volume/Quantity of a mixture of X and Y which is in the ratio a : b is mixed with V2 Volume/Quantity of another mixture X and Y (i.e the constituents of the 2 mixtures are the same in the ratio p : q, then the final ratio of the constituents is given by

\(\frac{X}{Y}\) = \(\frac{X \space from \space V_1 + X \space from \space V_2 }{Y \space from \space V_1 + Y \space from \space V_2} = \frac{(\frac{a}{a + b})*V_1 + (\frac{p}{p + q})*V_2}{(\frac{b}{a + b})*V_1 + (\frac{q}{p + q})*V_2}\)


Jar A has 120 red Pebbles i.e 1/5 * V1 = 120. Therefore V1 = 600. Number of blue pebbles in Jar 2 = 600 - 120 = 480


\(\frac{1}{2} = \frac{120 + (\frac{3}{5})*V_2}{480 + (\frac{2}{5})*V_2}\)

\(\frac{1}{2} = \frac{120 + 0.6*V_2}{480 + 0.4*V_2}\)

480 + 0.4V2 = 2 (120 + 0.6V2)

1.2V2 - 0.4V2 = 480 - 240

0.8V2 = 240

V2 = 300

Number of blue pebbles in Jar 2 = 2/5 * 300 = 120


Total Number of blue pebbles = 480 + 120 = 600