“The GMAT Project” intends to ensure its readers are well prepared for all aspects of the GMAT. If you follow our weekly postings of example problems and solutions, we expect you to be more prepared than ever to not only succeed on the GMAT, but to get into your graduate school of choice.
This week we will turn our attention to a GMAT Data Sufficiency question. Because the instructions regarding Data Sufficiency questions are highly specific we have included them.
GMAT Data Sufficiency Instructions: Each of the data sufficiency questions below consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statement plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise) you are to fill in oval:
- if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
- if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
- if BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
- if EACH statement ALONE is sufficient to answer the question asked;
- if statements (1) and (2) together are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Three consecutive integers represent the ages, in years, of three children. What is the age of the youngest child?
(1) In 6 years the average (arithmetic mean) age of the three children will be twice their average age now.
(2) In 5 years the oldest child will be 12 years old.
Word problems are very common in data sufficiency questions. You will want to represent the information mathematically and create formulas that you can work with. In this problem, the ages of the three children are three consecutive integers. Consecutive means that they follow each other in order, one unit apart. For example, the numbers 3, 4 and 5 are consecutive integers.
Let’s say that the youngest child has an age of x. It is helpful to use x for the youngest child because the question is asking for the youngest child’s age. Now, we want to represent the middle child. We could use another variable like y, but there’s a better option. Since the ages are consecutive, the middle child is one year older. Therefore, the age of the middle child could be represented as x + 1. The oldest is one year older than the middle child so the oldest child’s age will be represented as x + 2. The series of ages of these three children then are x, x + 1, and x + 2.
Notice that we have now represented three unknowns using only one variable, x. It is helpful to reduce the number of variables. The fewer the variables, the more likely it is that a solution can be found.
1) Break down each part of this sentence to create an equation. We’ll start with “In 6 years the average (arithmetic mean) of the three children.” Remember that the mean is calculated by adding all terms and dividing by the number of terms.
Average = Sum/Number of terms
The average of the three ages can be represented like this.
(x + x + 1 + x + 2)/3
However, the statement says we are looking at the ages in 6 years. This means that each age is 6 higher. The youngest would be x + 6, the next is x + 7, and the oldest is x + 8.
(x + 6 + x + 7 + x + 8)/3
The next part says “will be.” In other words, they are equivalent, so here is where our equal sign goes.
(x + 6 + x + 7 + x + 8)/3 =
The last part says “twice their average age now.” Take the average of the three ages and multiply it by 2.
(x + 6 + x + 7 + x + 8)/3 = 2(x + x + 1 + x + 2)/3
We now have a complete formula with one unknown. Generally speaking, an equation with one unknown can be solved, so you could decide to stop right here and say that the statement is sufficient. However, we’ll go ahead and solve this to make sure. Start by combining the terms in the sets of parentheses.
(3x + 21)/3 = 2(3x + 3)/3
On the right side of the equation, multiply the 2 and 3x +3 visit site.
(3x + 21)/3 = (6x + 6)/3
Now, we can simplify. Divide the terms in parentheses by 3.
x + 7 = 2x + 2
Subtract 2 on both sides.
x + 5 = 2x
Subtract x on both sides.
5 = x
The youngest child is 5, making the ages 5, 6, and 7. If you have extra time and want to go one more step, you can check that this answer works. The ages are 5, 6, and 7, so the average is 6. In 6 years, the ages will be 11, 12, and 13. The average would then be 12. This is twice as much. The first statement is sufficient.
2) For this statement, we won’t need to create formulas. In 5 years the oldest child will be 12, so the ages will be 10, 11, and 12. This means that the current ages are 5, 6 and 7. Again, we have a definite answer for the youngest child’s age. The second statement is sufficient.
Both statements are sufficient on their own, and the correct answer is (D).
By Robert Lynch