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Hey everyone..
I just took a practice GRE and I’m not sure how to (quickly) solve the following questions without a calculator..any help would be greatly appreciated.
1) Which is larger: 100,210 X 90,021 or 100,021 X 90,210
…I know how to multiply them (obviously) but there has to be some quicker way!
2) Which is larger: Sqrt(10)XSqrt(5) or 7.
The only way that I was able to figure this one out was to simplify it to 5XSqrt(2) and then "roughly" multiply 1.41X5. Is there not a more simple way to find this answer?
3) Which is larger: The greatest Prime Factor of 3^5 or the greatest Prime Factor of 5^3
any help on any of these problems would be greatly appreciated!
1. for the first one, I just estimated…I tried to ignore zeroes when possible…so for the first one, I just estimated 1002 x 9 =9018
for the second one, I estimated it as 1000×9.02=9020, so guessed the second one is larger
the first one is 9021001410
the second is 902289410
so the second one is slightly, slightly larger
2. on this one, the trick is to square both numbers…
square the square roots and get 10×5=50
square 7 and get 49
so the square roots are larger (if the square of a number is larger, its square root will be)
3. 3^5=3×3x3×3x3
5^3=5×5x5
so you can see the largest prime factor of the first is 3
and the largest prime factor of the second is 5