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by theCodeToGMAT » Tue Oct 22, 2013 3:07 am
3 + 2x3^1 + 2 X 3^2 + 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 + 2 X 3^7

3 + 2 ( 3^1 + 3^2 .... 3^7)

3 + 2 ( 3(3^7 - 1)/2) [using GP Sum formula]

3 + 3^8 - 3

3^8
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by [email protected] » Tue Oct 22, 2013 3:29 am
:(

Dint get the solution if u take 3+2 as common wnt u keep 1 in its position (within the bracket)? why haven't u added 1?


theCodeToGMAT wrote:3 + 2x3^1 + 2 X 3^2 + 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 + 2 X 3^7

3 + 2 ( 3^1 + 3^2 .... 3^7)

3 + 2 ( 3(3^7 - 1)/2) [using GP Sum formula]

3 + 3^8 - 3

3^8
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by theCodeToGMAT » Tue Oct 22, 2013 3:38 am
Follow the Underlined & Bold Texts

3 + 3 + 3 + 2 X 3^2 + 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 + 2 X 3^7

3 + 2x3^1 + 2 X 3^2 + 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 + 2 X 3^7

3 + 2x3^1 + 2 X 3^2 + 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 + 2 X 3^7

3 + 2 ( 3^1 + 3^2 .... 3^7) [ GP => 3^1 + 3^2 .... +3^7]

Sum of GP = a(((r^n)-1)/(r-1))

Here, A = 3^1 , r = 3 , n = 7

So, 3 + 2 ( 3(3^7 - 1)/2)

3 + 3^8 - 3

3^8

Is it now better?
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by GMATGuruNY » Tue Oct 22, 2013 4:41 am
[email protected] wrote:3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =

A. 3^7
B. 3^8
C. 3^14
D. 3^28
E. 3^30

Ans-B
Always look at the answer choices BEFORE you start to work.
Here, the answer choices are SPREAD OUT.
Thus, we can quickly BALLPARK the correct answer.
Since the greatest term = 2 * 3�, the sum of ALL the terms must be GREATER than 3�.
Eliminate A.

2 * 3� = 2 * 3³ * 3� = 2 * 27 * 81 ≈ 60*80 = 4800.
2 * 3� = (2 * 3�)/3 = 4800/3 = 1600.
2 * 3� = (2 * 3�)/3 ≈ 1600/3 ≈ 500.
The terms to the left of 2 * 3� will be relatively small and thus will have little effect on the final sum.
Thus, the correct answer ≈ 4800+1600+500 = 7000.

Look at the remaining answer choices.
C: 3¹� = 3� * 3� * 3� * 3² = 81*81*81*9 ≈ 80*80*80*10.
Thus, answer choices C, D and E are WAY too big.

The correct answer is B.
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by [email protected] » Tue Oct 22, 2013 7:13 am
Dint get how u derive this step:

2* 3� = 2 * 3³ * 3� = 2 * 27 * 81 ≈ 60*80 = 4800.
2 * 3� = (2 * 3�)/3 = 4800/3 = 1600.
2 * 3� = (2 * 3�)/3 ≈ 1600/3 ≈ 500.
The terms to the left of 2 * 3� will be relatively small and thus will have little effect on the final sum.



GMATGuruNY wrote:
[email protected] wrote:3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =

A. 3^7
B. 3^8
C. 3^14
D. 3^28
E. 3^30

Ans-B
Always look at the answer choices BEFORE you start to work.
Here, the answer choices are SPREAD OUT.
Thus, we can quickly BALLPARK the correct answer.
Since the greatest term = 2 * 3�, the sum of ALL the terms must be GREATER than 3�.
Eliminate A.

2 * 3� = 2 * 3³ * 3� = 2 * 27 * 81 ≈ 60*80 = 4800.
2 * 3� = (2 * 3�)/3 = 4800/3 = 1600.
2 * 3� = (2 * 3�)/3 ≈ 1600/3 ≈ 500.
The terms to the left of 2 * 3� will be relatively small and thus will have little effect on the final sum.
Thus, the correct answer ≈ 4800+1600+500 = 7000.

Look at the remaining answer choices.
C: 3¹� = 3� * 3� * 3� * 3² = 81*81*81*9 ≈ 80*80*80*10.
Thus, answer choices C, D and E are WAY too big.

The correct answer is B.
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by [email protected] » Tue Oct 22, 2013 12:00 pm
Hi shibsriz,

This question is more about how you "see and organize" your math than about doing calculations.

Here's a quick note before we begin: X + 2X = 3X. Remember this idea (combining like terms) as we work through this question.

3 + 3 + 3 = 9 = 3^2

What's 3^2 + 2(3^2)?.....3(3^2)

What's 3(3^2)? (3^1)(3^2) = 3^3
-------------
What's 3^3 + 2(3^3)?.......3(3^3)

What's 3(3^3)? (3^1)(3^3) = 3^4
------------
What's 3^4 + 2(3^4)?.......3(3^4)

What's 3(3^4)? (3^1)(3^4) = 3^5
-----------
etc.

The final line of this "string" is....

3^7 + 2(3^7) = 3(3^7) = 3^8

Final Answer: B

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