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5 PS answer explanation needed / GMATPrep Test 1

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by kourousafama » Thu Aug 12, 2010 5:29 am
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.

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by kmittal82 » Thu Aug 12, 2010 5:59 am
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
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by kmittal82 » Thu Aug 12, 2010 6:00 am
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
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by kmittal82 » Thu Aug 12, 2010 6:02 am
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
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by kmittal82 » Thu Aug 12, 2010 6:06 am
Question 5

Let # history majors = x

Thus, #English majors = 2x

# Mathematics majors = (2/3)x

Ratio history : maths = x : 2/3x = 3:2
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by kmittal82 » Thu Aug 12, 2010 6:12 am
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
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by Gurpinder » Thu Aug 12, 2010 8:28 am
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.
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
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by Gurpinder » Thu Aug 12, 2010 8:37 am
kmittal82 wrote: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?
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- Alfred A. Montapert, Philosopher.
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by clock60 » Thu Aug 12, 2010 9:18 am
kmittal82 wrote: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?
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by Baten80 » Thu Aug 12, 2010 9:21 am
Gurpinder wrote: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
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by kmittal82 » Thu Aug 12, 2010 9:49 am
Gurpinder wrote:
kmittal82 wrote: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
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by kmittal82 » Thu Aug 12, 2010 9:51 am
clock60 wrote:
kmittal82 wrote: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!) :D

Your answer is correct, I apologise for my mistake.
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