cards numbered 500 through 799 sre placed into a box. how many of the cards satisfy both of the condition shown below m. the first digit of the three digit number on the cards is odd. the three digit number on the card is divisible by 6

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04-11-2022
Mathematics

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cards numbered 500 through 799 sre placed into a box. how many of the cards satisfy both of the condition shown below m. the first digit of the three digit number on the cards is odd. the three digit number on the card is divisible by 6

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BrayF439657 BrayF439657 · Answer 1 · 2022-11-04T00:37:50+01:00

There are many numbers that satisfy the first condition. The numbers beginning with 6 are discarded. It means the number on the cards must begin with 5 or 7.

The second condition is more specific. To find the numbers on the cards that are divisible by 6 take into account that for a number to be divisible by 6, it needs to be divisible by 2 (the last digit must be a pair digit) and by 3 (the sum of its digits must be a multiple of 3). Remember that we already know that the number must begin with 5 or 7.

Make a list:

510

522

504

516

528

720

702

714

726

708

The smallest number from the numbers that begin with 5 is 504 and from the numbers that begin with 7 is 702. Start adding 6 to each number until you have obtained a number more than 599 and 799 respectively.

504

510

516

522

528

534

540

546

552

558

564

570

576

582

588

594

702

708

714

720

726

732

738

744

750

756

762

768

774

780

786

792

798

Now, count them.

There are 33 cards with a number that meets these conditions.