Picking Numbers in the GMAT
How do you solve a problem when you don't have all the information you need? You might try guessing, or you could just flip a coin. But sometimes there is a more reliable approach— picking numbers.
Not all the GMAT Problem Solving tasks of are easy to crack and solve quickly. Simple questions can require very complicated answers and depend on relatively sophisticated methods. Therefore, as you work your way through the test, you will face certain constraints and trade-offs.
The good news is that you can streamline your approach by using alternative methods in solving the problems of the GMAT. Here, we will try to help you find your way through the arithmetic maze using the Picking Numbers technique, and we will give you valuable hands-on experience.
Before we get down to examples, it is worth spelling out few important remarks. If you need to pick numbers, pick some that will be easy to calculate. For example, when you need three integers, it is better to go with 2, 3, and 5 instead of picking 127, 374, and 984.
If the numbers you pick don't yield a single correct answer, try picking other numbers. Sometimes it works.
Make sure you pick the right numbers according to the criteria of the problem. Reread the statement and make sure you understand the entire task, and then check whether your picked numbers meet the problem's criteria.
Andrew spent 1/4 of his total grocery budget on dairy products and 1/3 less than that for vegetables. What fraction of his grocery budget did Andrew spend on dairy products and vegetables together?
Trying to solve this problem using traditional methods may get you nowhere, and slowly. This is the place for picking numbers. Start with the smallest common denominator of 1/4 and 1/3, and suppose that Andrew's total grocery budget is $12.
That means that he spent 1/4 * $12 on dairy products, or $3, and $2 on vegetables ($3– (1/3 * 3).
Adding these two figures gives you $5 dollars combined expenditure on dairy and vegetables together.
Now in the question you've being asked what fraction of his grocery budget Andrew spent on dairy products and vegetables together.
With $5 dollars spent on two categories of products of a $12 dollars total grocery budget, the answer is 5/12 of the total grocery budget going for dairy products and vegetables.
Therefore, (A) is correct.
The arithmetic mean of five consecutive integers is an even number. Which of the following must be true?
I. The largest of the integers is odd.
II. The sum of the integers is even.
III. The difference between the largest and smallest of the integers is an even number.
A) I only
B) II only
C) III only
D) I and II
E) II and III
The easiest way to solve this task is to pick five consecutive integers and use them to test each answer choice. Why it is possible to pick any consecutive integers and check what answer choice is correct? Because what is true for any odd or even number is going to be true true for all odd and even numbers.
So pick 2, 3, 4, 5, and 6 as your five consecutive integers where the arithmetic mean is an even number (in this case, 4). Now test each statement using this series of number and pick the right answer choice.
Statement I says that the largest of the integers is odd. In your array, the largest is 6, even, so you can eliminate answer choices (A) and (D) because both endorse Statement I.
Statement II says that the sum of the integers is even. In your array, 2 + 3 + 4 + 5 + 6 = 20 is indeed even. Therefore, answer choices (B) and (D) may be correct, so you can eliminate (C) because it excludes Statement II.
Statement III asserts that the difference between the largest and smallest of the integers is an even number. In your case, that turns out to be true: 6 – 2 = 4. Now you have two true statements, II and III, so choice (E) has to be correct.
Heads up! Even though picking numbers may sometimes be the best approach to tackling a GMAT problem, don't be misled into thinking it will always work for you.
- GMAT Math: Picking Numbers
- Sample Math Questions: Picking Numbers
- Backsolving in the GMAT
- Guessing in the GMAT