One of those questions in which algebra works fastest because of the occurrence of perfect squares in the numbers.
==> x=224%(1/x) + 1/x
x=224%(1/x) + 100%(1/x)
x=324%(1/x)
x=3.24(1/x)
x^2=3.24=324/100
x=18/10=1.8
D is the correct answer.
It is a good idea to know the squares of integers between 1 and 20. Not compulsory to know, but still helpful if one does.
Another method (back-solving):
Alternatively, we could test the given options, find out which options is 3.24 times its reciprocal. It is also helpful to know the reciprocals of the first dozen positive integers, i.e. 1/1;1/2;1/3....1/12. Again, you don't have to know this, but it can help you convert into decimals easily.
Let us test the option.
A) 0.8 aka 4/5, whose reciprocal is 5/4 aka 1.25. ELIMINATE because the reciprocal is actually greater than the number, but we want the reciprocal to be (approximately) a third (or 1/3.24) of the number.
B) 1.1 aka 11/10, whose reciprocal is 10/11 aka is 0.909. ELIMINATE because the reciprocal is not approx a third of the number.
C) 1.5 aka 3/2, whose reciprocal is 2/3 aka 0.666. ELIMINATE because the reciprocal is not approx a third of the number.
D) 1.8 aka 18/10 aka 9/5, whose reciprocal is 5/9 aka 0.555. KEEP because the reciprocal is approx a third of the number. CORRECT ANSWER.
E) 2.2 aka 11/5, whose reciprocal is 5/11 aka 0.4545. ELIMINATE because the reciprocal is not approx a third of the number.
Both solutions yield D as the answer.
Personally, I find the method testing numbers easier faster to use, IN GENERAL, but for this particular question, algebra was far quicker. The testmakers design the questions with a specific "easier" solution in mind. It is important for the student to be flexible in order to use the "better" method to solve a PARTICULAR question. Hope you find this useful.
Cheers,
Der alte Fritz.
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+1 Kudos me - I'm half Irish, half Prussian.
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