## Arithmetic Concepts in GMAT Quant

# How to add multiples on the GMAT

Sometimes questions involving properties of integers and calling on you to add multiples can seem complex. However, if you apply the right rule, you can solve such questions quickly.

Consider the following question from GMAT Tutor:

*Zeta took several pictures with her new digital camera. Each picture was saved as a file, the size of which depended on the picture's resolution. A low-resolution image requires a 0.5-megabyte file, and a high-resolution image requires a 0.9-megabyte file. If the total size of all the files was 8.1 megabytes, which of the following is a possible number of pictures Zeta took with her camera?*

*A. 11B. 12C.13D. 14E. 15*

## How to add multiples quickly

- Rewrite the question in the form of an equation:
- 0.5x + 0.9y = 8.1
- Multiply by 10 to remove the decimal points
- 5x + 9y = 81

With the equation written like this, we are solving for **x + y**, or the total number of pictures.

Apply the appropriate rule: **A multiple of x + a multiple of x = a multiple of x.**

81 is a multiple of 9. 9y is also a multiple of 9. Therefore, 5x must also be a multiple of 9.

Since 5x must also be a multiple of 9, x must be a multiple of 9. The only possible value for x can be 9, since 18 or any larger multiple is larger than any of the answer choices.

So, if x = 9, let’s solve for y:

- 5(9) + 9y = 81
- 45 + 9y = 81
- 9y = 36
- y = 4
- With x = 9 and y = 4, then x + y = 13,
**which is answer choice C**.

In summary, applying the rule that **when you add two multiples of x, the result will be a multiple of x** helped us to solve this question quickly. It’s a good rule to remember!