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# Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS

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Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS [#permalink]  23 Jun 2008, 13:21
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Hi All!

I am taking the GMAT tomorrow .

I'm doing fine with on the "harder" MGMAT quant questions but am running into some small "simple" problems on the GMAT Prep that are hurting my score.

Please provide explanations for the following:

1. If (1/5)^m * (1/4)^18 = 1/[(2)(10)^35], what is the value of m?

2. What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8?

The answer is 2^9. I can find the answer by doing the long work but would like to know if someone knows a fast way to do it.

3. The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (NOTE: 1kg = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

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Re: Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS [#permalink]  23 Jun 2008, 13:40
quote="JovanneMBA"]Hi All!

I am taking the GMAT tomorrow .

I'm doing fine with on the "harder" MGMAT quant questions but am running into some small "simple" problems on the GMAT Prep that are hurting my score.

Please provide explanations for the following:

1. If (1/5)^m * (1/4)^18 = 1/[(2)(10)^35], what is the value of m?

(1/4)^18 = 1 / (2^36) = 1 / (2*2^35)
(1/5)^m * (1/4)^18 = [1/(5^m * 2 * 2^35)] = 1/[(2)(10)^35] which makes m = 35

2. What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8?

The answer is 2^9. I can find the answer by doing the long work but would like to know if someone knows a fast way to do it.

4 (1+1+2+4+8+16+32+64) = 4(128) = (2^2)(2^7) = 2^9

3. The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (NOTE: 1kg = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

1 cubic meter = 1,000,000 cubic centimeters; 800 kg = 800,000 grams
1,000,000 cubic centimeters / 800,000 grams = 1.25 cubic centimeters / 1.25 grams (divide 1,000,000 by 800,000)
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Re: Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS [#permalink]  23 Jun 2008, 13:46
1. If (1/5)^m * (1/4)^18 = 1/[(2)(10)^35], what is the value of m?

(10)^35 = (2*5)^35 = 2^35 * 5^35
(2)(10)^35 = 2 * 2^35 * 5^35 = 2^36 * 5^35
1/[(2)(10)^35] = 2^-36 * 5^-35

2^-36 = 2^-2*18 = 4^-18
(1/4)^18 = 4^-18
(1/5)^m = 5^-m
(1/5)^m * (1/4)^18 = 5^-m*4^-18
5^-m*4^-18 = 4^-18*5^-35
=> -m = -35
=> m = 35

2. What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8?
This is a GP series a + ar + ar^2 + ar^3 + ...
Sum of GP Series = a (1-r^n)/(1-r) Where a is first term, r is common factor between each successive terms and n is number of terms.
In this case we have a = 1, r = 2, n = 9 (I think your series start with 2^0 or 1 and not 2)
So Sum = 1 * (1 - 2^9) / (1-2) = 2^9 (approximately, 1 is too small in comparison to 2^9)

The answer is 2^9. I can find the answer by doing the long work but would like to know if someone knows a fast way to do it.

3. The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (NOTE: 1kg = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

800*1000 Gram = 1000000 cubic centimeter
1 Gram = 1000000/800*1000 = 10/8 = 1.25

Hope this helps.
Best of luck for your exam.
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Re: Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS [#permalink]  23 Jun 2008, 14:04
lucyqin wrote:
quote="JovanneMBA"]Hi All!

2. What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8?

The answer is 2^9. I can find the answer by doing the long work but would like to know if someone knows a fast way to do it.

I think the question is correct
it goes like..2^a + 2^a=2^(a+1)..

so 2+2=2^2...

2^2+2^2=2^3
2^3+2^3=2^4..and so on until you get 2^8+2^8=2^9
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Re: Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS [#permalink]  24 Jun 2008, 03:24
abhijit_sen wrote:
2. What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8?
This is a GP series a + ar + ar^2 + ar^3 + ...
Sum of GP Series = a (1-r^n)/(1-r) Where a is first term, r is common factor between each successive terms and n is number of terms.
In this case we have a = 1, r = 2, n = 9 (I think your series start with 2^0 or 1 and not 2)
So Sum = 1 * (1 - 2^9) / (1-2) = 2^9 (approximately, 1 is too small in comparison to 2^9)

There is no approximation.

The formula is in fact $$1 + r + r^2 + r^3 + ... + r^n = \frac{1-r^n^+^1}{1-r}$$

In this case : $$2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 1 + [ 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 ] = 1 + \frac{1-2^8^+^1}{1-2} = 1 - ( 1 - 2^9 ) = 2^9$$(exactly)
Re: Taking GMAT Tomorrow - NEED HELP WITH A FEW PROBLEMS   [#permalink] 24 Jun 2008, 03:24
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