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Diagnostic test -- question

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by XLogic » Sat Oct 09, 2010 5:06 pm
Hello All,

I just took the Official GMAT guide Diagnostic test (Math). And boy, I was sweating like a billy-goat!
I really need to get serious about studying.

Anyways, I was wondering if there are any short cuts to answering the question below. The guide does not explain the answer strategy properly.

Question 15. 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

Thanks for you help.

--Xlogic

PS. I did get the question right, but it took me a long time, some POE and guessing between C and D.
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by limestone » Sat Oct 09, 2010 9:05 pm
My approach:

List all prime numbers in this range:

2,3,5,7,11,13,17,19

Pair each of them:

2*5 = 10

3*7 = 21 = 10*2.1

11*19 = 10^2 * 1.1*1.9

13*17 =10^2 *1.3*1.7

The product will be: 10*10*10^2*10^2 * 2.1*1.1*1.9*1.3*1.7

=10^6 * 2.1*1.1*1.9*1.3*1.7

Take a look at the bold phrase :

1.1*1.9 is near to 2
1.3*1.7 is near to 2
2.1 is near to 2

So their product is aroud 2^3 = 8
Hence the total product is approximately equal to : 8* 10^6
Thus the answer should be 10^7.

Pick C
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by XLogic » Sat Oct 09, 2010 10:31 pm
limestone wrote:My approach:

List all prime numbers in this range:

2,3,5,7,11,13,17,19

Pair each of them:

2*5 = 10

3*7 = 21 = 10*2.1

11*19 = 10^2 * 1.1*1.9

13*17 =10^2 *1.3*1.7

The product will be: 10*10*10^2*10^2 * 2.1*1.1*1.9*1.3*1.7

=10^6 * 2.1*1.1*1.9*1.3*1.7

Take a look at the bold phrase :

1.1*1.9 is near to 2
1.3*1.7 is near to 2
2.1 is near to 2

So their product is aroud 2^3 = 8
Hence the total product is approximately equal to : 8* 10^6
Thus the answer should be 10^7.

Pick C
Well done. Thanks.

My approach was a bit crude. In the end I guessed between 10^6 and 10^7. I guess I got lucky.
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by GMATGuruNY » Sun Oct 10, 2010 3:52 am
XLogic wrote:Hello All,

I just took the Official GMAT guide Diagnostic test (Math). And boy, I was sweating like a billy-goat!
I really need to get serious about studying.

Anyways, I was wondering if there are any short cuts to answering the question below. The guide does not explain the answer strategy properly.

Question 15. 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

Thanks for you help.

--Xlogic

PS. I did get the question right, but it took me a long time, some POE and guessing between C and D.
Since the answer choices are very far apart, we can ballpark the product, and we don't have to be that exact. Every time we round one number down, let's round another number up in order to keep things balanced:

2*3*5*7*11*13*17*19 = ?
2*3*5*7 = 210 ≈ 200
11*13 ≈ 10*15 = 150
17*19 ≈ 15*20 = 300
200*150*300 = 9,000,000

Closest answer is 10,000,000 = 10^7.

The correct answer is C.

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by XLogic » Sun Oct 10, 2010 8:18 am
You guys make it look so easy. Thanks for the quick reply.
Now I just need to work on my timing.
It is taking me much too long to complete each section.

Any input is welcome.

Cheers.
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by this_time_i_will » Sun Oct 10, 2010 10:38 am
we need the value of:
2*3*5*7*11*13*17*19
=210*(10+1)*(10+3)*(10+7)*(10+9)....did a quick multiplication till the point it is easy and got 210.
=210*10*10*10*10 *(2+4+8+10)...took 10 common
=210*24*10*10*10*10
=210 has two 10s and 24 has one 10.
sp total 10s = 2+1+1+1+1+1 = 7
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