If a and b are both positive integers, is b^(a+1) - b(a^b) odd?
(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd
(2) b^3 + 3b^2 + 5b + 7 is odd
The trick to solving this question is to remember that for positive integers:
(a) Even^(positive integer) = even
(b) Odd^(positive integer) = odd
(c) even x even = even x odd = even
(d) even – even = even
(e) odd – odd = even
(f) even – odd = odd
Using statement (1):...
Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and T. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of T if J is negative?
This problem demonstrates a helpful note about statistics problems – quite often the key to solving a stats problem is something other than stats: number properties, divisibility, algebra, etc. The statistics nature of these problems is often just a way to make a simpler problem look more difficult.
Here, the phrase “factor of 34? should stand out to...
Two sides of a right angled triangle are 15 cm and 17 cm. Find the length of the third side
I. 8 cm II. 32 cm III. Sqrt.514 cm IV. 514 cm
A) II only
B) I only
C) I & III only
D) II & III only
E) I, II & III
Like a tae kwon do blackbelt or an icy road, the GMAT is perhaps most famous for its ability to use your own momentum against you. Few places is this as evident as on Critical Reasoning questions, in which the most common way to answer incorrectly is to allow your subconscious mind to lead you to a slightly-out-of-scope conclusion that the psychological warriors at GMAC have already anticipated you’d conclude. Accordingly, to perform well on Critical Reasoning questions it is, well, critical that you...
Find the area of the triangle QRS
A) 90 cm
B) 80 cm
C) 110 cm
D) 55 cm
E) 45 cm
Jay: "#IfObamaLoses trended on twitter for 4 hours on Oct 28th 2012. Therefore, Obama is likely to lose the election”
Which statement weakens the argument presented by Jay?
a) #IfObamaLoses was fourth in the twitter trending list
b) #IfObamaLoses was trending when most of the American twitter users were asleep, hence the twitter trend represents a small minority of active users in the US.
c) #IfObamaLoses was started by a news channel that is speculated to be the mouthpiece for the republican party
d) #IfObamaLoses was started as a joke by a well-known democratic supporter
e) #IfObamaLoses was used predominantly by the 18...
What is the greatest prime factor of 12!11! + 11!10!?
While it is common for students to simply look at the numbers 12!, 11!, and 10! and see that the highest naturally-occurring prime number is 11, it is important to know that this is an addition problem – the numbers 12!11! and 11!10! are combined to create a new number that may well have a higher prime factor than its factorial components.
When adding large numbers like factorials and exponents, it is often quite helpful to factor out common terms. In this case, it’s particularly important, because our...
In the Business program at a university, all candidates for the MBA in International Business who entered the program after 1990 took a seminar on Microeconomics, and all candidates for the MBA in International Business who entered the program after 1994 took a seminar on Applied Economics.
If a student in the Business program described above took a seminar on Microeconomics but did not take a seminar on Applied Economics, which of the following must be true?
(A) The student entered the Business program prior to 1995.
(B) The student entered the Business program after...
The argument in this passage relies on which of the following assumptions?
[A] All animals that are born after a short gestation period are born with some parts of their bodies underdeveloped.
[B] Well developed...
Market research has shown that the newest model of E-Phone gained widespread popularity not due to technical superiority but through seamless and intuitive design.
A. gained widespread popularity not due to technical superiority but through seamless
B. gained widespread popularity not only due to technical superiority but also through seamless
C. did not gain widespread popularity due to technical superiority but through seamless
D. did not gain widespread popularity in consideration of technical superiority but rather due to seamless
E. gaining widespread popularity not due to technical superiority but also through seamless
Natural selection, the central doctrine of
Darwinism, has been explained as the "survival of the
fittest." On this process has depended the progress
observable throughout organic nature to which the term
(5) evolution is applied; although there has been from time
to time degradation...
A leading board member of AutoSnip Co., makers of an automated home haircutting system, recently stated that the company was in terrible shape and headed for a disastrous year. His concern was that, since the introduction of the AutoSnip III last year, calls to the customer service line have nearly doubled, indicating that people are very unhappy with the new product. Although it's true that it is the job of responsible board members to raise issues of concern, in this case the board member's analysis of the situation is mistaken. The customer service line handles not only complaints but also sales, and the majority of the new calls have...
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...
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.
If n and a are positive integers, what is the units digit of n^(4a+2) – n^(8a)?
(1) n = 3
(2) a is odd
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
D) EACH statement ALONE is sufficient to answer the question asked;
E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,...
Conventional wisdom holds that financial markets are informationally efficient—that stocks are always priced and traded at the intrinsic value of their underlying assets. Thus, investors cannot expect to achieve returns consistently in excess of average returns, given information that is publicly available at the time, without taking on large economic risks akin to gambling risks. In other words, one can only obtain higher returns by purchasing riskier investments, and not through expert timing or speculative stock...