5 PS answer explanation needed / GMATPrep Test 1

[kourousafama]

Hi,

Could anyone help with the 5 attached PS questions answer explanation.
I have just past the GMATPrep Test 1 and would like to understand how I could have got these questions right.

Many thanks.

[kmittal82]

Hi Kourousafama,

Can you please post one question per topic in the future?

Question 1

1/(5)^m x 1/(4)^18 = 1/(2x(10)^35)

Lets inverse everything first

5^m x 4^18 = 2 x (10)^35

=> 5^m x 2^36 = 2 x 2^35 x 5^35 (4 = 2^2 and 10 = 2x5)

=> 5^m x 2^36 = 2^36 x 5^35

=> m = 35

[kmittal82]

Question 2:

The key is to realise that ABC is a right triangle, with ABC = 90

Area = 1/2 x BC x AC

= 1/2 x 1 x 2 = 1

[kmittal82]

Question 3

Let selling price = x

Markup = 0.4x

We get the equation:

x = 150 + 0.4x => x = 250

Thus, SP = 250, CP = 150, thus profit = 250 - 150 = 100

[kmittal82]

Question 5

Let # history majors = x

Thus, #English majors = 2x

# Mathematics majors = (2/3)x

Ratio history : maths = x : 2/3x = 3:2

[kmittal82]

Question 4:

Time taken by 6 machines to finish the work = 12 days

Let time taken by 1 machine = T. Now, Rate = 1/ time, and rates are additive

6/T = 1/12 => T = 72 [ 1/T + 1/T + 1/T + 1/T + 1/T + 1/T = 1/12]

So each machine takes 72 days to finish the work on it own

Number of machines needed to finish the work in 8 days = 72/8 = 9

Thus, #extra machines needed = 9 - 6 = 3

[Gurpinder]

Hello Mittal,

can you please explain the following part:

=> 5^m x 2^36 = 2 x 2^35 x 5^35 (4 = 2^2 and 10 = 2x5)


this is what i am doing and I don't understand how you got to yours.

(1/5^m)(1/4^18) = ..... since 5 and 4 = 20, i am just subtracting 18 from 35. hence I got 17 which is wrong.

[Gurpinder]

Question 3

Let selling price = x

Markup = 0.4x

We get the equation:

x = 150 + 0.4x => x = 250

Thus, SP = 250, CP = 150, thus profit = 250 - 150 = 100

Hey,

Where did you get the 250 from?

[clock60]

Question 2:

The key is to realise that ABC is a right triangle, with ABC = 90

Area = 1/2 x BC x AC

= 1/2 x 1 x 2 = 1

i have little doubt about right answer here
i agree that triangle ABC right triangle with ABC=90
but to me the area =1/2*base(BC)*leg(AB)=1/2*1*(3^1/2)=(3^1/2)/2. it is not hypotenuse*base as in above solution
what i am missing here?

[Baten80]

Hello Mittal,

can you please explain the following part:

=> 5^m x 2^36 = 2 x 2^35 x 5^35 (4 = 2^2 and 10 = 2x5)


this is what i am doing and I don't understand how you got to yours.

(1/5^m)(1/4^18) = ..... since 5 and 4 = 20, i am just subtracting 18 from 35. hence I got 17 which is wrong.

Let Know:
5^m x 2^36 = 2 x 2^35 x 5^35 (4 = 2^2 and 10 = 2x5)[/b]

= 5^m x 2^36=2^1 x 2^35 x 5^35
=5^m x 2x36=2^36 x 5^35
so, m=35

[kmittal82]

Question 3

Let selling price = x

Markup = 0.4x

We get the equation:

x = 150 + 0.4x => x = 250

Thus, SP = 250, CP = 150, thus profit = 250 - 150 = 100

Hey,

Where did you get the 250 from?

x = 150 + 0.4x
=> x - 0.4x = 150
=> 0.6x = 150
=> x = 150/0.6 = 250

Hope thats clear

[kmittal82]

Question 2:

The key is to realise that ABC is a right triangle, with ABC = 90

Area = 1/2 x BC x AC

= 1/2 x 1 x 2 = 1

i have little doubt about right answer here
i agree that triangle ABC right triangle with ABC=90
but to me the area =1/2*base(BC)*leg(AB)=1/2*1*(3^1/2)=(3^1/2)/2. it is not hypotenuse*base as in above solution
what i am missing here?

Crap, thanks for the correction clock, you are right I multiplied the hypotenuse by mistake (Glad this is not the real test day!)

Your answer is correct, I apologise for my mistake.