DS: InEqualities

Question:




Solution:

First, the question asks: is |x - z| + |x| = |z|. I find this easiest to think about if I understand what the equation says about distances. Remember that |a - b| is just the distance between a and b on the number line, and |a| is the distance from a to zero. So |x - z| + |x| = |z| just says "the distance between x and z plus the distance from x to zero is equal to the distance from z to zero". How can this happen? Draw a number line, try placing x and z in different orders and on either side of zero, and you can see that this can only happen in two ways:

z < x < 0
0 < x < z

So the question is just asking- can we be sure that one of the above inequalities is true?

Before looking at the statements, we know that zy < xy < 0. What does this tell us?

-Either y is negative, and both x and z are positive, or y is positive, and both x and z are negative.

-Because zy - xy <> x. If y is positive, z-x must be negative, and z < x (and, conversely, if z < x, y must be positive).

Okay, that was the tough part. Let's look at the statements:
1) z < x

If z < x, we know that y must be positive. If y is positive, x and z are both negative. So we know that z < x <0, and the answer to the question must be yes.

2) y > 0

If y is positive, well, this is exactly the same situation as we had with Statement 1.

Answer is D.

Link: http://www.beatthegmat.com/gmat-prep-t13180.html

SC: Griffith's cameraman Blitzer

Griffith's cameraman Blitzer was a mechanical wizard, and what skill was lacking in his visual composition was more than compensated by his ability to combine gadgets and props to produce the required cinematic effects.
(A) what skill was lacking in his visual composition was more than compensated by
(B) what skills he was lacking in visual composition, he more than compensated for in
(C) whatever his visual composition lacked, he more than compensated in
(D) whatever skills he lacked in visual composition, he more than compensated for by
(E) he more than compensated his lack of visual composition with

Solution:-

A) --> "Compensated By" -> Incorrect Idiom
B) --> "Compensated for" -> Correct Idiom. So it is CORRECT CHOICE
C) --> Altered Meaning. He lacked the skill of visual composition, not his visual composition lacked any skills.
D) --> Sounds good but "for by" is pinching to me.
E) --> [Though I am not still sure about the reason of omitting this option] trying to compare two different things. "Lack of visual composition" is not something that we can compare with his ability. I guess, it should be treated as "flaw" rather than "skills".

SC [An unusually strong cyclist]

An unusually strong cyclist can, it is hoped, provide enough power to set a new distance record for human-powered aircraft in MIT's diaphanous construction of graphite fiber and plastic.

(A) can, it is hoped, provide enough power to set
(B) it is hoped, can provide enough power that will set
(C) hopefully can provide enough power, this will set
(D) is hopeful to set
(E) hopes setting

Solution:

B - "provide enough power that will set" is unidiomatic. Better to say "enough power to set"
C - You have two independent clauses here: "An unusually strong...enough power" and "this will set a...fiber and plastic". Yet, only a comma connects the two. No good! You must have a conjunction or semicolon there to "glue" the two clauses together. A comma alone is never enough.
D - This is unidiomatic, too. Better to say "hopes to set." Also, this construction changes the meaning of the sentence -- the focus now is on a particular cyclist setting a record, whereas in the original sentence the issue was about enough power being generated by a cyclist in order to set the record.
E - Change in meaning as in D. Also, "hopes to set" over "hopes setting".

The correct answer is A.

NOTE: Always check the option seems to be correct should not change the meaning of original sentence.
I chose "D".

DS: Which is greatest?

Which is the greatest among x,y and z ?

1. x:y:z=3:4:5
2. xyz-y^2 is a positive integer

Solution:

1. x:y:z=3:4:5
This statement tell us about the magnitude of x, y and z but nothing about the sign. If all are positive numbers z is greatest, if all the negative z is smallest. INSUFFICIENT

2. xyz - y^2 is a positive integer
Do not oversimplify this! Y^2 is always positive. If we have (something) - positive = positive, then we know that something is positive and bigger in magnitude than what is subtracted. INSUFFICIENT

Combine the two, we know that z has the biggest magnitude and all the numbers are positive, thus Z is greatest.

The answer is (C).

Remember:

1. Do not forget to consider the impact of negative factor on the given equation.
2. In any relation like aX:bY:cZ, the value of variable (X, Y, Z) would be greater for which factor is greatest (a, b, c). This is only when all the factors are positive.

For example, X:3Y:5Z means Z is greatest in case X, Y and Z are positive in nature.

OG-11 CR [Benchmarking, identifying the exception]

One way to judge the performance of a company is to compare it with other companies. This technique, commonly called “benchmarking,” permits the manager of a company to discover better industrial practices and can provide a justification for the adoption of good practices.

Any of the following, if true, is a valid reason for benchmarking the performance of a company against companies with which it is not in competition rather than against competitors EXCEPT:

(A) Comparisons with competitors are most likely to focus on practices that the manager making the comparisons already employs.
(B) Getting “inside” information about the unique practices of competitors is particularly difficult.
(C) Since companies that compete with each other are likely to have comparable levels of efficiency, only benchmarking against noncompetitors is likely to reveal practices that would aid in beating competitors.
(D) Managers are generally more receptive to new ideas that they find outside their own industry.
(E) Much of the success of good companies is due to their adoption of practices that take advantage of the special circumstances of their products or markets.

Solution:

The question asked is ambiguous in nature. So read it carefully. Once you what is demanded then its easier to solve most of the questions. It actually asked to identify the statement which states that benchmarking to be done or done with the competitors rather than non competitors.

Statement (A): Against doing the comparison with competitors.
Statement (B): Again trying to say that benchmarking with competitors is extremely difficult.
Statement (C): Asking to do benchmarking with non competitors.
Statement (D): Asking to adopt idea outside their industry (i.e. non competitors).
Statement (E): Saying that success is employed by studying their products or market. (It means that benchmarking to be done with competitors). So this is correct statement which is exception to the requirement.

CR: A more than B type question [OG 10, Q 46]

Kale has more nutritional value than spinach. But since collard greens have more nutritional value than lettuce, if follows that kale has more nutritional value than lettuce.

Any of the following, if introduced into the argument as an additional premise, makes the argument above logically correct EXCEPT:
A. Collard greens have more nutritional value than kale
B. Spinach has more nutritional value than lettuce
C. Spinach has more nutritional value than collard greens
D. Spinach and collard greens have the same nutritional value
E. Kale and collard greens have the same nutritional value

Solution:

The above question states that K > S and C > L which leads that K > L

We need to identify the statement which state K < L.

On checking statements

Statement A, C > K and C > L (but it doest not mean that K > L. Therefore Kale may or may not has more nutritional value as compare to lettuce.)
Statement B, S > L and as K > S therefore, K > L
Statement C, S > C and as K > S therefore, K > L
Statement D, S > C and as K > S therefore, K > L
Statement E, K = C and as C > L therefore, K > L

Hence statement (A) is the desired answer.

DS: Odds/Evens problem

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

(1) t – p = p – m

(2) t – m = 16

Solution:

"For a product of integers to be even, at least one of those integers needs to be even. So the question is asking: is either one of m, p, or t even ? "

That is exactly what we look for.

(1)
t - p = p - m
t = 2p - m

-don't know if p is even or odd, but 2p is even.
-don't know if m is even or odd
t = 2p - even = even
t = 2p - odd = odd
N/S

(2)
t - m = 16
t = 16 +m
-don't know if m is even or odd
t = 16 + odd = odd
t = 16 = even = even
N/S

(1) and (2)

t = 2p - m
t = 16 + m

2p - m = 16 + m

16 = 2(p - m)
8 = p - m

-don't know whether p or m are even or odd.

N/S

DS [Algebra]

If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value
of c?
(A) d = 3
(B) b = 6

Solution:

Resolving the equation produces
bx +c = 2dx + d^2 for all values of x.

Point to remember:

Here we can equate co-efficient of x and constants.
i.e. b = 2dx and c = d^2

Now the question is pretty easy to solve, and both the statements alone are sufficient to deduce the correct answer.

Manhattan CAT # 4 (Percentage Increase)

Question:

If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?

A) (10,000z + 100z(x – y) – xyz) /10,000

B) (10,000z + 100z(y – x) – xyz) /10,000

C) (100z(x – y) – xyz) /10,000

D)(100z(y – x) – xyz)/10,000

E) (10,000)/100yz + xy

Solution:

Start with z.

z dollars was marked up by x percent:

z * (100 + x)/100
e.g. marked up by 20% is the same as multiplying by (100 + 20)/100 = 120/100 = 1.2


Then it was discounted by y percent:

z * (100 + x)/100 * (100 - y)/100
e.g. discounted by 20% is the same as multiplying by (100 - 20)/100 = 80/100 = 0.8


Calculate the final price by multiplying through:
z * (100 + x)/100 * (100 - y)/100
-> z * [(100 + x)*(100 - y)]/10000
--> z * (10000 - 100y + 100x - xy)/10000
---> (10000z - 100yz + 100xz - xyz)/10000
----> (10000z + 100z(x-y) - xyz)/10000

Original Post Link

CR [Unknown]

(1) All A are B.
(2) Some B are C.

Which of the following is true?
(A) All A are C.
(B) No A are C.
(C) Some A are C.
(D) No C are A.
(E) None of the above.

Solution:

Venn diagrams are one way we can keep track of this type of information.

Let's examine the two rules we have:

(1) all A are B.

From this, we know that if something is A, it's also B.

(2) Some B are C.

From this, we know that there's at least one B that's also C.

If we put the two statements together, we don't know anything for sure. Could some A also be C? Sure, but it's not definite.

Let's use a real-life example to make that clear:

All Dogs are Mammals.

Some Mammals are Cats.

Does this mean that some dogs are cats? Of course not!

Link to the actual post: http://www.beatthegmat.com/cr-question-t9070.html

Introduction

Everyday we use to solve GMAT problems either may be hosted at some website or may be done with some workbook. We are supposed to make the flash card to remember these entire problems (better say techniques) so that we can keep on revising them to beat the GMAT. But what I could figure out that making flash card is little bit cumbersome for me and retouching with the original problem would help me a lot rather than just revising through flash cards. Everyone has their own techniques. So, I just thought to make an online collection of those problems that troubled me a lot while solving them.

It may seems as I just duplicating the online resources and materials which could be directly used from the source website itself but the thing is like other I have also different skill sets. The thing that seems simple to you that may be tough for me and vice-versa. So, It's pretty clear that I need to collect those problems or area of problems that I find most difficult.

Strong Skills: (All logic problems)
Average Skills: CR, Quants (Probability, Venn diagrams, P&C)
Weak Points: RC and SC
Not ever touched: AWA

Although I have not started my actual GMAT preparation due to some unavoidable circumstance till the end of April 08, but still I am solving the problems hosted at http://www.beatthegmat.com whenever I get some time to solve them.

I am making a list of these problems (firstly to make DB for myself) and hosting it publicly to help others. Using it or not is always at the end up to you.

I have started making on off line word document at the moment and will be updating this blog at every Monday.

Thanks....
BTG760

Target score: 760+
Starting date of preparation: 1st May 08
Test Date: Somewhere between Aug 08 to Nov 08 (not decided yet, it would depend upon my preparation).