Standardized tests are based on the premise that you can categorize students based on test scores. In order to do this, the less “capable” students must get questions wrong and the more “capable” students must get questions right. To make sure some students get low scores, the tests are designed with questions specifically made to trick students with “less” ability (however the GMAT defines ability).
Value or Yes/No Questions
There are two basic types of questions used in data sufficiency problems.
Can you generate a value?
These questions comprise two-thirds of data sufficiency questions.
How much was a certain card worth in January 1991?
What is a + b?
Can you “prove” or “disprove” the statement?
“Always yes” or “Always no” are sufficient.
“Sometimes” is not sufficient information.
Is a + b a multiple of 5?
Is x < 0?
Note: “Disprove” and “false” are sufficient.
If you can prove a + b is NOT a multiple of 5, then it is sufficient.
If you can prove that x > 0, then it is sufficient.
There are several common tricks. The writers try to mislead you into common mistakes or time wasters.
Again, do not think in terms of “What is the exact value?” or “Is this true or false?”
Instead, focus on one issue: “Is there enough information to answer the question?”
Could I calculate the value? BUT don’t do the calculation.
Do I know this is correct? Also look to disprove or prove it’s false.
Example Don’t Calculate
How much was a certain Babe Ruth baseball card worth in January 1991?
(1) In January 1997 the card was worth $100,000.
(2) Over the ten years 1987-1997, the card increased in value by 10% each 12 months.
Statement (1) is insufficient. You don’t know the rate of change. You immediately know the answer must be B, C or E.
Statement (2) is insufficient. Without a value between 1987 and 1997, you can’t calculate the value.
Using statements (1) and (2) together, you could calculate the value in 1991. Since you need both statements to find the value, the answer is option (C).
The trick: Don’t do the calculation. For most “value” questions, you could calculate the value but calculations are a waste of time. The problem asks if there is enough information to answer the question, not for the actual answer.
Example Keep Separate
How many adults ride bicycles in city A if all adults in city A either ride bicycles or drive cars?
(1) 85% of the 10,000 adults in city A drive cars.
(2) 8,500 adults in city A drive cars.
Statement (1) is sufficient. Taking a percent of a total population allows you to calculate the drivers then the bike riders. (Don’t do the calculation.) You immediately know the answer is A or D.
Statement (2) is insufficient. Without the total population or other information, you can’t calculate the number of bike riders.
Since statement (1) alone is sufficient, the correct answer is option (A).
The trick: Keep separate the information from statement (1) and statement (2). Either the percentage or total population from statement (1) can make statement (2) sufficient.
Always read each statement individually.
When you read statement (2), forget what you read in statement (1) so you can evaluate statement (2) alone.
The only time to combine the statements is when each of them is insufficient alone.
Example Don’t Assume
Joe drove to the airport and back home again along the same roads without stopping. How long did it take him to get home from the airport?
(1) The car traveled at an average speed of 65 miles per hour.
(2) The entire trip took 3 hours to complete.
Solving will use the formula: distance = rate × time.
Statement (1) is insufficient. You don’t know distance or time.
Statement (2) seems to be sufficient. Over the same roads, the distance both going and coming will be the same. So it seems the answer is 1.5 hours.
Using statement (1) and statement (2) together, the average rate of speed reinforces the idea of the same speed going and returning.
But the average of 60 mph going and 70 mph returning also is 65 mph. At these speeds, the returning would not take 1.5 hours.
So even with both statements, there is not enough information. The answer is option (E).
The trick: Don’t assume. With the math being so simple, there must be a trick. Look again at the statements and try to see your assumptions.
This example also shows the importance of keeping the statements separate.
Example The Answer is No.
Is the two-digit integer tn, with t as the tens digit and n as the ones digit, a multiple of 7?
(1) t + n = 13
(2) t is divisible by 3.
In both calculation and data sufficiency questions, sometimes the simplest and quickest method is to plug in and try some numbers.
For Statement (1):
What digits add to 13?
9 + 4, 8 + 5, 7 + 6
What integers are created with those digits?
94 and 49, 85 and 58, 76 and 67
Only 49 is divisible by 7, so the answer is “sometimes.” Statement (1) is insufficient.
For Statement (2), it is easy to come up with numbers with a tens digit divisible by 3 that are and are not divisible by 7.
35 and 36, 63 and 64, 90 and 91
The answer is “sometimes.” Statement (2) is insufficient.
Combine statements (1) and (2). Looking at the integers from statement (1), only 94 and 67 have a tens digit that is divisible by 3 and neither are divisible by 7, so the answer is option (C).
The trick: The answer is “no.” The question is asking, “Is it true?” and you have enough information to say “no.” Remember, data sufficiency problems are only asking “Is there enough information to answer the question?”
Handling questions that aren’t algebra
As a rule, when you encounter a highly intimidating question such as the one above, you should Plug In possible answers. This question defies an algebraic solution, so it must be solved through methods such as Plug In or Backsolving.
Example You Only Need One.
What is the average (arithmetic mean) of 3x and 12z?
(1) x + 4z = 20
(2) x + z = 8
The question asks for the average of 3x and 12z.
3x + 12z/2=3(x + 4z)/2
Statement (1) gives the value of x + 4z. You could calculate the mean directly without using the second statement. Statement (1) is sufficient.
Statement (2) is insufficient.
Combining statements (1) and (2) gives 2 equations and 2 variables. Together the system can be solved to find the mean.
But since statement (1) alone is sufficient, the answer is option (A), not option (C).
Students commonly write us and say, “Sorry 800score, you are WRONG, the answer is (C).”
True, combining (1) and (2) can solve the question. But if (1) and/or (2) can do it alone, then the answer isn’t (C), it is (A) or (B).
In this problem, (1) can do it alone, so it doesn’t matter that (1) and (2) together can do it. The answer is (A).
The trick: You may only need one. Keep the statements separate. Always read each statement individually. In this question, don’t see the equations in statements (1) and (2) and jump into “two equations and two variables.”
Hint: Factoring or simplifying can be a good quick check in many data sufficiency problems.
Common Algebra Tricks
There are five common algebra tricks in data sufficiency problems. All the sections in this chapter have examples of these algebra tricks. The chapter about algebra in this Guide also reviews these topics.
- repeated equations
The 2 statements have the same equation written differently.
- number of equations
Don’t assume that as long as you have 2 equations, you have enough information to solve for 2 variables. Though 2 equations and 2 variables is the usual, 2 equations may not be enough to solve for 2 variables. For example, they may be the same equation. If solving for an expression not a variable, 2 equations may be enough if the 2 equations have 3 variables.
- denominator of zero
Be careful when working on fractions with variables in the denominator.
not always integers
The directions for data sufficiency problems say the numbers will be real numbers, not integers. When using the method of plugging in, you may need to test fractions.
Factoring and simplifying can show matches between expressions and equations.
Example Same Equation
Is it possible to find the value of x using these equations?
(1) 4x + 12y = 24
(2) x/3 + y = 2
The quick assumption is that 2 equations can solve for both x and y. The reality is that, if you look closely, both statements say the same thing.
Equation (1) is simply 12 times equation (2). You don’t have two equations, you have only one. This means that the two statements aren’t sufficient.
The answer is option (E).
Example How Many Equations
Is it possible to find the value of z using these equations?
(1) 2x + 4y = 12
(2) z/x + 2y= 2
The quick assumption is that two equations can’t solve for three variables. But here you are solving for one variable, and two equations can allow you to do that.
The trick is to factor and simplify the equations.
2x + 4y = 12 → x + 2y = 6
z/x + 2y = 2 → z = 2(x + 2y)
Substituting equation (1) into equation (2) gives the value for z.
Combining the statements is enough to find the value z (which is 12, but you don’t even need to calculate that).
The answer is option (C).