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May 2nd, 2018, 01:17 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Please solve my 2 doubts in this solution.
The resultant number of each row is to be worked out separately based on the following rules and the question below the rows of number to be answered. The operation of numbers progress from left to right. 1) If an odd number is followed by a prime odd number, the first number is to be divided by the second number. 2) If an even number is followed by a perfect square, the even number is to be subtracted from the perfect square. 3) If an even number is followed by a composite odd number, they are to be multiplied 4) If an even number is followed by odd number which is not a perfect square they are to be added. 5) if an odd number is followed by an even number, the first number is to be subtracted from the second number. 4 9 9 4. X. 7 If X is resultant of the first row, then what is the resultant of the second row? A). In first row, 4. 9. 9 Here 9 is a perfect square and 4 is an even number. Based on rule 2, 94 =5,which is an odd number, 9 is a composite odd number. Based on rule 3, 5x9 = 45=X In the second row 4 (45) 7 Here 4 is an even number and 45 is an odd number . Based on rule 4, 4 + 45 = 49. Which is an odd number 7 is a prime odd number. Based on rule 1 $\dfrac{49}{7}=7$ The resultant of the second row is 7 I have two doubts here, 1) how can we know result of two subtracting numbers,which is 5 is referred in rule 3? 2) how can we conclude 45 is X in second row? 
May 2nd, 2018, 03:52 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
Since 9 is both "a composite odd number" and a "perfect square" you could apply either rule 2 or rule 3. The two rules conflict. Also, you say "the question below the rows of number to be answered". "X" does not constitute a "question"!

May 2nd, 2018, 08:49 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1 
how can we conclude 45 is X in second row?

May 3rd, 2018, 04:26 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
From what is written here, we can't! That's what I said in my previous answer. We could argue that the three numbers in the first line are "4 9 9" and, working from the left, observe that "4" is an even number and that "9" is a perfect square so, by rule 2, we subtract "4" from "9" to get "5". We could then replace the "4" and "9" by that "5" to get "5 9" although the rules you give say nothing about what to do with "5" after we have subtracted the even number from the perfect square. We now have "5 9". In your first post you said "Based on rule 3, 5x9 = 45=X" but "rule 3" was "3) If an even number is followed by a composite odd number, they are to be multiplied" and "5" is not an even number! Of the 5 rules you give, only "1) If an odd number is followed by a prime odd number, the first number is to be divided by the second number" and "5) if an odd number is followed by an even number, the first number is to be subtracted from the second number" deal with an odd number followed by another number and neither of them applies here the second number, 9, is neither "a prime odd number" nor "an even number". In any case, going back to the start, instead of appealing to "2) If an even number is followed by a perfect square, the even number is to be subtracted from the perfect square" we could have used "3) If an even number is followed by a composite odd number, they are to be multiplied". "4" is an even number and "9" is a composite odd number so instead of "9 4= 5" we couldhave use "4*9"= 36. That would have given X, in the second row, equal to 36 rather than 5. 

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