Yes I agree, not all problems can be solved using pick numbers strategy or not always will be able to come up with ideal pick numbers under pressure. At times for complex problems, you need pen down that lengthy/heavy algebraic computations. However, giving 5 seconds to think about execution method (pick numbers, backsolving or algebraic) after reading the problem, can help saving over 40-50 seconds of 'extra' time taken by algebraic method.
In this specific problem, I tried to visualize how can I increase 100 to certain number and decrease to obtain 90?? First comes 110, but reducing it by 20 doesnt give integer percentage on 110. Next we have 120 that includes 20% increase and then 25% decrease gives 90..bingo! It took 5-7 seconds to think & 15-20 seconds to back-solve, but saved 40-50 seconds of algebraic calculations!
Picking number requires strategy of identifying optimum numbers using
LCM, LCD, prime factors, multiples of 10/100s.
How do we get used to this method? Practice!!
When solving
OG or practice problems, always see if you can solve it using multiple ways. Try same problem with
Algebra, back-solving, pick numbers, hybrid approach (whichever methods are applicable) and even try guessing it. You may also automatically build that intuition over the time.
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Thanks,
Prashant Ponde
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