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).