GMAT Math

Dear all,

Please help me ! I don't know how to deal with the following questions!


Q1. Company S produces 2 kinds of stereo: Basic & Deluxe. Of the stereos produced by Company S last month, 2/3 were basic & the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all stereos?

A. 7/17
B.14/31
C. 7/15
D.17/35
E. 1/2

Ans. A


Q2. This year Henry will save a certain amount of his income , and he will spend the rest . Next year Henry will have no income , but for each dollar that he saves this year , her will have 1+r dollars available to spend . In term of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year??

A. 1/(r+2)
B. 1/(2r+2)
C. 1/(3r+2)
D. 1(r+3)
E. 1/ (2r+3)

Ans. C


Q3. If the sequence X1, X2, X3...Xn is such that X1=3 & X(n+1)=2Xn-1 for n=1, then X20- X19=?

A. 2^19
B 2^20
C. 2^21
D. (2^20) -1
E (2^21)-1

Ans. A

Q4. A certain quantity is measured on two different scales, the R-scale & the S0scale , that are related linearly. Measurements on the R-scale of 6 & 24 correspond to the measurements o the S-scale of 30 & 60 respectively. What measurement on the R-scale corresponds to the measurement of 100 on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

Ans. C

Q5. Does the decimal equivalent of P/Q, where P & Q are positive integers , contain only a finite number of nonzero digits?
(1) P>Q
(2) Q=8

Ans. E

(Why not B??)


Q6. If 1/4 of the larger of 2 number is greater than 5 times the smaller of the same 2 numbers , is the smaller number less than 4?
(1) The larger number is greater than 70.
(2) The larger number is less than 80.
Ans B.

Q7. What is the value of X^2yz+ XY^2z+ XYZ^2

(1) X+Y+Z= 18
(2) XYZ=10
ANS. C


Q8. Year 93 Revenue: 6 (billions of dollars)
Year 94 Revenue: 8 (billions of dollars)
Year 95 Revenue: 10 (billions of dollars)
Year 96 Revenue: 11.3 (billions of dollars)


The graph above shows the combine revenue , in billions of dollars, of a chain of food stores for each year over a 4-year period. In 94, a certain stores' revenue accounted for 2% of the combined revenue for that year, and in 95, the same store accounted for 2.3% of the combined revenue for that year. What was the approximate % increase in revenue for this store from 94 to 95?

A. 0.3%
B. 15%
C. 25%
D.30.4%
E.43.8%

Ans. E

Q9. What is the median number of employees assigned per project for the project at Company Z??
(1) 25% of the projects at Company Z have 4 or more employees assigned to each project.

(2) 35% of the projects at Company Z have 2 or few employees assigned to each project.

Q10. The annual interest rate earned by an investment increase by 10% from last year to this year. if the annual interest rate earned by the investment this year was 1 %, what the annual interest rate last year?
A. 1%
B. 1.1%
C.9.1%
D. 10%
E. 10.8%

Ans. C

Q11. An equilateral triangle that has an area of 9 (3)^ (1/2) is inscribed in a circle . What is the area of the circle?

A. 6 pi
B. 9 pi
C. 12 pi
D. 9pi(3)^(1/2)
E. 18 pi (3)^(1/2)

Ans C.


Best Wishes,
may

Q1. Say t = total number of stereos. Then you get that d (deluxe) = 1/3t and b (basic) = 2/3t. Now, say you spend h amount of time to produce one basic stereo. Since the total production off basic stereos was 2/3t, this means 2t/3 * h = 2th/3 hours were spent in producing the basic stereos last month.
You spend 7/5h amount of time to produce one deluxe stereo, so the total amount of time spent on producing deluxe stereos last month was t/3 *7h/5 = 7th/15.
This puts us at 2th/3 + 7th/15 = 17th/15 amount of time spent last month on producing stereos. Out of this, you spent 7th/15 to produce deluxe stereos, so the fraction you are looking for will be (7th/15)/(17th/15) = 7/17.
Answer A.

Q2. Henry saves x amount of money and he will have (1 + r)x amount of money to spend next year (r is actually the interest). Now, this year he spends total - x, or t - x, which has to be twice as much as he spends next year. This means that t - x = 2x(1 + r) or that t = x + 2x + 2xr = x (3 + 2r). Now, the fraction that Henry has to save will be (amount saved)/(total), or x/[x(3 + 2r)] = 1/(3 + 2r). Answer C.

Q3. Is this section correctly written: "X1=3 & X(n+1)=2Xn-1 for n=1"? Please double check and maybe we can do smth after that.


(to be continued)

4.) A certain quantity is measured on two different scales, the R-scale & the S0scale , that are related linearly. Measurements on the R-scale of 6 & 24 correspond to the measurements o the S-scale of 30 & 60 respectively. What measurement on the R-scale corresponds to the measurement of 100 on the S-scale?
The key word in this word problem is the word "linearly". Linearly means that this word problem can be solved by using the equation of a line. So, let's do this:
SOLUTION: (X,Y) X=R-Scale Y=S-Scale
(6,30) (24,60)

m=60-30/24-6=5/3

y-y1=m(x-x1)<--- Point slope formula of a line
y-30=5/3(x-6)
y=5x/3+20
We want to know what R-Scale value corresponds to a value of 100 on the S-Scale. So, all we do is:

100=5x/3+20 [Solve for x]
x=48

10.)The annual interest rate earned by an investment increase by 10% from last year to this year. if the annual interest rate earned by the investment this year was 1 %, what the annual interest rate last year?
Let x=the annual interest from last year. We know what the annual interest rate from last year to this year increased by 10%, so:
1.10(x)=1
x=.9090909...<--- This is the rate but it's not a percent. In order to convert the rate into a percentage, we have to multiply the rate by 100:
.909x100=approx 9.1%

For Q11, see attached diagram to help...

An equilateral triangle has 3 60 degree angles and 3 equal sides.
When inscribed in a circle, the verticies of the triangle will each touche the side of the circle and the midpoint of the circle will be on the line that is the height of the triangle, which is the midpoint from one veritice to one side, forming two 30-60-90 triangles.

Let's say that X is 1/2 length of the side of the equilateral triangle. This is also the length of the smallest side of either of the 30-60-90 triangles that make up 1.2 the equalat triangle.

For a 30-60-90 triangle, the ratio of the sides is x: x*sqrt3 : 2x, so the height of the equalat triangle is x * sqrt3

Area = 9 * sqrt3 = x * x*sqrt3
9 * sqrt3 = x^2 * sqrt3
9 = x^2
x = 3 (can't be -3, since we are dealing with a real length here).

Now, draw the radius from the center of the circle to a verticie. This will bisect the 60 degree angle at the verticie creating a small 30-60-90 triangle where the radius is the hypotenuse and x is the long side. we know x = 3 so in our 30-60-90 side ratio, 3 = x* sqrt3 so the x in the small triangle = 3 / sqrt3
The hypotenuse of this small triangle is also the radius of the circle is 2x, so is 2 * (3/sqrt3) = 6/sqrt3

Area of the circle = Pi r^2
Pi * (6/sqrt3)^2
Pi * 36/3
12Pi

Ans = C

-Carrie

PS - It would be nicer to deal with each of these in their own post.

Dear Eric, DanaJ & Carrie,

Thank you so much for your help!
I have learned a lots from all of you as I am the first time to deal with GMAT and have no idea about how to get a satisfied result!

I 'm really sorry for causing any inconvenience for asking too many questions in one post !!

I will follow the rules later!!

Anyway, I 'm very pleased that i can be a member here!!

Best Wishes,
May