Question #1
If n is an integer, is n - 1 even?
(1) n - 2 is odd
(2) n + 1 is even
(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.
Answer:
(D) is correct.
This question asks whether the information in one or both statements is sufficient to answer a yes or no question. The interesting thing about this type of Data Sufficiency question is that a "no" is just as conclusive as a "yes;" as long as the answer is always a "yes" or always a "no," the information is sufficient. The information is insufficient when using that information leaves both "yes" and "no" answers possible (in other words, when the answer is "maybe," the information is insufficient).
If n - 2 is odd, then we know that n itself must be odd. Not sure about that? Make up some numbers and test it out. So if n is odd, then n - 1 must be even. Statement (1) is sufficient.
Statement (2) tells us that n + 1 is even. That means that n is odd, which means that n - 1 is also even. Statement (2) is also sufficient!
The credited response is D: Each statement, when considered independently, leads to an absolute answer in all circumstances (for the record here, both "yes").
Question #2
If c = 4x + 5 and r = 21 - 2x, then for what value of x is c = r?
A. 3⁄8
B. 8⁄3
C. 13⁄3
D. 8
E. 13
Answer:
(B) is correct.
8⁄3 is the credited response.
The question states that c = r. So 4x + 5 must equal 21 - 2x. Set the expressions equal to one another and solve for the value of x:
4x + 5 = 21 - 2x
6x = 16
x = 16⁄6 = 8⁄3
Question #3
Apartments are labeled 2 through 56 consecutively on the first floor of a building. What is the probability that a tenant living there will have an apartment with a tens digit of 3?
A. 9⁄55
B. 2⁄11
C. 5⁄27
D. 10
E. 55
Answer:
(B) is correct.
This is a more basic probability question. First, remember that to calculate the number of apartments from 2 through 56, we should combine:
56 - 2 + 1 = 55 apartments. We add 1 because we're including both endpoints in the calculation; normal subtraction only counts the distance moved from one endpoint to another on a number line, so it essentially leaves one of two endpoints out.
Next we consider the element of probability. The formula for probability is number of desired outcomes⁄total possibilities, and keep in mind that since probability expresses likelihood, it is always somewhere between 0 (no chance) and 1 (100% certainty). It's most commonly presented as a fraction.
In this scenario, there are 10 apartments that begin with the tens digit of "3" (30 - 39), so we have a total of 10 desirable outcomes. And we already determined that there are 55 total possibilities (55 possible apartments labeled 2 through 56), so 10⁄55 = 2⁄11
Question #4
4. Sally writes her brother a check for $55, which represents her repayment of 20% of an earlier loan. If this is Sally's first payment on the loan, and if her brother charges her no interest, how much does she still owe him?
A. $11
B. $44
C. $220
D. $275
E. $1100
Answer:
(C) is correct.
$220 is the credited response.
You could solve algebraically, by first finding the amount loaned, and then the balance, but it is much faster and easier to solve for the balance directly:
If the $55 payment is equal to 20% of the loan, then the balance is equal to 80%. 80% is four times 20%, so the balance is 4*$55, or $220.
You could also have done this with fractions, using 1/5 and 4/5 in place of 20% and 80%.
Question #5
4.7☆◎3
If ☆ and ◎ each represent single digits in the decimal above, what digit does ☆ represent?
(1) When the decimal is rounded to the nearest tenth, 4.8 is the result.
(2) When the decimal is rounded to the nearest hundredth, 4.77 is the result.
(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.
Answer:
(E) is correct.
This question asks whether the information in one or both statements is sufficient to find a specific value.
By statement (1), we know that the hundredths digit (represented by ☆) must be equal to 5, 6, 7, 8, or 9. We cannot narrow it down further than that, so statement (1) is not sufficient.
Statement (2) shows us the hundredths digit, but it has been rounded. Since we do not know the thousandths digit, we cannot be sure whether the hundredths digit is indeed 7, or if it was rounded up from 6. Because we cannot be sure of ☆'s value, this is not sufficient.
Even combined, we do not have enough information to answer the question.
The credited response is E: The statements don't provide sufficient information to find the value in question, not even when considered together.
Question #6
For members of various bygone Inuit cultures in the far northern hemisphere, sled dogs were a vital element of daily life, to provide feasible transportation across the vast arctic landscape.
A. to provide
B. a means to provide
C. as a means providing
D. providing
E. as a provision of
Answer:
(D) is correct.
Although our focus is tightly drawn in this sentence, a complex sentence structure makes this question tougher than it might first appear. The sentence could logically end at the comma, but we’ve got a phrase tacked on at the end, and the underlined portion begins that phrase. Since there’s a comma, that portion of the sentence must describe the subject of the phrase that precedes it, “sled dogs.” And although there’s a verb in the underlined portion, it’s not being used as a verb... at least not outright. In situations like this, use logic to guide your decision. Start with the longer choices to see if you can rule them out. Calling sled dogs “a means” is awkward and just doesn’t make sense, and it’s not proper idiom. Finally, we have to choose the proper verb form from among the remaining choices, so think about time.
Question #7
Not all stars emit energy as visible light. Some stars emit energy at high frequencies outside the realm of visible light, such as gamma rays. Other stars, particularly in the Milky Way galaxy, will emit energy in the form of invisible X-rays.
If the statements to the left are true, which of the following conclusions is best supported?
A. A thorough analysis of visible light emissions is insufficient to monitor star energy emissions.
B. Gamma rays are also a common type of energy emission in the Milky Way galaxy.
C. X-rays emissions found outside the Milky Way galaxy are always paired with visible light emissions from the same star.
D. Dying stars are more likely to emit gamma rays.
E. Telescopes capable of observing gamma rays are incapable of observing visible light frequencies.
Answer:
(A) is correct.
The passage presents statements about both gamma rays and Xrays. The best conclusion will offer a general statement that applies to both, rather than a specific statement about either one or the other. Both gamma rays and Xrays are outside the spectrum of visible light, so it is true that measuring visible light emissions alone is insufficient.
Question #8
Both Manny Industries and Scotch Industries manufacture the same type of metal gaskets. Raw material supplies represent 12 percent of the cost to manufacture gaskets at each company. Manny Industries should lower its raw material supplies costs to gain a competitive advantage over Scotch Industries.
Which of the following, if true, casts the most doubt on the argument stated above?
A. The cost of raw materials has steadily climbed over the past decade, mostly due to increased freight costs.
B. Unionization makes it difficult for metal gasket manufacturers to lower wages or fire existing employees.
C. In order to lower its raw materials costs, Manny Industries would need to sacrifice the quality of their finished product.
D. Scotch Industries has outperformed Manny Industries by a small margin for the last three quarters.
E. The main raw materials supplier for Manny Industries also caters to Scotch Industries.
Answer:
(C) is correct.
It is easy to say Manny Industries should cut costs to gain an advantage, but what are they losing by cutting costs? If they sacrifice quality, they may actually lose their competitive edge against competitor with a product of superior quality.
Question #9
Very often one hears a person who has become famous or successful in their field or endeavor say that they "knew it all along." Although there may be a bit of rosy hindsight in such a claim, the fact remains that self-confidence is an indispensable component of success.
The author of the following passage would most likely agree with which of the statements below?
A. It is not possible to become successful in one's field of endeavor unless one has a certain amount of self-confidence.
B. Self-confidence is an innate trait, and cannot be influenced by such factors as environment and circumstance.
C. What famous and successful people claim, and what is actually the case, are very often two different things.
D. Although there may be successful people who are self-confident, there are many more self-confident people who are not successful.
E. Once a person is famous, self-confidence becomes less important than quotidian considerations such as careful planning and foresight.
Answer:
(A) is correct.
The author of the argument says that although there is a bit of after-the-fact confidence in statements like “I knew it all along,” eventual success requires self-confidence. The author, then, would agree with (A), which says exactly this: Success requires self-confidence. We have no idea what the author would think of (B), (C) plays off of the author’s small concession to rosy hindsight but grossly exaggerates the conclusion, (D) suggests the author’s views on whether or not most self-confident people are successful. For all we know, the author may believe that very few self-confident people are unsuccessful. And finally, (E) suggests that the author considers self-confidence more important in achieving success than maintaining it. Again, this is another issue about which we don’t know the author’s thoughts.
Question #10
The Christmas holiday brought a brief respite to opposing armies during World War I in that an unofficial ceasefire spread along the Western Front on Christmas Eve, 1914.
A. armies during World War I in that an unofficial ceasefire spread along the Western Front on Christmas Eve, 1914
B. armies during World War I, spreading an unofficial ceasefire along the Western Front on Christmas Eve, 1914
C. armies during World War I when they spread an unofficial ceasefire along the Western Front on Christmas Eve, 1914
D. armies during World War I, for an unofficial ceasefire spread along the Western Front on Christmas Eve, 1914
E. armies during World War I by the spread of an unofficial ceasefire along the Western Front on Christmas Eve, 1914
Answer:
(D) is correct.
Both proper idiom and the logic of the sentence must guide our selection of the correct answer choice. We need to consider how the second portion of the sentence relates to the first portion: the second portion describes how the Christmas holiday brought respite to the opposing armies. In a cause-and-effect relationship, verbal clues help to clarify the relationship. We're looking for a conjunction that suggests a cause-effect relationship.
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