If P =4.a2b and Q =5.ba3, is the product of P and Q after rounding the

Question

If P = 4.a2b and Q = 5.ba3, is the product of P and Q after rounding them at their units digits less than 27 ?

(1) The sum of P and Q after they are rounded to the hundredths place is 10.1
 
(2) a - b = 6

chetan2u · Answer

Let us see what we can make out of the given statement. 
 Extreme/largest possible value of each.  
1) Even if P was largest possible, that is closer to 5, Q would still require to be more than 27/5=5.4
2 ) Even if Q were largest possible, that is closer to 6, P would still require to be a more than 27/6=4.5

So,  if we can say that P<4.5 or Q<5.4, the answer would surely be No. Otherwise, we will have to check both P and Q

(1) The sum of P and Q after they are rounded to the hundredths place is 10.1
  The extremes tested above tell us the minimum values in two possible scenarios will be 5+5.4 or 6+4.5 
Both the values are above 10.1, so P*Q<27
Sufficient

(2) a - b = 6
We know a can be 9 at the maximum, 9-b=6 or b=3.
But b has to be at least 4.
Hence, P*Q<27.
Sufficient

D

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If P =4.a2b and Q =5.ba3, is the product of P and Q after rounding the

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