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# The product of all the prime numbers less than 20 is closest

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Intern
Joined: 07 Dec 2009
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The product of all the prime numbers less than 20 is closest [#permalink]

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20 Jan 2010, 06:27
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Difficulty:

75% (hard)

Question Stats:

49% (00:59) correct 51% (01:13) wrong based on 201 sessions

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The product of all the prime numbers less than 20 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html

ALL OG13 QUESTIONS WITH SOLUTIONS ARE HERE: the-official-guide-quantitative-question-directory-143450.html
[Reveal] Spoiler: OA

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Manager
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20 Jan 2010, 08:12
The primes < 20 are 2,3,5,7,11,13,17,19. I would round up/down and estimate using 2,3,5,10,10,10,20,20.

So I have 30x 10^5 = 10^1 x 10^5 = 10^6

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Concentration: General Management, Strategy
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22 Jan 2010, 10:12
1
KUDOS
used the same approach as mr. black but he forgets to use 2s out of last two factors. so it should be 30x4x10^5 = 10^2 x 10^5 = 10^7

IMO the OA is C

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Intern
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Properties of number question from GMAT Review 12th Edition [#permalink]

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18 Apr 2010, 23:54
Question 15 on GMAT Review Diagnostic Test

The product of all the prime numbers less than 20 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

The solution in the book makes you CALCULATE the exact number then compare it to the answers, very time consuming without a calculator.

BTW - Are questions in the diagnostic test harder than normal GMAT questions? Or are they the hardest in each category? I find them so much harder than the regular CAT test.

[Reveal] Spoiler:
OA: C

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Manager
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Re: Properties of number question from GMAT Review 12th Edition [#permalink]

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19 Apr 2010, 08:15
If you do the calculation using estimation and rounding, it's actually not too bad.

Yes, there are some difficult questions in the diagnostic test, and they get progressively more difficult throughout the section. They seem to be more "model" GMAT questions than the ones that actually appear on the exam. In order words, they lend themselves to solving easily using methods and tricks. That's not always true on the exam itself.
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Re: Properties of number question from GMAT Review 12th Edition [#permalink]

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19 Apr 2010, 23:16
thanatoz wrote:
Question 15 on GMAT Review Diagnostic Test

The product of all the prime numbers less than 20 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

The solution in the book makes you CALCULATE the exact number then compare it to the answers, very time consuming without a calculator.

BTW - Are questions in the diagnostic test harder than normal GMAT questions? Or are they the hardest in each category? I find them so much harder than the regular CAT test.

[Reveal] Spoiler:
OA: C

this one can be done easily as shown below.
the prime numbers <20 are 2,3,5,7,11,13,17,19
taking the product of two at a time, we get 6, 35, 77, 221 and 19
on further applying this method of rounding and approximating, we see that the product nears 10^7
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CHEERS
fivezero7

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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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26 Sep 2013, 07:54
melissawlim wrote:
The product of all the prime numbers less than 20 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

Official Guide 12 Question

 Question: 15 Page: 22 Difficulty: 700

Find All Official Guide Questions

Video Explanations:

Hi Bunnuel,

Any thoughts on this one?

Cheers!

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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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26 Sep 2013, 08:17
jlgdr wrote:
melissawlim wrote:
The product of all the prime numbers less than 20 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

Official Guide 12 Question

 Question: 15 Page: 22 Difficulty: 700

Find All Official Guide Questions

Video Explanations:

Hi Bunnuel,

Any thoughts on this one?

Cheers!

The product of all the prime numbers less than 20 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

We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.

# of different approximations are possible.

Approach #1:

2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);

$$2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}$$.

Approach #2:

2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)

$$2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html

ALL OG13 QUESTIONS WITH SOLUTIONS ARE HERE: the-official-guide-quantitative-question-directory-143450.html

_________________

Kudos [?]: 132619 [0], given: 12326

Re: The product of all the prime numbers less than 20 is closest   [#permalink] 26 Sep 2013, 08:17
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