G tips

绝望的小老鼠

quote: You surely don't know whether you are right or wrong when you are wrong.

QUANT session

ground floor：  PS--  be 100 percent sure
first floor：        PS--  exponent problems（high score problem type）
2nd floor：       PS--  roots（errors）
3rd floor:          PS--  extra equation strategy (errors)


#6:                   PS--Extra Combinatorics & Probability (errors)

绝望的小老鼠

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40 percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer’s gross profit from the purchase and the sale of the desk?
A. $40
B. $60
C. $80
D. $90
E. $100

the answer: E

This question plays upon a common issue in percent questions on the GMAT: a percent is always taken OUT of something, and it is imperative that you answer this very important question whenever you deal with percents: What is this percent taken FROM?

In the case of the question above, the markup is 40% of the selling price. Not of $150 (the purchase price), but of a selling price, as yet unknown. How do we determine the selling price? The selling price is composed of the purchase price (=$150), plus a markup that is 40 percent of itself. From this, we learn that the purchase price is the remaining 60 percent of the selling price. Say that out loud:

[size=12.800000190734863px]$150 is 60 percent of the selling price.

绝望的小老鼠

Different Bases, Multiplication or Division
If , what is the value of x?

[size=12.800000190734863px]When you see different bases and multiplication ordivision, the key is to break the bases down to prime factors. Here’s what you’ll get if you break each number in the problem down to prime factors:

[size=12.800000190734863px]

[size=12.800000190734863px]

so


Same Bases, Addition or Subtraction
If , what is the value of x?

When you see the same base and addition orsubtraction, you can factor out. you can take out the greatest common factor, ，and .




Here is another tough example:

What is the sum of the distinct prime factors of ?

[size=12.800000190734863px]Once again, we can factor out.

[size=12.800000190734863px]

[size=12.800000190734863px]

[size=12.800000190734863px]So the greatest common factor is .

[size=12.800000190734863px] and  

[size=12.800000190734863px]If we were to write the prime factorization of this number, it would be:

[size=12.800000190734863px].

[size=12.800000190734863px]So the distinct prime factors are 2 and 7 (distinct means different), and the sum of the distinct prime factors is 9.

drill:

绝望的小老鼠

notice the estimation technique!

绝望的小老鼠

pay attention to the given information! And be accurate when calculating!  The third query gives a smarter solution, study and learn it.

绝望的小老鼠

When the problem of combinatiorics is in disguise, it appears like this:

绝望的小老鼠

求问一道题~~

答案是C