Question

There were between 2200 and 2600 guests invited
to a marriage party. The event manager decided
that she would arrange the seating so that each
table would seat an equal number of guests, and
the number of guests at each table would be an odd
number. She worked out that three guests per table
would not work as two guests would be leftover,
neither would five per table, which would leave four
guests without a table, neither would seven per
table, which would leave six over, and nine per table
would leave eight left. However, when she tried
seating 11 guests per table it worked exactly, and
none were left over. Write down the total number
of guests who were invited to the party?​

Answer 1

Answer:

2519 is the answer. You can check by dividing it by 3,5,7 and 9.

Answer 2

Given :-

• There were between 2200 and 2600 guests invited to a marriage party .
• The number of guests at each table would be an odd number.
• if 3 guest per table , 2 guest left over .
• if 5 guest per table , 4 guest left over .
• if 7 guest per table , 6 guest left over .
• if 9 guest per table , 8 guest left over .
• Exactly divisible by 11 .

To Find :-

• The total number of guests who were invited to the party ?

Solution :-

we have to find a number between 2200 and 2600 which if divides by 3,5,7 and 9, gives remainder as 2,4,6 and 8 respectively and completely divisible by 11.

As we can see :-

• (3 - 2) = (5 - 4) = (7 - 6) = (9 - 8) = 1 .

So,

LCM of 3,5,7 and 9 :-

→ 3 = 3 * 1

→ 5 = 5 * 1

→ 7 = 7 * 1

→ 9 = 3 * 3

LCM = 3 * 3 * 5 * 7 = 315 .

then,

→ Smallest number which satisfy the remainder condition = (LCM of 3,5,7,9) - 1 = 315 - 1 = 314 .

Now , Number Must be divisible by 11 .

So,

→ Let the required number be in the form = (315k - 1) /11 = remainder 0, where k = 2,3,4,5 _______

• if k = 2 => (315*2 - 1)/11 => 629/11 => Remainder 2 .
• if k = 3 => (315*3 - 1)/11 => 944/11 => Remainder 9 .
• if k = 4 => (315*4 - 1)/11 => 1259/11 => Remainder 5 .
• if k = 5 => (315*5 - 1)/11 => 1574/11 => Remainder 1 .
• if k = 6 => (315*6 - 1)/11 => 1889/11 => Remainder 8 .
• if k = 7 => (315*7 - 1)/11 => 2204/11 => Remainder 4 .
• if k = 8 => (315*8 - 1)/11 => 2519/11 => Remainder 0 .

Now also,

• 2200 < 2519 < 2600 .

Hence, the total number of guests who were invited to the party were 2519 .

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