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The product of the first seven positive multiples of three is closest

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The product of the first seven positive multiples of three is closest [#permalink]

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New post 10 Jan 2012, 07:28
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Difficulty:

  55% (hard)

Question Stats:

55% (01:21) correct 45% (01:10) wrong based on 97 sessions

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The product of the first seven positive multiples of three is closest to which of the following powers of 10?

(A) \(10^9\)
(B) \(10^8\)
(C) \(10^7\)
(D) \(10^6\)
(E) \(10^5\)

How to solve it in less than two minutes?
[Reveal] Spoiler: OA

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Re: The product of the first seven positive multiples of three is closest [#permalink]

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New post 10 Jan 2012, 10:44
The product will be 3^7 * 1 * 2 * 3 * 4 * 5 * 6 * 7
=3^7 * 5140
= 9^3 * 15420
= ~135000 * 9 * 9
= ~1220000 * 9
= ~11000000 which is very close to 10^7

The correct answer is therefore (C)
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Re: The product of the first seven positive multiples of three is closest [#permalink]

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New post 10 Jan 2012, 20:07
GyanOne wrote:
The product will be 3^7 * 1 * 2 * 3 * 4 * 5 * 6 * 7
=3^7 * 5140
= 9^3 * 15420
= ~135000 * 9 * 9
= ~1220000 * 9
= ~11000000 which is very close to 10^7

The correct answer is therefore (C)


I could not understand the question. Can you please help me on that. According to me the product must be only 3^7.

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Re: The product of the first seven positive multiples of three is closest [#permalink]

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New post 10 Jan 2012, 20:21
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subhajeet wrote:
I could not understand the question. Can you please help me on that. According to me the product must be only 3^7.


Multiples of 3: 3*-2, 3*-1, 3*1, 3*2, 3*3 and so on....
first seven positive multiples of three: 3, 6, 9, 12, 15, 18, and 21

Multiply them all, and you will get (since each of the seven multiples have one '3'): 3^7 * (1*2*3*4*5*6*7) = (3^7)*(7!)
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Re: The product of the first seven positive multiples of three is closest [#permalink]

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New post 10 Jan 2012, 21:56
I took a bit of a gamble.

I quickly took the first seven positive multiples of 3:

3
6
9
12
15
18
21

At a quick glance, I determined that the final product would probably be a seven-digit number. Hence, C.

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The product of the first seven positive multiples of three is closest [#permalink]

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New post 04 Jan 2018, 14:19
solved using approximation may not always work

(3, 6) = 18
(9) = 10 (approx)
(12, 15) = 180
(18, 21) = (20 x 20) = 400 approx

180 * 180 * 400 = 324 * 4 * 10000
still approximating = 300 * 4 * 10000 = 12000000 = approx
closest is \(10^7\)

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The product of the first seven positive multiples of three is closest   [#permalink] 04 Jan 2018, 14:19
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