A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
This question asks whether the information in one or both statements is sufficient to find a specific value. But we don't actually have to determine the value, just know that it can be determined.
(1) Quadratic equations have two solutions. However, sometimes those two solutions are identical with each other. If they are different, then solving this equation will lead to two possible values of x, and presumably also two possible values of f(x), so this would not be sufficient. But if they are the same, i.e. if there's really only one solution to this equation, then we would definitely know x, definitely know f(x), and...
(GMAT 800) Data Sufficiency Quadratic Equations with Explanation
Top 10 Tips to Ace GMAT Data Sufficiency
Ever heard of a Math problem that you actually don't have to solve. If you have just started your GMAT prep, then this can be confusing. Don't worry! With some practice, your mind will be trained to think like a DS Wizard. Follow these 10 tips and you will be on your way to mastering GMAT Data Sufficiency.
1. Familiarize with the Answer Choices
No excuses: On Data Sufficiency, they’re always the same! Know in the blink of an eye what choice C is. On test day, if you find that Statement 1 is insufficient, be able to cross out choices A and D without hesitation.
2. Takes notes efficiently
Each statement alone will be sufficient if both of the statements on their own contain all the information necessary to answer the question. The statements will be sufficient together if they contain every piece of necessary information between them. Take the area of a parallelogram: Do you need to know every side length to determine the area? If you have every side length, can you find the area?
3. Don’t look at the statements together.
Statement 2 may tell you that x is negative, but that fact has no bearing on Statement 1 when viewed by itself. Explore all the possibilities offered by each statement individually. If you’ve...
GMAT Word Problems - Basics
Word problems on the GMAT get an unfair reputation for being especially challenging. However, it’s helpful to think of them as just dressed-up algebra. The real challenge is that they are (1) long, (2) boring, and (3) require translation from ‘English’ to ‘Math.’ Here are a few questions to ask yourself to make sure you fully break down and understand the problem BEFORE you start to solve!
What is the problem really asking?
Make sure to understand what the answer choices represent. Are they the total number of dollars of profit? The profit accumulated by Jenny only? The percent increase in profit from June to July? Taking the time to do this will also ensure you never leave a problem half finished. If you dive into setting up an equation too quickly, you may realize half-way through that you’re solving for the wrong variable. Sometimes word problems will add an extra step at the end. You may be busy solving for “x” and forget that the problem is asking for the value of “1/x”.
What information am I given?
How to identify Style or Tone in GMAT Reading Comprehension
One question type you are bound to encounter on the GMAT Reading Comprehension is a style or tone question. Style and tone questions are particularly rare because most of the passages will be informational articles with neutral tones. For example, it would not be very challenging if you were asked to identify the tone of a passage about the many types of metamorphic rock - such a passage would surely be neutral.
The tone of any given passage is the author’s emotion or feeling, usually towards his subject. An author’s style is the particular way he uses language to reflect his unique authorial voice. Most style or tone questions will include the words “attitude,” “tone,” “style,” “feeling,” etc. A typical question of this type might look like this:
• The author’s attitude toward global warming might best be described as which of the following?
• Which of the following best describes the tone of the passage?
• Based on the statements in lines 43-46, which of the...
GMAT Fractions - Don't get lost in the calculations
Have you wondered how writers can make a seemingly simple GMAT topic like fractions into time-consuming calculations. One strategy that GMAT test takers must adopt to simplify the calculations. For example
Dividing by 5 is the same as multiplying by 2/10. For example:
• 840/5 = ?
• 840/5 = 840*(2/10) = 84*2 = 168
Multiplying or dividing by 10’s and 2’s is generally easier than using 5’s. 90% of the time, fractions will be easier to perform arithmetic. Decimals are sometimes more useful when comparing numbers relative to one another, such as in a number line, but these questions are the exception. Even if given a decimal (or percent) looks easy, quickly convert to a fraction. Some common ones to memorize:
• 1/9 = 0.111 repeating
• 1/8 = 0.125
• 1/7 = ~0.14
• 1/6 = 0.166 repeating
• 1/5 = 0.20
• 1/4 = 0.25
• 1/3 = 0.333 repeating
• 1/2 = 0.5 repeating
Note: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easily be derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)
Denominators are super important. A denominator of a reduced fraction with a multiple of 7 will not have a finite...
How to score well in GMAT Number properties?
GMAT Number properties may sound scary, but they just constitute elementary mathematical principles. You probably know most of these principles by memory; if not, you could easily execute a calculation to ascertain them. The best option, though, is to study these principles enough that they seem intuitive. The GMAT Quantitative section is all about saving time; making number theory second nature will definitely save you some valuable seconds.
1.Odds and Evens
Even + even = even (12+14=36)
Odd+ Odd = even (13+19=32)
Even + Odd = odd (8 + 11 = 19)
To more easily remember these, just think that a sum is only odd if you add an even and an odd.
Even x even = even (6 x 4 = 24)
Odd x odd = odd (5 x 3 = 15)
Even x odd = even (6 x 5= 30)
To more easily remember these, just think that a product is only odd if you multiply two odds.
If r is even and t is odd, which of the following is odd?
How to Ace GMAT Critical reasoning application questions
GMAT Critical reasoning application questions go one step further than Inference questions, asking you to apply what you have learned from the passage to a different or hypothetical situation. For these questions, it’s important to ignore the answer choices until you’ve effectively broken down the passage. Understand the author’s argument. Some application questions will focus on the author’s point of view. Just like you would for a critical reasoning passage, identify the author’s conclusion and the evidence provided. Put yourself in the author’s shoes and ask yourself questions. What is my argument? What would make my argument stronger? What might weaken it?
1) Focus on process
2) Pay attention to how a particular process is performed
For example, if the passage focuses on describing an experiment, you must clarify step-by-step how the experiment is carried out, before you can apply that same method to a different situation.
3) Go back through the passage and list the verbs on your scratch pad. This will help you to understand the steps of the process and not confuse the sequence.
You may feel confident with the most commonly tested grammar rules on the GMAT Sentence Corrections - subject-verb agreement, verb tense, pronoun reference, pronoun number, misplaced modifiers, parallelism, idioms, false comparisons, and quantities. It’s hard to imagine any other grammar rules that could possibly be tested, but you can bet the GMAT test writers are pretty exhaustive. Here are four grammar rules that don’t receive as much attention; you’ll need to master these if you’re going for a top score.
1. Subjunctive Mood
You won’t see the subjunctive mood tested on college entrance exams like the SAT and ACT; it’s purposely reserved for the GMAT for good reason. Most of the English verbs we use are in the indicative mood - that is, verbs that have happened, are happening, or will happen. The subjunctive mood is used to express wishes or possibilities that have not happened.
The most common subjunctive verb that you might encounter is were, the subjunctive form of was.
Example 1: If he were athletic, he could make the football team. (He is not actually athletic, so the verb communicates an idea that does not really exist).
Notice that “If he was athletic…” would be incorrect, even though you may not reconize such an error in speech or writing.
Example 2: The teacher requires...
How to Draw Diagrams accurately for GMAT Geometry?
Drawing diagrams accurately in GMAT Geometry questions will allow you to capture the essential information from the Question. It’s not always easy. Here is a hands-on Experience for you: Draw the diagram as your read the question(below) and then go through the analysis.
Q) A circular table consists of a glass center surrounded by a metal ring of uniform width. If the metal ring has a width of 2 inches, and the glass center has a diameter of 4x inches, what fraction of the table’s surface is made up by the metal ring, in terms of x?
There’s no underhanded trick in this question, nor is there anything super complicated to incorporate into your diagram. But you should always be very mindful of the details of the question while drawing your diagram, since after you do so, you’re less likely to look at the information given in the problem. Indeed, it’s a waste of time to do so, since the information is presented much more usefully in your diagram! But this also means that if you make a mistake in the diagram, you may not correct it – and it’s very frustrating to get a problem wrong simply because your diagram was drawn incorrectly.
If it helps you to think figuratively, consider this metaphor I’ve *ahem*...
GMAT Data Sufficiency Strategy - The Obvious Answer Trap
Data Sufficiency questions are supposed to be hard; more so than any other question type they tend to represent a chess match between you and the author, as the author has two chances to get you to make a mistake. She won’t likely waste either statement giving you an easy pass – the questions have to elicit something from you in terms of efficiency or ingenuity in order to answer them correctly, so if an answer choice seems obvious within 15-20 seconds and you can’t spot a trap, well, you just fell into the trap. Consider the question:
What is the value of x?
1) 3x + 2y = 15
2) y = (-3/2) (x – 5)
This should pretty obviously be C.
Two equations, two variables, neither works alone but both work together, right?
But that is too easy, and the GMAT won’t often give you the answer that quickly. Much as though the author had moved a pawn...
How to identify modifying Phrases In GMAT Sentence Correction
A common trick used by GMAT test makers is to insert modifying phrase incorrectly. Here are some sentences that incorrectly use modifying phrases:
Sentence A: Ever since her paw was crushed in the front door, Mrs. Benson has been worried about Muffin, her pet cat.
Sentence A starts off with the modifying phrase “Ever since her paw was crushed in the front door,” and then talks about Mrs. Benson and her worry for her cat. But Mrs. Benson sounds like a person, and as a person, she probably doesn’t have a paw to be crushed. It’s MUCH more likely that Muffin’s paw got crushed, causing Mrs. Benson’s worry. This sentence needs to be corrected to put the modifying phrase next to the item it modifies.
Here are a couple of ways that we can do that, depending on where the sentence’s underlining is placed:
Sentence A1: Ever since her paw was crushed in the front door, Mrs. Benson has been worried about Muffin, her pet cat.
If the modifying phrase isn’t underlined, we don’t have the opportunity to fix it-- but we can rearrange the rest of the sentence so that the thing that is modified (...
Solving GMAT Questions with two linear equations and two unknowns
In order to solve such equations, you need at least 2 distinct equations involving these unknowns.
For example, if we are trying to solve for x and y, we won't be able to solve it using these 2 equations.
2x + y = 14
4x + y - 14 = 14 - y
Why? Because the two equations on top are the same. If you simplify the second equation, you get 4x + 2y = 28 which reduces to 2x + y = 14 - the same equation as the first. If the two equations are the same, then there will be infinitely many values for x and y that will satisfy the equations. For example, x = 2 and y = 10 satisfies the equation. So does x = 4 and y = 8. And so does x = 6 and y = 2.
In order to solve for an actual value of x and y, we need 2 distinct equations.
For example, if we had
2x + y = 14 --------(1)
x - y = 4 ----------(2)
Then from equation (2), we can get x = 4 + y and substitute that into equation (1) to get:
2(4 + y) + y = 14 We can then solve for y. See if you got y = 2 Once you've got y = 2, you can substitute that into x= 4 + y to get x = 6.
An important lesson here is that you need as many distinct equations...
(GMAT 800)The function g(x) is defined for integers x such that if x
The function g(x) is defined for integers x such that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5. Given that g(g(g(g(g(x))))) = 19, how many possible values for x would satisfy this equation?
The easiest way to approach this problem is probably to work backwards, at least until we see a pattern.
With g(...) = 19, then we can consider which operation applied to (...). If it was x/2, then (...)= 38. 38 is even so that is fair. If it was x + 5, then (...) was 14. 14 is even, so that operation would not have been applied.
On paper, you could make a tree, with 19 as the root, and 38 as the first node.
Next consider 38. 38 could have come from 76/2 or 33 + 5. Two possibilities give us two nodes branching from 38:
19 -> 38 -> 76, 33.
We can now observe the pattern that with an odd number, it must have come from an even, but an even could come from either of two numbers.
Therefore our 76 will branch into 2 numbers, and the 33 into just one.
33 -> 66
76 -> 73, 152..
We can represent this as shown here:
International Students - Are you ready for GMAT Verbal?
For some international students who are new to the language, ESL classes might be a necessary step before they even start thinking about business school . For others, whose foundation in English grammar is stronger, study time may be better spent reading books in English, writing essays, taking practice tests, or doing focused grammar drills. So how can you know whether your English is at the right level for the GMAT?
Simply put, to do well on the GMAT you should know enough English to function in a university environment. First, check your proficiency by listening to sample lectures on Youtube. This is a practical recommendation that pertains to spoken as well as written English. In business school you will be expected to make arguments, back up opinions, and discuss case studies in depth. You should be comfortable stating your opinions and answering questions. Though you want to have better grammar than Borat or Jackie Chan, don’t worry if you have an accent or make a few mistakes when speaking.
Here’s an easy test: Watch a movie in English without subtitles; try something business related, like Glengarry GlenRoss, Wall Street, or Working Girl if you can. When you’re done, read a detailed summary of its plot online. If you find that you missed out on...
GMAT Sentence Correction Strategies - Spot Decision Points
As stated in GMAT SC - Use Logic, the pool of required grammar knowledge for the GMAT is likely shallower than you would think; those who memorize hundreds of idiomatic rules or read the cover off of their copy of Strunk & White’s “Elements of Style” are studying counter to the real purpose of the GMAT’s inclusion of Sentence Correction: the idea of “core competencies.” Corporate Strategy courses in business school will spend quite a bit of time on that notion that each business needs to recognize the handful of things it does extremely well and find opportunities to leverage that. When businesses stray from their core competencies they tend to struggle mightily, throwing away resources and providing diminishing returns with increased risk.
For example, McDonald’s has a set of core competencies that allow it to run extremely efficient fast-food operations in high-traffic areas. It’s natural, then, to acquire Chipotle and replicate the same processes with a different type of fast food...
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