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02 Jul 2012, 02:21
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C
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52% (01:51) correct
48%
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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
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
02 Jul 2012, 02:22
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SOLUTION
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);
\(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\).
Answer: C.
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)
\(2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7\).
Answer: C.
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);
\(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\).
Answer: C.
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)
\(2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7\).
Answer: C.
25 Oct 2013, 04:45
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I have approached in the following way:-
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 10 x 21x 11 x 13 x 17 x 19 = 10 x 10 x 2.1 x 10 x 1.1 x 10 x 1.3 x 10 x 1.7 x 10 x 1.9 = 10^6 x (2.1 x1.1 x 1.3 x 1.7 x 1.9)
The approximation of the (2.1 x 1.7 x 1.9 x 1.3 x 1.1) will be close to 10, so the answer is 10^7
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 10 x 21x 11 x 13 x 17 x 19 = 10 x 10 x 2.1 x 10 x 1.1 x 10 x 1.3 x 10 x 1.7 x 10 x 1.9 = 10^6 x (2.1 x1.1 x 1.3 x 1.7 x 1.9)
The approximation of the (2.1 x 1.7 x 1.9 x 1.3 x 1.1) will be close to 10, so the answer is 10^7
