Questions about Quantitative Reasoning

[donald78]

hello all,

i'm preparing for the gre and have trouble solving the following questions. can anybody tell me the answer but most importantly the associated formula?

In the sunshine, an upright pole 12 feet tall is casting

a shadow 8 feet long. At the same time, a nearby

upright pole is casting a shadow 10 feet long. If the

lengths of the shadows are proportional to the

heights of the poles, what is the height, in feet, of

the taller pole?

A 10

B 12

C 14

D 15

E 18

If c and d are positive integers and m is the greatest

common factor of c and d, then m must be the

greatest common factor of c and which of the

following integers?

A c + d

B 2 + d

C cd

D 2d

E d ^ 2

The average (arithmetic mean) of 100 measurements is 23, and the average

of 50 additional measurements is 27.

Quantity A

The average of the 150 measurements

Quantity B

25

If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is

A

m/2

B m-1

C m+1

D 2m

E m^2

btw, how do can I post images of a pdf doc?

[IRToni]

For 1:

It's simple proportionality.

length of pole A: shadow of A= length of B:shadow of B.

12:8=x:10.

x=120:8=15.

For 2:

What does it mean that m is greatest common factor of c and d? It means that c and d can both be divided by m. In addition, there's no number greater than m that is a factor in both c and d.

Let's try to look at the answers first: Clearly, B is out, since 2+d will in general not have the same factors as d.

C is out as well, since the GCF of c and cd is clearly c, which is a priori greater than m.

For the others, try putting in numbers, let's go with 9 and 15 for now.

C=9, D=15. For a: c+d=24. 9 and 24 have the GCF of three, so that would work.

For D:

Let's assume that we have c=12 and d=10 for now. You get: 2*d=20, so the GCF of 2d and c is 4, not 2. D's out.

For E:

Same example as D: You get: d^2= 100, DCF is 4.

There's a rule that says that cd and c have the same GCF as c and d as well, but I can't think of a way for you to do that in the exam without putting in numbers. When putting in numbers, remember to try different, qualitatively different numbers (e.g. if they have an answer that multiplies by two, try getting numbers where that could make a difference. These are questions that you should ignore the first time you go through the test and only come back to when you have time, since there's no formula to learn (which would enable you to answer all such questions).

3:

So, average is: you add all the numbers and divide it by the number of numbers.

In this case: you get: (100*23+50*27)/150= 24,333.

Alternatively, the faster way would be to: notice that it would be 25 is there were 75*23 and 75*25 (since 25 is exactly between 23 and 27). Since there are more 23's than 27s, it's smaller than 25, which is all you need to know.

4:

If you don't know the rule: Try putting in numbers:

(1/2)^2+(1/2)^2=1/4+(1/4)=1/2=(1/2)^1.

so x=m/2.

Hope that helps. If you have any more questions, feel free to ask.

[donald78]

perfect, now i have no problem solving these questions. thank you very much!