# Application of “Doubling and Halving” and “By Addition and By Subtraction”

In a TV quiz show, the prize for each correct answer is double that of the previous question: P1k for the first question, P2k for the second, P4k for the 3rd and so on until the 10th question when P512K is awarded. If Rene won a total of P772K, how many questions did he answer correctly? A) 7; B) 6; C) 5; D) 4; E) 3

This type of question was given in every category in the Online 3^{rd} MATH-Inic Vedic Mathematics National Challenge last April 10, 2023 with only the number of questions and the total winnings changed.

In the Junior category where that actual question was given, only 33 out of the 459 or only about 7% of the participants answered it correctly.

If the study of base numbers, particularly binary numbers has been included in the current curriculum, high school students would easily get the correct answer by dividing the total winnings successively by 2 until 0 is reached and noting the remainder in each division.

772 ÷ 2 = 386 r. 0

386 ÷ 2 = 193 r. 0

193 ÷ 2 = 96 r. 1

96 ÷ 2 = 48 r. 0

48 ÷ 2 = 24 r. 0

24 ÷ 2 = 12 r. 0

12 ÷ 2 = 6 r. 0

6 ÷ 2 = 3 r. 0

3 ÷ 2 = 1 r. 1

1 ÷ 2 = 0 r. 1

The number of times there was a remainder of 1 is the answer – 3.

If the remainders from the bottom to the top are listed in sequence, it will give the binary equivalent of 772 which is 1100000100. And just by looking at the occurrence of 1s in that binary figure, starting from the right, we can say that the contestant answered the 3^{rd}, 9^{th} and 10^{th} questions correctly.

But how can those who have absolutely no knowledge of binary numerals answer that type of question? By simply using the Vedic techniques “By Addition and By Subtraction” and “Doubling and Halving”!

“By Subtraction” of the prize in the 10^{th} question from the total winnings, we have 772k – 512k = 260k.

By halving 512k, we get 256k, the prize for the 9^{th} question.

By Subtraction 260K – 256K = 4K

Now since the question stated ”… the prize for each correct answer is double that of the previous question: P1k for the first question, P2k for the second, P4k for the 3^{rd}…”, we now know that he also answered the 3^{rd} question correctly.

To check, we have P512K + 256k + 4K = P772k.

Try to solve this question given in the primary category: In a TV quiz show, the prize for each correct answer is double that of the previous question: P1k for the first question, P2k for the second, P4k for the 3rd and so on until the 8th question when P128K is awarded. If Rene won a total of P235K, how many questions did he answer correctly?