GMAT MASTER SET
What words in critical reasoning passages indicate it's a conclusion?
Future words: plan, proposal, prediction, hypothesis, will, should Opinion words: claim, argument Concluding words: therefore, thus, hence, so
What is the purpose type of reading-based critical reasoning question?
Has one or two bold-face statements
When is it acceptable to average the given speeds in a rate problem?
NEVER. NEVER average the speeds. Compute it out if you have to, but never average the speeds.
Can prime numbers be negative?
No
What are the three reading-based question types?
PIE Purpose Inference Explain
What is the trick to solving the following problem: What is the difference in the sum of all of the even and odd integers from 1 to 100 inclusive?
We know that there are 100 terms here since 100 + 1 - 1 = 100. If there are 100 terms, than 50 are even and 50 are odd. Thus, we can solve for the sum of 1 to 10 and multiply by 10. 1+3+5+7+9 = 25*10 = 250 2+4+6+8 = 30 * 10 = 300 300- 250 = 50
What is the trigger in the following problem? Quantity A: x²+2x/x+2 Quantity B: x
While it is easy to see x^2 + 2x and say this simplifies to x, which is same for quantity A and B, it does not say that -2 is not a viable option, where A would be undefined and B would be -2. Thus, unless otherwise stated we have think about extraneous solutions
What is the strengthen/weaken or flaw type of assumption-based critical reasoning question?
Provides additional evidence that, if true, asked you which helps strengthen/weaken/evaluate the argument NOTE: This will be slightly out of scope!!
What are the four assumption-based question types?
SAFE Strengthen/Weaken Assumption Flaw Evaluate
What are the assumptions when the argument structure is a plan, proposal, or prediction?
The assumption is that all the unstated requirements will be met "Everything will go right, and nothing will go wrong"
What is the assumptions for when the argument structure is comprised of a study/poll/survey/experiment/anecdote?
The assumption is that the sample is representative of the population
What is the assumption when words are being used interchangeably (ie a new word shows up in the conclusion)?
The assumption is that the words are all equivalent
What is the assumption when the argument structure contains a percent (such as safety/average/rates/growth)?
The assumption is the percent is equal to an actual number
Are √16*49 and √16 * √49 equal?
Yes
Is √3*√2 equal to √6?
Yes
What do you do when given multiple unit sizes?
Convert every measure to the smallest unit size
What is the trigger on the following problem: Quantity A: x^0.75^4 Quantity B: x^3
The trigger here is that the superscript makes this different. READ THE QUESTION CAREFULLY.
What is the first step when approaching average problems?
Write out the formula for an average and fill in what you know
How do you solve the following, and where did I go wrong? If 150 were increased by 60% and then decreased by y percent, the result would be 192. What is the value of y?
First, we can increase 150 by 60% by multiplying 1.6 * 150, which is 240 (150 * 160/100 = 150/100 * 160 = 240). We then know that 240 multiplied by y/100 will equal 192. Thus, y/100 * 240 = 192. When solving for y, we find that y is 80. If y is 80, then 240 would have been decreased by 20% (80/100 = 20% decrease). I went wrong by answering 80% as the value for which 240 was decreased. While I correctly found that 80/100 * 240 totals to 192, this does not mean that 242 decreased by 80%, rather it decreased by 20%.
What is -11² and (-11)² ?
-11² equals -121 (-11)² = 121 In the first expression (-11²), the negative applies to the full expression of 11². Conversely, in the second expression, the value being squared is -11. THESE ARE NOT THE SAME, AND HAVE OPPOSITE ANSWERS.
What are the steps to approaching critical reasoning questions?
1) Analyze the question stem (assumption based [SAFE] or reading based [PIE]) 2) Analyze the passage 3) Predict the correct answer 4) Evaluate the answer choices
What are the three assumptions when the argument structure is causality (A -> B, one thing leads to another)?
1) There is no other cause (x != B) 2) The relationship is not reversed ( B != A) 3) The contrapositive is true (not B -> not A)
What is the explain type of reading-based critical reasoning question?
Asks for additional information that helps explain something
What is the inference type of reading-based critical reasoning question?
Asks what must be true based on the given information
What is the flaw type of assumption-based critical reasoning question?
Asks you to identify what is wrong with the passage's assumption
How do you solve the following, and where do I have a tendency to go wrong with this type of question? In sequence Q, the first number is 3, and each subsequent number in the sequence is determined by doubling the previous number and then adding 2. In the first 10 terms, how many times does the digit 8 appear in the units digit?
From the question, we can write the equation of this sequence to be Sn = [ S(n-1) * 2 ] + 2, where S1 = 3. When applying this, we can calculate the following: S₁ = 3 [GIVEN] S₂ = 8 S₃ = 18 S₄ = 38 S₅ = 78 ... After term four of five, STOP and notice the pattern that ever term will have the number 8 in the units digit. Thus, the answer is 9 (10 terms minus the first one). While calculating all ten terms in the sequence is doable, it is highly unnecessary. I typically would not stop and notice the pattern. I MUST look for patterns on sequence and similar questions. Calculating all ten terms is a massive waste of time here and is unacceptable. Patterns are the backbone of the GMAT.
How do you solve the following, and where did I go wrong initially? In a certain box of cookies, 3/4 of all the cookies have nuts and 1/3 of all the cookies have both nuts and fruit. What fraction of all the cookies in the box have nuts but no fruit?
Here, I got tripped by the words "all cookies". While language is important, it is important to think of the whole here. 1/3 of all the cookies that contain nuts and fruit is the same as saying 1/3 of the cookies that contain nuts. If it had said that, then I would known what to do. Thus, it is important to visualize and break down the problem outside of the specific wording.
How do you solve the following, and where did I go wrong initially? What is a fraction to represent 7.583 where the 3 is repeating?
Here, I wrongly stipulated that 7.583 is equal to 7.583(repeating). Thus, 7,583/1000 does not include a repeating three. Suppose I had realized I could not simply divide 1,000 by 7,538, this question also tests my ability to break challenging questions into smaller pieces. Especially for questions seemingly ridiculous to compute without a calculator, I need to figure out how to break the problem down into pieces to solve.
How do you solve the following and where did I go wrong initially? What is the value of the following expression? √3/2 - √2/3
I incorrectly believed that the if two elements of an expression are square rooted, than the expression can be rewritten as the square root of the entire expression. Instead, I needed to apply the square root to the numerators and denominators to find a common factor.
How do you solve the following and where did I go wrong initially? If x is 150% greater than 200, x is what percent greater than 50% of 500?
I went wrong by concluding that 150% greater of 200 meant 1.5 * 200. This is incorrect because the term "greater than" means 150% of 200 AND 200. 300 (which is 1.5 * 200) is 150% of 200, NOT 150% greater than 200. This is was key concept tested by this question.
How do you solve the following, and where did I go wrong initially? 1/4 of all the juniors and 2/3 of all the seniors at a certain school are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the junior and senior students are not going on the trip?
I went wrong by not realizing that plugging in numbers is a way to find the answer. While there might be a way to solve this using variables, when it was not working, I did not realize that I could revert to using smart numbers instead. This was my most critical mistake here.
What is true about the units digit in multiplication and exponentiation (when an integer is raised to a power)?
In both multiplication and exponentiation (when an integer is raised to a power), the units digit is determined solely by the product of the units digit. Example: The units digit in 73⁴ is equal to the units digit in 3⁴, which is 1.
What is the assumption type of assumption-based critical reasoning question?
Looking for the unstated bridge between the premise and the conclusion
What is the premise comprised of in critical reasoning questions?
Premise = Evidence Data (ie. experiment, survey, poll, census, report), facts, the past, can be an opinion
How do you solve the following, and where do I have a tendency to go wrong with this type of question? S is a sequence such that Sₙ = (-1)ⁿ for each integer n >= 1. What is the sum of the first 20 terms in S?
The correct way to solve this problem is to look for a pattern rather than solve out 20 iterations of the sequence. To do this, calculate the first five numbers in the sequence: S₁ = (-1)¹ —> (-1) —> -1 S₂ = (-1)² —> (-1 * -1) —> 1 S₃ = (-1)³ —> (-1 * -1 * -1) —> -1 S₄ = (-1)⁴ —> (-1 * -1 * -1 * -1) —> 1 S₅ = (-1)⁵ —> (-1 * -1 * -1 * -1 * -1) —> -1 The pattern clearly demonstrates the answer alternates between -1 and 1, with even numbers outputting to positive 1 and odd numbers outputting to -1 (which follows number properties). Thus, the sum of first 20 terms, which includes 10 even and 10 odd numbers will be 0. I typically either solve this using brute force by calculating all combinations when it is possible, or giving up when it is not possible. The important takeaway from this problem is to always look for patterns as they are the backbone of the GMAT.
What is the key to solving the following problem: If set S consists of all positive integers that > are multiples of both 2 and 7, how many numbers in set S are between 140 and 240 inclusive?
The first step here is to find the LCM of 2 and 7, which is 14. Thus, we are looking for multiples of 14. Since 14 only goes into 100 neatly 7 times, we can just list out all of the permutations here. The trigger here for me was not writing out the permutations when they can be listed out with such little effort here to guarantee an answer.
What is the trigger and process for the following problem? Joe drove from Springfield to Shelbyville at x miles per hour. He then drove from Shelbyville to Bakersfield at (1.5)x miles per hour. If the distance between Springfield and Shelbyville is twice the distance between Shelbyville and Bakersfield, what was Joe's average speed for the entire trip?
The key here to write in words what we would need: Total Distance / Total Time Total Distance = Pt. 1 Distance + Pt. 2 Distance Total Time = Pt. 1 Time + Pt. 2 Time We know that the distance from Pt. 1 is twice that of Pt. 2, so if we call it y, it would be 2y + y Using that, we know that time is distance / rate. Thus, Pt. 1 is 2y/x and Pt. 2 time is y/1.5x We can combine and divide (2y +y)/(2y/x + y/1.5x), which simplifies to 9/8x. The trigger here is writing out what we need in words and then creating it using the variables, you cant just jump in.
What is the formula to calculate the median of an evenly-spaced set of numbers?
The median of a set of evenly-spaced numbers is equal to the sum of the first term and the last term divided by two Example: The median of set of numbers from 4 to 47 inclusive is (47+4)/2 or 25.5
What is the trigger on the following problem? The ratio of 16 to g is equal to the ratio of g to 49. What is g?
The set up here is very easy, but the trigger is understanding that g is 28 or -28. You ultimately find that g equals the square root of 16*49 which equals 28. HOWEVER,> this is either 28 or -28, but without more information, WE DON'T KNOW. When you square root something, ALWAYS CONSIDER +/-
How do you find the sum of a set of evenly-spaced numbers?
The sum of a set of evenly-spaced numbers, s s = median * # of terms Example: What is the sum of all integers from 1-10 inclusive? --> median = (first+last)/2 = (1 + 10)/2 = 5.5 # of terms = 10+1-1 = 10 Sum: 5.5 * 10 = 55
What is the trigger in the setup to the following problem: Originally, 70% of the clients at Bob's Dating Bistro were male. After z of the female clients left, the service still had 74 clients. Which of the following could be the value of z? I.6 Il. 12 Ill. 16
The trigger here is that the proportion of males is 7c and the proportion of females is 3c. There is a c because it can be ANY multiple of c (for example, 7 & 3, 70 & 30, 700 & 300). This means that the number of males and females must always be a multiple of 10 (7c + 3c = 10c). To find the answer, we add the values of z to the new total, and determine which totals result in multiples of 10.
What is the trigger on the following problem? On a number line, the distance from A to B is 4 and the distance from B to C is 5. What is the distance between A to C?
The trigger here is that we do not know the order of A, B, and C. While we resort to putting them into alphabetical order, this is NOT necessarily the case. Do not assume, and think through the options.
What is an assumption in critical reasoning questions?
The unstated bridge between the premise and conclusion Can you this for assumption-based questions: Denial/Negation Test: If you deny the central assumption, the premise no longer leads to the conclusion (so the argument falls apart)
What does producing complete units with each individual worker entail?
This means that each worker's individually produced must be rounded down to the nearest integer, and then multiplied by the number of workers. If each worker works individually, you CANNOT combine their parts of incomplete units.
How do you construct a formula/functions based on the following problem? What is the trigger here? Randi sells forklifts at a dealership where she makes a base salary of $2,000 per month, plus a commission equal to 5% of the selling price of the first 10 forklifts she sells that month, and 10% of the value of the selling price of any forklifts after that. If all forklifts have the same sale price, s, which of the choices below represents Randi's monthly pay, P, as a function of number of forklifts sold, f, in months in which she sells more than 10 forklifts? (Assume Randi's pay is made up entirely of base salary and commission, and no deductions are taken from this pay.)
To construct the equation here, the key is remember the words in the question "in which she sells more than 10 forklifts" This implies that Randi will definitely get the first commission, so there does not need to be two variables for the number of forklifts and the selling price, ONLY the selling price multiplied by 10 As for the second commission, this will be the selling price of each additional forklift over 10, so the forklifts should be substracted by 10. P = 2,000 + 0.05(10)(s) + 0.10(s)(f-10) P = 2,000 + 0.5s +0.1s(f-10) The trigger here is reading the question carefully and recognizing the shortcut available under the assumption that Randi sells more than 10 forklifts
What is the trigger in solving the following problem? In a certain children's class, there is a 2 to 3 ratio of boys to girls. The ratio of students y from the north side of town to students from the south side of town is 4 to 3, and no student is from anywhere else. What is the smallest possible number of students in the class?
To solve this problem, you need to recognize that the answer is a multiple of 5 and 7, the smallest multiple of which is 35. The trigger here that the lack of overlap means we have to consider the multiples here. You can even have done this by trying > to plug in numbers. This is very similar to the party cranberry/ fancy lemonade question which is also concerned with multiples for non-relational ratios.
What is the trigger in solving the following problem: If a dak is a unit of length and 14 daks =1 jin, how many squares with a side length of 2 daks can fit in a square with a side length of 2 jins?
To solve this, you need to convert every measure into the smallest unit size. In this case, since 1 jin is 14 days, daks are the smallest unit size. After converting, you can rewrite the following question as how many squares with a side length of 2 can fit into a square with a side length of 28. After drawing it, you see that you are dividing (28*28)/(2*2), which is really just 14*14 or 196. The triggers here are the following: 1) Converting all measures in to the smallest unit size 2) Drawing a picture is exceptionally important
What is the following problem being tested here? What is the trigger? Lou has three daughters: Wen, Mildred, and Ayla. Three years ago, when Lou was twice as old as Tyler, he was 30 years older than Mildred. Now, he is 47 years older than Wen. In 4 years, Wen will be half as old as Tyler. What is the sum of the current ages of Lou an his three daughters.
To solve this, you need to set up four equations in order to solve the four-variable system of equations. The key here is the shifting of equations/ variables to reflect the past or future time. The four variables here (say, L, W, M, and T) y all represent the ages of each of those people TODAY. Thus, when creating equations of ages in the past or future, this variables need to be shifted. Testing whether or not you properly shift these variables was my trigger here.
If the ratio of A to B is 3:5, what is an equation relating A and B
We know that A/B = 3/5, thus 3A = 5B. We CANNOT say that 3A = 5B, this is entirely false. Think of the table or cross multiplication to prove it.
How do you solve the following and where did I go wrong initially? If f(2a) = 2f(a) and f(6) = 11, what is the value of f(24)?
We know that if f(6) = 11 and 2f(a) = f(2a), then 2 * f(6) = f(12) = 11* 2 = 22. Repeating this, we know that if f(12) = 22 and 2f(a) = f(2a), then 2 * f(12) = f(24) = 22 * 2 = 44. Thus, f(12) = 44. I did not break the problem down enough here. I needed to realize that if I multiply f(a) by 2, then I can also say that the product equals f(2a) since the problem tells me that is the case. This is only element that makes this problem challenging. Next time, I need to think more high level.
How do you solve the following, and where did I go wrong? The number of years it would take for the value of an investment to double at 26% interest compounded annually, is approximately how many years?
While we can apply the growth formula here where f(n) = 1 * (1.26)ⁿ and f(n) = 2, thus 2 = 1.26ⁿ, However, this does not help us because we cannot compute log(2) / log(1.26) without a calculator. Rather, since it will not take long to double 1 to 2 at 26%, it is easier to multiply out. Year 0: 1 Year 1: 1 * 1.26 = 1.26 Year 2: 1.26 * 1.26 = 1.588 Year 3: 1.588 * 1.26 = 2.000 Thus, we can clearly see that it takes approximately 2 years. While it is great that I correctly applied the growth rate formula, I did not know where to go when I realized that I could not solve for x given the presence of logarithmic expressions. My most critical mistake was not breaking down the problem to realize that it probably wouldn't take more than 4-5 years to double, so multiplying is very possible. Regardless, multiplying it out was my only remaining option. In the future, I need to look at the problem from a high level and think of the only alternate approach to solving with the growth rate formula.
What are the triggers for the following problem? Party Cranberry is 3 parts cranberry juice and 1 part seltzer. Fancy Lemonade is 1 part lemon juice and 2 parts seltzer. An amount of Party Cranberry is mixed with an equal amount of Fancy Lemonade. Quantity A: The fraction of the resulting mix that is cranberry juice Quantity B: The fraction of the resulting mix that is seltzer
You CANNOT simply add the parts because the parts are not necessarily the same. Since the party cranberry sum is a multiple of 4 (3x + 1x = 4x), and fancy lemonade is a multiple of 3 (1x + 2x = 3x), you need to find the lowest common multiple to compare parts. The LCM of 3 and 4 is 12. Which means you can add the parts together and compare. This is a multiples trigger question, since the two ratios are NOT to be treated as the same. Thus, these should be combined by finding the lowest common multiple among them. This problem is very similar to the ratio of boys/girls and north side/south side problem, which is also concerned with multiples for non-relational ratios.
If you know the value of something, and want to find what 70% off that value is, how do you set that up in an expression?
You can set this up with the following: I = initial value D = discounted value 70% off = 30% of the initial value 0.3 * D = I
What is the formula for an average?
[ sum / # of terms ] = Average
