GMAT Pop Quiz
Try out the following questions to test your GMAT skills. If you've already answered the questions on a Pop Quiz flier, you can find the correct answers and explanations below.
1. Twenty-seven employees of the Silver City Shoe Store worked at least one day this weekend, which was a normal two-day weekend. How many of these employees worked only one of the days?
(1) Two more employees worked on Saturday than worked on Sunday
(2) Nineteen employees worked on Saturday, and seventeen employees worked on Sunday
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient
D. EITHER statement BY ITSELF is sufficient to answer the question
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question
The critical point to understand in preparing for Data Sufficiency questions is that the answer choices never change. You must take advantage of this by learning and practicing a systematic approach that will allow you to consistently and efficiently determine correct answers. In this case, the question in the stem asks how many employees worked only one of the days. But that's actually not the critical question. The real question is...do we have enough information to determine how many employees worked only one of the days?
To assess whether we have sufficient data to answer the question, we'll first want to consider what information we would need in order to answer the question. Data Sufficiency questions commonly present scenarios such as this one, in which we are given several different variables. In this case, we have 3 unknowns: the number of Saturday workers, Sunday workers, and Saturday/Sunday workers. Skilled test takers understand that with 3 variables, 3 distinct equations will yield sufficiency. The first sentence in the question stem can be translated into one equation. So we need two more distinct equations. We'll proceed to the answer choices with this as our guideline.
First, let's assess statement (1) by itself. This statement will yield one equation, one that will not give enough information to determine how many people worked both days. Statement (1) is insufficient. Now, we'll look at statement (2) by itself. Here we see two new equations. Combining these with the equations from the question stem yields 3 distinct equations with 3 variables. Statement (2) by itself yields sufficiency. We know that with the information in statement (2) we could solve the question in the stem, but we don't need to. Instead we'll click on the second answer choice and move on to the next question.
2. In semicircle O above, PQ is parallel to OS. What is the measure of angle ROS?
A. 34 degrees
B. 36 degrees
C. 54.5 degrees
D. 72 degrees
E. 73 degrees
On Test Day, when you begin a question with a diagram such as this, you'll want to re-draw the diagram on your noteboard. This way you can keep track of information on the diagram rather than in your head. 10 to 15 seconds spent re-drawing the diagram in the beginning will save you much more time in the end. In this case, it will be worthwhile to mark the angle in question, ROS, in some special way—perhaps with a question mark. We want to keep our focus on the end goal.
When you are given a question with multiple shapes, look for ways to use one shape to learn about the other. For example, since this is a semicircle, the lines OP, OQ, OR, and OS are all radii, and they're all equal. Now with this noted on our diagram, we see that the three triangles are isosceles triangles. Isosceles triangles have two equal sides, and also two equal angles. So we know that angle OPQ is 70 degrees, OQR is x degrees, and ORS is x + 1 degrees. We're writing this information down on our diagram as we discover it.
We know that all the angles in a triangle add up to 180 degrees. That leaves 40 degrees for angle POQ. Angle QOR is 180 - 2x degrees, and angle ROS is 180 - 2(x + 1) degrees. Now if we look at the straight line at the bottom of the semicircle, we have information about 3 of the 4 angles around point O that add up to 180 degrees. If we can find angle SOT, then we'll be able to solve for x.
What about the information in the question stem? We know that the GMAT rarely gives information that is not critical to finding the right answer. So, how can the fact that PQ is parallel to OS help us here? Whenever you're given two parallel lines intersected by another line (called a transversal), look for corresponding angles, which will be equal. In this case, PT is a transversal to PQ and OS. PQO and SOT are corresponding angles, and both equal 70 degrees.
Now we can write an equation and solve for x. The four angles POQ, QOR, ROS, and SOT add up to a straight line, or 180 degrees. So 40 + (180 - 2x) + (180 - 2(x + 1)) + 70 = 180. We isolate x and determine that x = 72. 72 is one of the answers but, remember, it's not what the question is asking for! One final check of the question reminds us that we're solving for angle ROS. Since ROS is a triangle and x + 1 = 73 degrees, angle ROS equals 180 - (73 + 73), or 34 degrees.
This was a challenging question because it involved so many steps. But each step we took to solve it was actually quite simple. The keys to succeeding on a question such as this are mastery of content and careful tracking of information.
3. A fair coin is tossed 6 times. What is the probability that exactly 2 heads will show?
Kaplan GMAT students review probability concepts that commonly appear on the GMAT, such as problems involving coin tosses. Since on any given coin toss the probability of heads or tails landing up is 1/2, the probability of any specified sequence of heads and tails in 6 tosses is (1/2)6 = 1/64.
How many such sequences exist in which two heads and four tails appear? The quickest way to find the answer is to use the combination formula, n!/[k!(n - k)!], where n is the number of items in the set, and k is the number of items in the sub-set. Here, 6!/[2!(6 - 2)!] = 15. A longer solution, which many students might apply, especially if they have not taken a Kaplan GMAT course, is to write the scenarios in which 2 heads appear. They are HHTTTT, HTHTTT, HTTHTT, HTTTHT, HTTTTH, THHTTT, THTHTT, THTTHT, THTTTH, TTHHTT, TTHTHT, TTHTTH, TTTHHT, TTTHTH, and TTTTHH.
Now multiply the number of possible scenarios, 15, by the probability of each, 1/64, to find the answer, 15/64.
Directions: The following question consists of a sentence that is either partly or entirely underlined. Below it are five versions of the underlined portion of the sentence. The first of these duplicates the original version. The four other versions revise the underlined portion of the sentence. Read the sentence and the five choices carefully, and select the best version.
4. In 1981, chemists thought they discovered new uses for Styrofoam pellets which would greatly reduce the environmental damage, but subsequent studies convinced them that these new uses did not significantly reduce the emissions of ozone destroying chlorofluorocarbons.
A. discovered new uses for Styrofoam pellets which would greatly reduce the environmental damage
B. discovered new uses for pellets, made of Styrofoam, which would greatly reduce environmental damage
C. had discovered new environmentally friendly uses for Styrofoam pellets
D. were going to reduce environmental damage greatly, had discovered new uses for Styrofoam pellets
E. were discovering new uses for Styrofoam pellets, and that this would greatly reduce environmental damage
The first thing we need to do in a Sentence Correction problem is read the entire sentence to determine whether the underlined portion contains an error. In this case, the tense of "discovered" is incorrect. It should be "had discovered." At this point we can eliminate any choice that doesn't make this correction—eliminate (A), (B), (D), and (E). This leaves us only Choice (C).
Before you choose an answer, however, be sure to read the choice back into the original sentence to see whether it fits the context. Kaplan-trained students know that often a choice that looks correct in isolation doesn't work when inserted back into the original sentence. In this case, though, if we read Choice (C) back into the sentence it creates a grammatically and stylistically acceptable sentence. So Choice (C) is the best answer.
Although we were able to eliminate 4 out of the 5 choices based on a single error, this isn't always the case in sentences that contain more than one error. Another error here was the clumsy "reduce the environmental damage." The use of "the" here is unclear—which environmental damage? Also, the use of "which" in the original sentence, and in choice (B), is confusing and ambiguous, and therefore wrong. It is not clear if "which" refers to "pellets" or "uses." A good rule of thumb: the simpler the sentence, the better.
5. Parents of high school students argue that poor attendance is the result of poor motivation. If students' attitudes improve, regular attendance will result. The administration, they believe, should concentrate less on making stricter attendance policies and more on increasing students' learning.
Which of the following, if true, would most effectively weaken the parents' argument?
A. Motivation to learn can be improved at home, during time spent with parents.
B. The degree of interest in learning that a student develops is a direct result of the amount of time he or she spends in the classroom.
C. Making attendance policies stricter will merely increase students' motivation to attend class, not their interest in learning.
D. Showing a student how to be motivated is insufficient; the student must also accept responsibility for his or her decisions.
E. Unmotivated students do not perform as well in school as do other students.
We're asked to weaken the parents' argument. Remember that "to weaken" doesn't mean "to destroy." All we need to do is find a choice that suggests the parents might not be on the right track. The parents' argument is as follows: in order to increase attendance, the school administration should focus on improving students' attitudes toward learning rather than simply imposing tough attendance policies.
Does Choice (A) suggest that the parents' plan won't work? No, because it doesn't even address the parents' argument. Eliminate.
What about Choice (B)? Well, if a student's interest depends on the amount of time she spends in class, then it makes sense to enforce policies designed to keep her there. This means that the parents might not be correct in letting up on truants, since, according to Choice (B), attendance is essential to a good attitude toward learning. This one looks good, but just to be sure we'll take a look at the rest as well.
Choice (C) states that making policies stricter won't improve students' attitudes. This actually strengthens the parents' argument and must be wrong. Kaplan-trained students know to expect such trap answers designed to appeal to students who did not read the question carefully.
Choice (D) states that improving a student's attitude wouldn't be enough; the student would also have to take responsibility for his or her actions. Even if an improved attitude isn't sufficient to produce the desired result by itself, its importance isn't negated. Thus, this choice does not weaken the parents' argument. Eliminate.
Choice (E) states that unmotivated students don't do as well in school. Does that weaken the parents' argument in any way? No, it doesn't even address the issue of absenteeism. Eliminate. Choice (B) remains the best answer.