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Monday, September 17, 2012

GMAT Mixture Problems



GMAT blog, GMAT mixtures, GMAT ratios, GMAT quantitative problemsMixture problems show up frequently on the quantitative section of the GMAT and fall into two basic categories.  As each type of mixture question will be approached in fairly different ways, it is important that you know the difference between them.
First, there are mixture problems that ask you to alter the proportions of a single mixture.  These questions could, for example, tell you that you have a 200 liter mixture that is 90% water and 10% bleach and ask how much water you would need to add to make it 5% bleach.  The key in this type of question is the part of the mixture that is constant – in this case the bleach.  While we are adding water, the amount of bleach stays the same.  First, determine how much bleach we have.  10% of 200 is 20 liters.  Next, we know we want those 20 liters to equal 5% of our total.  Since 20 is 5% of 400, our new total should be 400 liters.  To go from 200 liters to 400 liters, you would need to add 200 liters of water, which would be the answer .
The other type of mixture problem will ask you to combine two mixtures.  For example, you could be told that mixture A is 20% bleach and 80% water, while mixture B is 5% bleach and 95% water.  You could then be asked in what ratio these mixtures should be combined to achieve a mixture that is 10% bleach.  You should solve problems such as this algebraically.
Both sides of your equation will represent the amount of bleach in the combined mixture.  On one side you will represent the amount of bleach in terms of the individual mixtures.  This will give you .2A + .05B.  On the other side of the equation you will represent the amount of bleach overall, which is .1(A + B).  Note that in these expressions A represents the total amount of mixture A and B represents the total amount of mixture B.  Because these expressions both represent the total amount of bleach, we can set them equal to each other.  This gives us .2A + .05B = .1(A + B).  The ratio of A to B can be solved as follows:
.2A + .05B = .1(A + B)
.2A + .05B = .1A + .1B
.1A = .05B
A/B = .05/.1
A/B = 1/2

Question:
Two brands of detergent are to be combined. Detergent X contains 20 percent bleach
and 80 percent soap, while Detergent Y contains 45 percent bleach and 55 percent
soap. If the combined mixture is to be 35 percent bleach, what percent of the final
mixture should be Detergent X?
(A) 10%
(B) 32_ 1_ 2 %
(C) 35%
(D) 40%
(E) 60%

Solution:
Step 1: Analyze the Question
This is a complex question, but there is a straightforward
solution. We are creating a new mixture from two others,
X and Y. X is 20% bleach, and Y is 45% bleach. The new
mixture is to be 35% bleach.
In other words, some amount of a 20% bleach mixture plus
some amount of a 45% bleach mixture will balance each
other out to a 35% bleach mixture.

Step 2: State the Task
Because this involves finding a particular balance between
Detergents X and Y, you can use the balance approach to
solve. We could use Algebra or Backsolving, but balance is
the most efficient. This will let us calculate the proportion
of Detergent X in the final mixture.

Step 3: Approach Strategically
The question does not state how many parts of Detergent
X are used, so call this x. And the question does not state
how many parts of Y are used, so call this y.
GMAT blog, GMAT mixtures, GMAT ratios, GMAT quantitative problem







So 0.10y = 0.15x.  To solve for a proportional amount, view
this as a ratio. Divide both sides by y and by 0.15 to get
the ratio:
0.10y = 0.15x
0.10 / 0.15 = x / y
10 / 15 = x / y
2 / 3 = x / y
So x:y is 2:3. Add the total to the ratio to determine how x
relates to the total: x:y:total = 2:3:5.
Thus x:total = 2:5. That’s 2 /5 , or 40%.
Answer (D) is correct.

Saturday, July 28, 2012

GMAT Integrated Reasoning - Two-Part Analysis Problems

GMAT Quant Concept Videos

Almost all basic concepts required on GMAT Quant section are covered in the following videos.

Work Rates :

http://www.youtube.com/watch?v=Sc1MpH2bDv4

Union and Intersection of Sets :

http://www.youtube.com/watch?v=ktav02fitiQ

Sets :

http://www.youtube.com/watch?v=mgGiqsnb9xw

Motion :


http://www.youtube.com/watch?v=-lMTbML86l4

Geometry – Symmetry :


http://www.youtube.com/watch?v=lNGZbajRfaQ

Geometry – Spheres :

http://www.youtube.com/watch?v=HozOG8e0tD0

Geometry – Rectangular Solids :

http://www.youtube.com/watch?v=SJycga8V02M

Multiplying Decimals :

http://www.youtube.com/watch?v=GsL39QrqPKw

Intersecting Lines and Figures :

http://www.youtube.com/watch?v=iX1rDRKSVfA

Dividing Fractions :

http://www.youtube.com/watch?v=9fE6MCD_Lzk

Geometry – Diagonals :

http://www.youtube.com/watch?v=F5zDDgUs70k

Decimal or Percentage Expressions of Probability :

http://www.youtube.com/watch?v=PZ6TgH7UWbI

Geometry – Cylinders :

http://www.youtube.com/watch?v=tWHxuw9xQsU

Problem Solving - Circles :

http://www.youtube.com/watch?v=51P-ww1bils

Adding and Subtracting Decimals :

http://www.youtube.com/watch?v=IavJlscG60w

Square Roots :

http://www.youtube.com/watch?v=d0ScfdcfJxU

Permutations vs. Combinations :

http://www.youtube.com/watch?v=MbzqmEH4SlA

Solving Simultaneous Equations using Substitution :

http://www.youtube.com/watch?v=qx1vkRVpbPY

Solving Linear Equations with One Variable :

http://www.youtube.com/watch?v=CKLU_LrRKHs

Slope of a Line :

http://www.youtube.com/watch?v=q6qLOsFhZv4

Negative Bases :

http://www.youtube.com/watch?v=PhfMHo3JTRo

Fractional Exponents :

http://www.youtube.com/watch?v=hvEJrp9UzQo

Variables :

http://www.youtube.com/watch?v=229MTmwxwXc

Percents in the Answer Choices :

http://www.youtube.com/watch?v=02jCcEchlBs

The Data Sufficiency Question Type :

http://www.youtube.com/watch?v=Puo6Ja9HBG8

Number Properties :

http://www.youtube.com/watch?v=3FrJfs59kHM

Calculation vs. Conceptualization :

http://www.youtube.com/watch?v=XA3MYXP31_s

Combining Statements in Data Sufficiency :

http://www.youtube.com/watch?v=5-a0eZpoO5o

More on Picking Numbers :

http://www.youtube.com/watch?v=sHaLGB5ytVo

Strategic Guessing: Elimination :

http://www.youtube.com/watch?v=h4psEqWOOTQ

Fractions and Decimals :

http://www.youtube.com/watch?v=1pJ-g9MUewc

Equations :

http://www.youtube.com/watch?v=qIFZ4fOQ8Q4

Circles :

http://www.youtube.com/watch?v=CuGbgZIekKA

Inequalities :

http://www.youtube.com/watch?v=t9E7c25C-w4

Quadratic Equations :

http://www.youtube.com/watch?v=FmFJG8JeQkk

Probability :

http://www.youtube.com/watch?v=aWlekctXiZ8

Rates and Speed - Converting Rates :

http://www.youtube.com/watch?v=5lW-1fWSgws

Geometry - Multiple Figures :

http://www.youtube.com/watch?v=td15KTZrngg

Saturday, July 14, 2012

Next Generation GMAT - Perfect 800 Score

GMAT Club member NonYankee does the unthinkable. "I raised my hand to be dismissed and shakily walked with Vladislav to his station, where he printed out my unofficial score report and scanned my palm one last time. He said it was the first time in two years that he'd seen a perfect score."
Read the full debrief here :  Link

Tuesday, June 5, 2012

How To Solve A Sentence Correction Problem




Before you start: Keeping track of your thinking / answers
One of the biggest mistakes people make is not keeping track of their thinking as they assess the answers. On verbal in general, we’re usually going to do two passes through the answers. On our first pass, we’re deciding between “this is definitely wrong – I’m never going to look at this again” and “maybe…” We don’t try to decide which answer is the right answer when we haven’t even seen all of the choices yet.
Then, on our second pass, we’ll look only at the “maybe” choices. Perhaps we’ll only have one, in which case we now have our right answer. If we have more than one, then we’ll have to start comparing the two and figure out how to narrow down from there. Okay, now on to Sentence Correction specifically.

Read the original sentence in its entirety
Another big mistake people make is focusing too much on the words in the underline and not enough on the rest of the sentence. The part that isn’t underlined is correct, of course, and can’t be changed – and that’s exactly why we need to pay attention to it. Often, there are things in the non-underlined part that tell us what we need to have in the underlined part in order to match.
As you’re reading the original sentence in its entirety, ask yourself: is this all okay? Are there any definite errors? Does anything sound not-quite-right?
If we spot an actual error in the original sentence, we immediately cross off answer choice A on the scratch paper. (Remember that answer A is always identical to the original sentence.) We then scan the other answers in the same location to find any that repeat the same error and cross those off, too. Every time you find an error on SC, immediately look at the remaining answers to see whether you can cross off any others for the same reason. We repeat this process with any other actual errors in the original. (But don’t spend a ton of time hunting for those errors; if we don’t see anything pretty much right away, we should move on to another approach.)
If something sounds not-quite-right, then we ask ourselves why. Which part, specifically, sounds not quite right? How else is that particular part written in the other answer choices? If we can use these questions to identify an actual error, then we deal with it as described in the previous paragraph. If we can’t get beyond “it just doesn’t sound right,” we don’t do anything with that information; instead, we start looking for something else to use. In particular, unless we can find a definite error, we do not eliminate answer choice A at this stage.

Processing answers B, C, D, and E
After we’ve dealt with everything that we can deal with in the original sentence (and sometimes we can’t find anything to do!), we start processing the other answers. Possibly we have crossed some off already; possibly we still have all five answer choices left. Our next task is to scan the remaining answer choices vertically to find differences, or “splits.” Splits represent differences in the answer choices for the same general part of the sentence. The “split” might be as simple as a difference in one word (e.g., has vs. have) or as complicated as re-wording or moving an entire clause (e.g., changing a modifier into part of the sentence core or placing a modifier at the beginning of the sentence vs. the end).
There are typically multiple splits in any SC problem. There are a couple of important things to know about splits:
  1. A split does not always indicate an error! Sometimes, differences are introduced but both variations are grammatically correct; the test writers are trying to get us to waste time on something that won’t actually help us answer the question.
  2. There is always a split at the beginning of the underline and there is always a split at the end of the underline. That is, at least one answer choice among B, C, D, and E will vary from the original sentence at the beginning of the underline, and at least one answer choice among B, C, D, and E will vary from the original sentence at the end of the underline.
How do we use that information? First, we always know exactly where two of the splits will be: at the beginning of the choices and at the end. We can look there first to see what kinds of differences exist in this sentence (though we have to remember that a difference doesn’t necessarily mean an error).
We do not need to deal with the splits in any particular kind of order. Each person simply looks for the first one that she/he knows how to process. If we can deal with it, we deal with it and cross off any answer choices that use the version that we decided was incorrect. If we don’t know how to deal with a particular split, then we shouldn’t even try. Instead, we should immediately look for something else that we do know how to do.

Educated guessing
Hopefully, the above process will get us down to just one answer choice; this doesn’t always happen, of course. As a result, we also need to study how to make an educated guess, so that we will know what to do when we do have to guess on a problem. For example, generally speaking, in a split between “like” and “such as,” the latter form, such as, is more commonly a part of the right answer. Generally speaking, in a split between “being” and some other form that expresses the same meaning, some other form is more commonly part of the right answer. If we can put an action noun in “regular” noun form rather than gerund form, then that is also somewhat more likely to be correct. These are not actual rules – we will not always get the question right by following these guessing procedures. But we can increase the odds that we might guess right.
Go back to a bunch of SC problems you’ve already done from one category (e.g., modifiers). Identify some splits and develop some hypotheses about how and why you would guess between those splits if you weren’t sure of the rule. Then try to apply that thinking to new SC problems in future in order to see whether your guessing strategy is valid. If it isn’t working, abandon that hypothesis and try another. (This is also something you can discuss on the forums with the experts and your fellow students.)

Take-aways
On all Sentence Correction questions:
(1) Keep track of your thinking on your scrap paper. Your first pass is to decide between “definitely wrong” and “maybe.” Your second pass is to determine which of the “maybe” choices you’re actually going to pick.
(2) Read the original question in its entirety. Unless you can pinpoint a specific error, don’t eliminate answer choice A.
(3) Whenever you find an error, immediately scan any remaining choices and eliminate those that repeat the same error.
(4) Practice making educated guesses and study how you are going to make the decision when you do have to guess.

Difference between '"As" and "Like"

Two seemingly simple words – like and as – often create havoc in the minds of test takers when they both appear in the answer choices in a sentence correction question. People wonder about the following two points:

1. For stating comparison should I use “as” or “like”?
2. When is “as + noun” correct and when is “as + clause” correct?

Lets consider for example the following GMATPrep question.

As with those of humans, the DNA of grape plants contains sites where certain unique sequences of nucleotides are repeated over and over.
A. As with those of humans, the DNA of grape plants contains sites where
B. As human DNA, the DNA of grape plants contain sites in which
C. As it is with human DNA, the DNA of grape plants, containing sites in which
D. Like human, the DNA of grape plants contain sites where
E. Like human DNA, the DNA of grape plants contains sites in which

The two main things to keep in mind to solve such questions are as follows:
Understand what meaning like and as communicate
• Understand the intended meaning of the sentence so that you can wisely choose the appropriate word.


In this article we will first discuss why there is a confusion with regards to usage of like and as. Then we will apply our knowledge in a structured step by step manner to solve the above GMATprep question.


LIKE AND AS - THE POINT OF CONFUSION

‘As’ plays multiple roles and thereby is used in different grammatical constructions, one of which coincides with how like is used.

Image

Both ‘like’ and ‘as’ are used for stating a comparison. So often people are confused whether they should use ‘like’ or ‘as’ to state the comparison. Furthermore, ‘as’ is also used to present function. And this brings us to another point of confusion. How to use 'as' correctly when presenting a comparison and when presenting a function. The table below provides the answers. Note the similarity in usage between the shaded portions.

Image

Because ‘as’ and ‘like’ are followed by nouns but they do so while presenting two different meanings, there is often a confusion regarding the intended meaning communicated by the sentence and the grammatical correctness of the sentence.

Now lets see this in detail.


LIKE AND AS -STATE COMPARISON

Both ‘like’ and ‘as’ are used to state comparisons. For example:
• Amy takes care of the children in the day care like a mother. 
• Amy takes care of the children in the day care as a mother does.
Both sentences are correct. Both the sentences above convey the meaning that Amy takes care of the children “in the same way” as a mother takes care of her children.
But notice the usage here – ‘like’ is followed by a noun and ‘as’ is followed by a clause. This grammatical construction should be kept in mind.

Image


AS - CAN ALSO PRESENT FUNCTION
Apart from stating comparison, “as” can also be used to state “role” or “function”. For example:

John has joined the organization as a researcher.

In this sentence, ‘as’ does not show a comparison. This sentence implies that John is indeed a researcher in the new organization. Notice that per this sentence John has not been compared to a researcher. John is indeed a researcher. So his role has been presented. And hence ‘as’ is used to present role or function of a person.

Notice the grammatical construction – ‘as’ has been followed by a noun. This should always be kept in mind.

Image

LIKE AND AS – CONFUSION RESOLUTION


Now that we understand the source of confusion between like and as, lets see how we can resolve this confusion. The most sure shot way of resolving this confusion is to understand from the context of the sentence whether a comparison needs to be presented or function needs to be presented. Once you determine this, then you may use like and as appropriately to state the intended meaning.

Lets take John’s example again:
John has joined the organization as a researcher.
Here is my thought process:

Step 1. I see the word “as”.

Step 2. I ask the question – “does the sentence intend to draw a comparison or state a role”?

Step 3. I answer the question from the context –
i. John has joined the organization.
ii. Lets first find out if comparison makes sense here.
• Saying that John has joined organization as a researcher does – is non-sensical. It is not a common characteristic of a researcher to join organization. So stating comparison is not logical here.
iii. Lets now find if role has been presented here.
• Saying that John will play a role of a researcher in this new organization makes perfect sense. So here as has been used to present role.

Step 4. I check if grammatically “as” has been used appropriately.
i. Yes, since “as” is used to present function, it should be followed by a noun. In this sentence “a researcher” is a noun. So correct.

Lets take another example:


John has joined Biotech industry as his brother.
Here is my thought process:
Step 1. I see the word “as”.

Step 2. I ask the question – “does the sentence intend to draw a comparison or state a role”?

Step 3. I answer the question from the context –
i. John has joined the organization.
ii. Lets first find out if comparison makes sense here.
• Saying that John has joined biotech industry as his brother did makes sense. His brother joined biotech industry and so did John. So stating comparison is logical here.
iii. Lets now make sure that stating a “role” is clearly non-sensical
• Saying that John will play a role of his own brother in biotech industry is non-sensical. What does being a brother in an industry mean? Nothing. Yes being a researcher in an industry means something but not being a brother. So notice how context drives the logical and illogical meaning.

Step 4. I check if grammatically “as” has been used appropriately.
i. No, since “as” is used to present comparison, it should be followed by a clause. In this sentence “his brother” is a noun and hence this sentence is not correct. It should be corrected in one of the following ways:
• John has joined Biotech industry as his brother did.
• John has joined Biotech industry like his brother.