ELEMENTARAY ARITHMETICS – SAT/GMAT QUESTION?
Without using any calculator or electronic device, compute the value of 22/7 – 7/22, to the nearest integer?
A) 0
B) 1
C) 2
D) 3
E) 4
Use only arithmetic (fraction) skill and mathematical reasoning to prove your answer and show the steps of your computation (please no calculator because this is a standardized test question and calculator is not allowed).
Please give detailed and step-by-step explanation of your answer.
Thanks very much for sharing your mathematics prowess.
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Verified answer
This is easy. Do it by estimation. Sinse 7x3 is 21, this is very close to 22. 22/7 is then going to be 3 with a remainder of 1 or 3 1/7. 7/22 is close to 7/21 with is one third. 3 1/7 minus one third is just a little under 3. Answer D. The important point here is that it is to the nearest integer and therefor you do not need exact calculations.
22/7 is the fractional equivalent of pi, which is 3.1415....
You could also reason it out. 22/7 is the same as 3 and 1/7. 1/7 is less than a half, so 22/7 is closer to 3 than it is to 4.
If all else fails, do long division. 7 goes into 22 3 times. 7 times 3 is 21. 22 minus 21 is 1. Bring down the 1 and add a 0 to get 10. 7 goes into 10 1 time. 7 times 1 is 7. 10 minus 7 is 3. Repeat.