2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = ... ?
Is there a simple method to calculate a multiplication such the one stated above?
Thx,
fractal
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = ... ?
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This question will never be asked at the Gmat, and incase it is asked, then they will ask it is near which power of 10 or similar questions!
So, don't worry!
So, don't worry!
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Here's a quick way to calculate utilizing difference of squares formula:
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
(2 * 5) * (3 * 7) * (11 * 19) * (13 * 17)
(10 * 21) * (15 - 4)(15 + 4) * (15 - 2)(15 + 2)
(210) * (15^2 - 4^2) * (15^2 - 2^2)
210 * 209 * 221
The answer will be slightly above 200^3, or (2*10*10)^3 = 8 * 10^6. This brings the answer very close to 10^7.
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
(2 * 5) * (3 * 7) * (11 * 19) * (13 * 17)
(10 * 21) * (15 - 4)(15 + 4) * (15 - 2)(15 + 2)
(210) * (15^2 - 4^2) * (15^2 - 2^2)
210 * 209 * 221
The answer will be slightly above 200^3, or (2*10*10)^3 = 8 * 10^6. This brings the answer very close to 10^7.
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Also, you can regroup and approximate!Fractal wrote:2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = ... ?
Is there a simple method to calculate a multiplication such the one stated above?
Thx,
fractal
5 * 19 approx 10^2
2*3*17 approx 10^2
7*13*11 approx 10^3
total 10^7 approx
Kevin Armstrong
GMAT Instructor
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GMAT Instructor
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