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O.G 12 Question

by sachin_yadav » Thu Apr 14, 2011 12:40 pm
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

Answer is C

The book says the product of the prime numbers = 9,699,690 is closest to 10^7. But i found this method as time consuming. Is there any fast method to solve this question ?

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Sachin
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by Ian Stewart » Thu Apr 14, 2011 1:10 pm
sachin_yadav 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

The book says the product of the prime numbers = 9,699,690 is closest to 10^7. But i found this method as time consuming. Is there any fast method to solve this question ?
The instant you see the phrase 'closest to' in the question, you can be sure they are testing your ability to estimate. You'd certainly lose a lot of time if you actually completed the multiplication exactly. When I'm estimating, I first look at the answer choices to get some idea of how precise an estimate I need. Here, the answers are *very* far apart (10^8 is 10 times bigger than 10^7, for example), so even if we make a very rough estimate, we'll still be able to easily pick the right answer. There are many ways to continue at this point; for example:

2*5 is equal to 10
3*7 is roughly 20
11 is roughly 10
13 is roughly 10
17 is roughly 20
19 is roughly 20

Notice that if I round some numbers down, I round others up to compensate somewhat. So our product should be fairly close to 10*20*10*10*20*20 = 8*10^6, which is closest to 10^7.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by sachin_yadav » Thu Apr 14, 2011 1:42 pm
Ian Stewart wrote:
The instant you see the phrase 'closest to' in the question, you can be sure they are testing your ability to estimate. You'd certainly lose a lot of time if you actually completed the multiplication exactly. When I'm estimating, I first look at the answer choices to get some idea of how precise an estimate I need. Here, the answers are *very* far apart (10^8 is 10 times bigger than 10^7, for example), so even if we make a very rough estimate, we'll still be able to easily pick the right answer. There are many ways to continue at this point; for example:

2*5 is equal to 10
3*7 is roughly 20
11 is roughly 10
13 is roughly 10
17 is roughly 20
19 is roughly 20

Notice that if I round some numbers down, I round others up to compensate somewhat. So our product should be fairly close to 10*20*10*10*20*20 = 8*10^6, which is closest to 10^7.
Thank you so much Ian. This method is amazing and will save a lot of time. Really appreciate for your help.

Regards
Sachin
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