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
A) 10^9
B) 10^8
C) 10^7
D) 10 ^6
E) 10^5
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then $127/mo
better method? mine was too long
Source: Beat The GMAT — Problem Solving |
sorry, miscalculated
Last edited by Osirus@VeritasPrep on Thu Jun 04, 2009 4:30 pm, edited 1 time in total.
Find a way to do only very easy multiplication and use logical deduction on the rest.pathaniaus 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
(210 x 11 ) x (13 x 17) x 19.
To mulitply any two digit number by 11, separate the two numbers and put their sum in the middle. This easily gives
2310 x (13 x 17) x 19
Now 10 x 20 x 20 = 4000 cannot be too far from 13 x 17 and 19.
Whatever the real values are u know the 2 reamaining numbers each has 4 digits. When the smallest 4 digit number is squared you get 10^6=1 million and you know the 2 numbers above are each greater than 1000.
You can easily see that 2000 x 4000 = 8 x 10^6. 6 zero's but 8 million which is way above 1 million.
So the correct answer must be closer to 10^7
Choose C.
I did it with extreme approximation, not sure if it is acceptable:
2 x 5 x 3 x 7 x 11 x 13 x 17 x 19
=> 10 x 21 x 11 x 13 x 17 x 19
=> Approximate as follows: 21=2X10, 11=10, 19=2X10, 17=2^4
=> 10 x 2 x 10 x 10 x 13 x 2^4 x 2 x 10
=> 10^4 x 2^6 x 13
=> Approximate 13 to be 2^4
=> 10^4 x 2^6 x 2^ 4
=> We know 2^10 = 1024 ~ 10^3
=> 10^7
2 x 5 x 3 x 7 x 11 x 13 x 17 x 19
=> 10 x 21 x 11 x 13 x 17 x 19
=> Approximate as follows: 21=2X10, 11=10, 19=2X10, 17=2^4
=> 10 x 2 x 10 x 10 x 13 x 2^4 x 2 x 10
=> 10^4 x 2^6 x 13
=> Approximate 13 to be 2^4
=> 10^4 x 2^6 x 2^ 4
=> We know 2^10 = 1024 ~ 10^3
=> 10^7
