## How to deal with Data Sufficiency questions in the GMAT exam.

The GMAT exam is a distinctive beast among standardized tests. You probably know this already – you’ve put in the time and you’ve put in the effort and are very aware of the format of the exam: the AWA, the “Quant”, the VR, and the dreaded IR. In this post we’ll be focusing on the Quant and the Data Sufficiency type questions.

Data Sufficiency questions are special because they depend on your mathematical knowledge, but also on reasoning skills and quick thinking. It is the part of the test that is most relevant to your future career as an administrator because it tests the rudiments of decision making.

My advice when dealing with DS questions is to take it in stride. Don’t read all the information in one gulp – question, statements, options. Read the question. What math concepts is it relating to? What information can be inferred from it? Think of this part as the moment where you gear up before the problem hits you with all it’s got. It’s where you build your scaffolding techniques that will enable to interpret the information from statements (1) & (2) in a more efficient manner.

Here is a sample problem:

If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house?

(1) The selling price minus the real estate agent’s commission was $84,600. (2) The selling price was 250 percent of the original purchase price of$36,000.

Just reading the information in the opening statement/question, we can deduce the following: label P the selling price of the house. Then 0.06P will be the commission the agent got. Seems like trivial information, but the process of transforming that information into algebraic expressions will make all the difference in the next step.

Statement (1) would translate into the following equation: P – 0.06P = 84600. Can you solve for P there? If your math fundamentals are strong, the answer is a quick “Yes”. Therefore (1) is sufficient. A similar process applies to (2).

In short, you want to take it step by step and make sure you’ve inferred as much information as possible before moving to the next phase in the problem solving strategy. Then there’s the technique of keeping track of the logical interdependency of the answer choices. This method will be explained in a future post. There’s also the type of question that determines the answer … Stay tuned for more!

## 11 Películas con Matemáticas

Buscamos buenas historias donde la gente que la protagoniza sea matemática, es decir, gente cuya facilidad para comprender la abstracción de la naturaleza ha decidido sus caminos. Acá vamos a ver películas inspiradoras (como la del profesor de colegio), fuertes (como Straw Dogs), entretenidas (como la del muchacho que participa en la Olimpiada Internacional de Matemáticas), biográficas (como la de la matemática griega) y sobre todo, películas que nos hagan pensar en algo que va más allá que sólo mostrar símbolos matemáticos en la pantalla.

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## Woman arrested for stinking up bathroom and closing down restaurant

DAVE WEZL

CEDAR RAPIDS, IA – Police and fire-paramedics were called to a restaurant when it had to close its doors early on Tuesday evening after a woman spent 45 minutes in the bathroom causing ‘unbearable, inhuman stench’.

The 34 year old woman kicked open the restaurant doors, shouting “out of the way, I’m prairie-dogging!” and ran through the dining area, which was at capacity.

“We were so crowded, people were waiting up to two hours for a table,” says the hostess. “In comes this crazy woman, already smelling like she dumped her pants, running towards the bathroom.”

One customer adds, “I couldn’t breathe. I knew she was in there blasting fudge monkeys, but the smell was toxic. I had to take my son to the hospital, they thought he was exposed to sulphur. This woman is a monster, human beings are not capable of something so foul.”

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## Bing’s House

Cool diagrams

So there’s this example of a 2-complex that’s contractible, but not obviously so. Well actually, once you see it, it’s not too hard to see. Bing’s house with two rooms.

Blah. It’s not so apparent what’s going on. It’s a 2-complex, so let’s draw in the relevant 1-complex.

You can see two vertices and four edges. The surfaces of this 2-complex are all disks, and they make threefold incidences to the edges. The two loop edges bound disks, but they don’t show up since they’re the same translucent color as everything else. And all the corners can be somewhat misleading… Here’s a slicker picture with those two disks colored.

There has recently been a few words about it at MathOverflow where it’s pointed out that the contractiblity of Bing’s house is explained in Hatcher’s text and Cohen’s text. In this post, let’s see how this contraction works.

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## Trying out latex in WP v2.0

Found this blog

trying out some $\LaTeX$ in wordpress.

How did it come out? Please comment below.

## Topological maps or topographic maps?

While surfing the web the other day I read an article in which the author refers to a “topological map.” I think it is safe to say that he meant to write “topographic map.” This is an error I’ve seen many times before.

A topographic map is a map of a region that shows changes in elevation, usually with contour lines indicating different fixed elevations. This is a map that you would take on a hike.

A topological map is a continuous function between two topological spaces—not the same thing as a topographic map at all!

I thought for sure that there was no cartographic meaning for topological map. It turns out, however, that there is.

A topological map is a map that is only concerned with relative locations of features on the map, not on exact locations. A famous example is the graph that we use to…

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## Cayley-Menger determinants

Nice

Niccolo Fontana Tartaglia, whom you may recognise from having discovered Cardano’s solution to the general cubic equation, also discovered a generalisation of Heron’s formula to compute the volume of a tetrahedron:

As you may expect, this can be generalised to compute the volume of any n-simplex (n = 2 reducing to Heron’s formula for the area of a triangle). I wondered how one would go about proving this identity, and then realised it can be accomplished by elementary facts about determinants. Firstly, it is easy to show the following result:

• The volume of an n-simplex S with vertices at {, e_1, …, e_n} is equal to 1/n!, where e_i is the ith standard basis vector.

This can be proved, for instance, by subdividing a unit cube into n! simplices, each of which is congruent to S. Now…

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## Notes from Ring Theory

A list of notes, by date Nov 8 – Densidad…
Nov 15

• Pere Menal ($\cross\sim$ 1992) Ver si un módulo artiniano tiene $\End()$ semilocal. Rosa Camp & W. Ricki $\rightarrow$ Sí.
• Krull ’34 $\rightarrow$ Módulos Artinianos satisfacen el Teorema de Krull-Schmidt? No es difícil ver que si ${M_R}$ es artiniano ${\Rightarrow}$ \footnotesize(se forma una cadena descendiente)\normalsize ${M_R=N_1\oplus\cdots\oplus N_s}$, ${N_i}$ indescomponibles. Es la única descomposición bajo isomorfía y reordenación de los sumandos? (Teorema de Krull-Schmidt). Facchini, H Levy, Vamos ’96 ${\rightarrow}$ No.
• Un ${R}$-módulo ${M}$ generado por ${r}$ elementos – ${M}$ es imágen homomórfica de ${R^r}$

Ene 13

• Módulos proyectivos finitamente generados ${\leadsto}$ submonoides…
• “full affine”
• Monoids are tricky… why? No they’re not. They just have associativity and the presence of an identity
• Fundamental theorem of abelian groups ${\left(\math{N}^k\subseteq\math{Z}^k\right)}$
• ${P/PJ(R)}$ finitely generated ${\nRightarrow}$ ${P}$ finitely generated. Counterexample given by Geramnov, Sakhaev
• Fair-sized projective modules by Pavel (${A_5}$)
• The trace ideal is a bi-lateral ideal: ${Tr(P)=\sum_{f\in P^*}{f(P)}}$${(P\rightarrow R)\in P^*=\Hom_R(P,R)}$. Verify that ${\left[Tr(P)\right]^2=Tr(P)}$
• Whitehead, as cited in Pavel’s article: ${I}$ a bi-lateral idempotent ideal of ${R}$ such that ${_RI}$ is finitely generated ${\Rightarrow I=Tr(P_R)}$, with ${P_R}$ a projective ideal
• Hyman Bass ${\rightarrow}$ Big proyective ideals

\chapter{Features of the Standard LaTeX Report Class}

1. Section

Use the \verb”

2. Section

” command for major sections, and
the \verb”

2.1. Subsection

” command for subsections, etc.

2.2. Subsection

This is just some text under a subsection.

\subsubsection{Subsubsection}

This is just some text under a subsubsection.

\paragraph{Subsubsubsection}

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\subparagraph{Subsubsubsubsection}

This is just some text under a subsubsubsubsection.

3. Typesetting Commands

Select a part of the text then click on the button Emphasize (H!),
or Bold (Fs), or Italic (Kt), or Slanted (Kt) to typeset
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You can also apply the special, mathematics only commands
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You can apply the size tags — Format menu, Font size submenu —
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Insert, Quotations, Short Quotations:

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I am not a crook. Richard Nixon

I did not have sexual relations with that woman, Miss Lewinsky.
Bill Clinton

The Quotation environment is used for quotations of more than one
paragraph. Following is the beginning of The Jungle Books
by Rudyard Kipling. (You should select the text first then click
on Insert, Quotations, Quotation):

It was seven o’clock of a very warm evening in the Seeonee Hills
when Father Wolf woke up from his day’s rest, scratched himself,
yawned and spread out his paws one after the other to get rid of
sleepy feeling in their tips. Mother Wolf lay with her big gray
nose dropped across her four tumbling, squealing cubs, and the
moon shone into the mouth of the cave where they all lived.
Augrh” said Father Wolf, “it is time to hunt again.”
And he was going to spring down hill when a little shadow with a
bushy tail crossed the threshold and whined: “Good luck go with
you, O Chief of the Wolves; and good luck and strong white teeth
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It was the jackal—Tabaqui the Dish-licker—and the wolves of
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Use the Verbatim environment if you want \LaTeX to preserve
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#include // is used for standard libraries.
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{
cout << ”This is a message.”;
// Send to output stream.
}

(After selecting the text click on Insert, Code Environments,
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4. Mathematics and Text

It holds \cite{KarelRektorys} the following

Theorem 1
(The Currant minimax principle.) Let ${T}$ be completely continuous
selfadjoint operator in a Hilbert space ${H}$. Let ${n}$ be an
arbitrary integer and let ${u_1,\ldots,u_{n-1}}$ be an arbitrary
system of ${n-1}$ linearly independent elements of ${H}$. Denote

$\displaystyle \max_{\substack{v\in H, v\neq 0\\(v,u_1)=0,\ldots,(v,u_n)=0}}\frac{(Tv,v)}{(v,v)}=m(u_1,\ldots, u_{n-1}) \ \ \ \ \ (1)$

Then the ${n}$-th eigenvalue of ${T}$ is equal to the minimum of these
maxima, when minimizing over all linearly independent systems
${u_1,\ldots u_{n-1}}$ in ${H}$,

$\displaystyle \mu_n = \min_{\substack{u_1,\ldots, u_{n-1}\in H}} m(u_1,\ldots, u_{n-1}) \ \ \ \ \ (2)$

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• Bullet item 1
• Bullet item 2
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• Description List Each description list item has a term
followed by the description of that term.
• Bunyip Mythical beast of Australian Aboriginal legends.6. Theorem-Like Environments

The following theorem-like environments (in alphabetical order) are available
in this style.

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Corollary 2
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Definition 3
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Example 1
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Exercise 1
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Lemma 4
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Proof:
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$\Box$

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Theorem 6
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Proof: This is the proof.
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\appendix

\chapter{The First Appendix}

The appendix fragment is used only once. Subsequent appendices can be created using the
Chapter command.

\chapter{The Second Appendix}

\chapter{The Third Appendix}

Some text for the third Appendix.

This text is a sample for a short bibliography. You can cite a
book by making use of the command \verb”\cite{KarelRektorys}”:
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single set of square brackets you must type all of the citation
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is an example: \cite{Bertoti97, Szeidl2001, Carlson67}.

{9}
\bibitem {KarelRektorys}Rektorys, K., Variational methods in Mathematics,
Science and Engineering
, D. Reidel Publishing Company,
Dordrecht-Hollanf/Boston-U.S.A., 2th edition, 1975

\bibitem {Bertoti97} \textsc{Bert\'{o}ti, E.}: On mixed variational formulation
of linear elasticity using nonsymmetric stresses and
displacements
, International Journal for Numerical Methods in
Engineering., 42, (1997), 561-578.

\bibitem {Szeidl2001} \textsc{Szeidl, G.}: Boundary integral equations for
plane problems in terms of stress functions of order one
, Journal
of Computational and Applied Mechanics, 2(2), (2001),
237-261.

\bibitem {Carlson67} \textsc{Carlson D. E.}: On G\”{u}nther’s stress functions
for couple stresses
, Quart. Appl. Math., 25, (1967),
139-146.

## The Fredholm Alternative

I came across this theorem while reading basic algebraic properties of Petri Nets and I wanted to know how many of you are acquainted with it. Please post in the comments!

One of the most useful theorems in applied mathematics is the Fredholm Alternative.  However, because the theorem has several parts and gets expressed in different ways, many people don’t know why it has “alternative” in the name.  For them, the theorem is a means of constructing solvability conditions for linear equations used in perturbation theory.

The Fredholm Alternative Theorem can be easily understood if you consider solutions to the matrix equation  $latex A v = b$, for a matrix $latex A$ and vectors $latex v$ and $latex b$.  Everything that applies to matrices can then be generalized to infinite dimensional linear operators that occur in differential or integral equations.  The theorem is:  Exactly one of the two following alternatives hold

1. $latex A v = b$ has one and only one solution
2. $latex A^* w = 0$ has a nontrivial solution

where $latex A^*$ is the transpose or adjoint of A. …

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## What riding my bike has taught me about white privilege

trending topic in the USA right now