Consider the set E=\ 5,6,7,8,9\ . For any partition \ A, B\ of E , with both A and B non empty. Consider the number obtained by adding the product of elements of A to the product of elements of B . Let N be the largest

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Quantrex Academy · Accepted Answer

Correct answer: 17

one of the set A or set B contain only odd number Set A Set B Comment Case I 5 6,7,8,9 5+6 × 7 × 8 × 9=3029 Which is divisible by 13 II 7 5,6,8,9 7+5 × 6 × 8 × 9=2167 Which is divisible by 11 III 9 5,6,7,8 9+5 × 6 × 7 × 8 is multiple of 3 IV 5,7 6,8,9 5 × 7+6 × 8 × 9=467 which is prime V 5,9 6,7,8 5 × 9+6 × 7 × 8 is divisible by 3 VI 7,9 5,6,8 7 × 9+5 × 6 × 8 is divisible by 3 VII 5,7,9 6,8 5 × 7 × 9+6 × 8 is divisible by 3 Hence N is 467 Sum of the digit of N is 17

Consider the set E=\ 5,6,7,8,9\ . For any partition \ A, B\ of E ,...

Correct answer

Step-by-step solution

More from Permutation and Combination

	Set A	Set B	Comment
Case I	5	6,7,8,9	$5+6 \times 7 \times 8 \times 9=3029$ Which is divisible by 13
II	7	5,6,8,9	$7+5 \times 6 \times 8 \times 9=2167$ Which is divisible by 11
III	9	5,6,7,8	$9+5 \times 6 \times 7 \times 8$ is multiple of 3
IV	5,7	6,8,9	$5 \times 7+6 \times 8 \times 9=467$ which is prime
V	5,9	6,7,8	$5 \times 9+6 \times 7 \times 8$ is divisible by 3
VI	7,9	5,6,8	$7 \times 9+5 \times 6 \times 8$ is divisible by 3
VII	5,7,9	6,8	$5 \times 7 \times 9+6 \times 8$ is divisible by 3