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Help with Quant Q's

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Joined: 09 Jan 2009
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Help with Quant Q's [#permalink]

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New post 24 Jan 2009, 11:10
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can someone please tell me how the following answers were derived (the practice test only gives me the answer but no explanation)
1) (1/5)^m * (1/4)^18=1/2(10)^35 Answer is m=35 ?
2) In a pet shop, 1/3 of the pets are dogs and 1/5th of the pets are birds. How many pets are dogs? The answer that "there are 20 more dogs than birds" is sufficient to answer the question by itself?
3) At college there are twice as many English majors as History majors and there are three times as many English majors as Math majors. What is the ratio of the number of History majors to the number of math majors? The answer is 3 to 2. I though it would be 6:1?
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Re: Help with Quant Q's [#permalink]

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New post 24 Jan 2009, 16:26
jaycurtis wrote:
Can someone please tell me how the following answers were derived (the practice test only gives me the answer but no explanation)
1) (1/5)^m * (1/4)^18=1/2(10)^35 Answer is m=35 ?
2) In a pet shop, 1/3 of the pets are dogs and 1/5th of the pets are birds. How many pets are dogs? The answer that "there are 20 more dogs than birds" is sufficient to answer the question by itself?
3) At college there are twice as many English majors as History majors and there are three times as many English majors as Math majors. What is the ratio of the number of History majors to the number of math majors? The answer is 3 to 2. I though it would be 6:1?

(1)
(1/5)^m*(1/4)^18 = 1/2(10)^35
(1/5)^m*(1/2)^36 = 1/2(10)^35 {since 2^2=4}
(1/5)^m*(1/2)^m*(1/2)^(36-m) = 1/2*1/(10)^35
(1/10)^m*(1/2)^(36-m) = 1/2*(1/10)^35
equate indices from both sides. i.e. equate index of (1/2) and (1/10).
left hand side =1/2*(1/5^35)*(1/2)^35 hence, m=35
(2)
you get one equation from stem:pet/3=dog, pet/5=bird; dogs = 20+birds. by substitution we can determine the answer.
(3)
english:history = 2 e/h=2
english:math = 3 e/m=3
h/m = h/e*e/m = 1/(e/h)*e/m= 1/2*3
h/m=1/(e/h)*e/m=3/2

Hope it is clear.
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Last edited by tusharvk on 26 Jan 2009, 16:27, edited 1 time in total.
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Re: Help with Quant Q's [#permalink]

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New post 25 Jan 2009, 06:22
Thanks so much. That was really helpful
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Re: Help with Quant Q's [#permalink]

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New post 26 Jan 2009, 15:02
Sorry to ask but is there anyway you can clarify the last steps that you used to solve 1 and 3.
In #1 I dont understand the last step. In #3 I was hoping you could clarify the formula that you used in the last line?

Sorry to need so much help.
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Re: Help with Quant Q's [#permalink]

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New post 26 Jan 2009, 16:23
jaycurtis wrote:
Sorry to ask but is there anyway you can clarify the last steps that you used to solve 1 and 3.
In #1 I dont understand the last step. In #3 I was hoping you could clarify the formula that you used in the last line?

Sorry to need so much help.


edited. pls see the edits.

no problem. give and take kudos.
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Re: Help with Quant Q's [#permalink]

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New post 26 Jan 2009, 22:02
jaycurtis wrote:
Sorry to ask but is there anyway you can clarify the last steps that you used to solve 1 and 3.
In #1 I dont understand the last step. In #3 I was hoping you could clarify the formula that you used in the last line?

Sorry to need so much help.


Explanation for #3.

According to the Q:
English 2 : 1 History;
English 3 : 1 Math;

Let's imagine we have 6 students that have english major.
English 6:3 History;
English 6:2 Math;
History 3:2 Math; - The answer.

Hope its clear
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Re: Help with Quant Q's [#permalink]

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New post 28 Jan 2009, 08:21
I have a few more from a practice test last night:

1) How do you get 6*square root of 2pie from square root of 72pie? What is the rule for breaking down square roots like this?

2) (3^x)-3^(x-1)=162 what does x(x-1)= the answer is 20? what is the rule for manipulating exponents with like bases but subtration?

3) How much time did it take a certain car to travel 400km?
If the car's avg speed had been 20km/hr greater than it was, it would have traveled the 400km in 1hr less time than it did. How is this sentence sufficient?
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Re: Help with Quant Q's [#permalink]

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New post 28 Jan 2009, 08:53
jaycurtis wrote:
I have a few more from a practice test last night:

1) How do you get 6*square root of 2pie from square root of 72pie? What is the rule for breaking down square roots like this?

2) (3^x)-3^(x-1)=162 what does x(x-1)= the answer is 20? what is the rule for manipulating exponents with like bases but subtration?

3) How much time did it take a certain car to travel 400km?
If the car's avg speed had been 20km/hr greater than it was, it would have traveled the 400km in 1hr less time than it did. How is this sentence sufficient?

1)=>sqrt(72*pie) = sqrt(72)*sqrt(pi) = sqrt(36*2)*sqrt(pi) = sqrt(36)*sqrt(pi)*sqrt(2)=6*remaining.
You need to break the given number into something which has integer as sqrt.
2)you need to factor it out: so
3^(x-1)*3-3^(x-1)=3^(x-1)(3-1)=162. Then find x.
3)let v be the original speed and t be the original time.
(v+20)*(t-1) = 400
vt=400 =>v=400/t
Thus, you can solve for t.
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Re: Help with Quant Q's [#permalink]

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New post 28 Jan 2009, 09:06
jaycurtis wrote:
I have a few more from a practice test last night:

1) How do you get 6*square root of 2pie from square root of 72pie? What is the rule for breaking down square roots like this?

2) (3^x)-3^(x-1)=162 what does x(x-1)= the answer is 20? what is the rule for manipulating exponents with like bases but subtration?

3) How much time did it take a certain car to travel 400km?
If the car's avg speed had been 20km/hr greater than it was, it would have traveled the 400km in 1hr less time than it did. How is this sentence sufficient?



jaycurtis,

Post one question in a thread. Do not post many questions at a time. One thread is for one question. Posting each question seperately earns multiple responses.

Read etiquette for forum participation: 7-t59508
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Re: Help with Quant Q's   [#permalink] 28 Jan 2009, 09:06
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