An open Blog with tentative solutions and discussion of GMAT questions
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Paredes - Portugal
Friday, February 17, 2006
PS - square root of 463
The square root of 463 is between (A) 21 and 22 (B) 22 and 23 (C) 23 and 24 (D) 24 and 25 (E) 25 and 26
The problem becomes quite clear if we think in the relation 20^2 = 400. This is a usefull relation, since 20 is a "base" to the alternative answers, as well as 400 is a base for the square. So, how about thinking of solving the equation (20+i)^2 = 400 + 63? The first member can be developed by the square of a sum: 20^2 + 2x20xi + i^2. Thus we can eliminate the 400 term on both members, yielding: 40i + i^2 = 63. This is quite simple to analyse, as for i=1 one obtains in the first member 41 (less than 63), whereas for i=2 we obtain 84 (more than 63). This points clerrly to the conclusion that the solution lies between (20+1) and (20+2), thus the correct answer will be (A)
The problem becomes quite clear if we think in the relation 20^2 = 400. This is a usefull relation, since 20 is a "base" to the alternative answers, as well as 400 is a base for the square. So, how about thinking of solving the equation (20+i)^2 = 400 + 63?
ReplyDeleteThe first member can be developed by the square of a sum: 20^2 + 2x20xi + i^2. Thus we can eliminate the 400 term on both members, yielding: 40i + i^2 = 63. This is quite simple to analyse, as for i=1 one obtains in the first member 41 (less than 63), whereas for i=2 we obtain 84 (more than 63). This points clerrly to the conclusion that the solution lies between (20+1) and (20+2), thus the correct answer will be (A)