Ratios & Proportions: Ratio Changes by Addition/Subtraction

The only real number presented by the question is [-2 marshmallows] - the change. The corresponding item must be the change in ratio.

However, before we find the change in ratio, the ratios need to be modified so that they are comparable. Right now, these two ratios do not have the same multiplier.

Here's the situation right now:

                           M        P

Original ratio         2   :    3

change                                 --->     -2 marshmallow

New ratio              4   :    9

What should you do next?

Incorrect.

Correct.

To further illustrate the problem, here's the final ratio box of this process. Note that the change in marshmallows gets its own row.

Drawing the box is recommended, but not essential for quickly solving this type of question. It is enough to remember the basic premise - the multiplier is the same for all members of a ratio. Focus on finding the multiplier, and the problem is half solved. 

To sum up our discussion of ratio change problems:

[[summary]]

Now that you have encountered problems with two or more ratios, we can discuss the concept of ratio changes.

You've already seen that expanding and reducing a ratio doesn't change it at all. a ratio of 1:2 expanded times 2 remains essentially the same ratio - 2:4.

However, Some GMAT problems introduce the concept of a change in ratio through addition and subtraction.

A candy box contains only marshmallows and pralines at a ratio of 2:3. A hungry hippo sneaks in and steals 2 marshmallows, leaving the marshmallows and pralines at a new ratio of 4:9. How many pralines are in the box?

Notice the essential ingredients provided by this type of question:

1) An original ratio - 2:3

2) A change (through addition or subtraction) -2 marshmallows

3) A new ratio - 4:9

In order to find the real number of Pralines, we have to find the multiplier. Usually, we'd put the data in a ratio box and find the multiplier by dividing the real numbers presented in the question with the corresponding ratio in the same line. However, the presence of two different ratios makes this difficult. Organize the ratios in a diagram:

                           M        P

Original ratio         2   :    3

change                                 --->     -2 marshmallow

New ratio              4   :    9

Recall the lesson on ratio comparison: To combine different ratios you must equate the number representing the member common to both ratios.

Since the real number of Marshmallows changes during the question, it is no longer a common member to both ratios. The real number of Pralines is unchanged in both ratios, so this is the common member - expand the original ratio by 3 to get the same number of ratio units of Pralines.

After expanding the original ratio times 3, this is the new situation:

                           M        P

Original ratio  2×3=6  : 3×3=9

change                 -2                    -->       -2 marshmallow

New ratio              4   :    9

Since a drop of 2 in the marshmallow ratio (from 6 to 4) corresponds to a drop of 2 in real (2 marshmallows stolen by the hungry Hippo), the multiplier is simply ×1. 

The question asks for the number of Pralines, which is simply 9×1 = 9.

Good question.

Remember that the multiplier you have found is the same for all ratios in the box. However, the multiplier of ×1 is only relevant to the ratios after the expansion. Thus, If the question asks for the original number of Marshmallows, use the original ratio in its expanded form: not 2:3, but 6:9.

Therefore, the original number of marshmallows is 6×1=6.