Problem Solving

When a florist makes garlands with 7 flowers each, she is left with 2 flowers.
if she makes garlands with 9 flowers each she is left with 7 flowers.

If the florist has minimum possible number of flowers but above 500
How many flowers are left if she makes garlands with 16 flowers each?

a) 9
b) 5
c) 3
d) 8

7x+2 = 9p+7
=> 7x = 9p+5

Since no of flowers are more than 500, look for a multiple of 9 above 55(55*9+5=500) that results into remainder of 2, and we quickly get it with 57.

so 9*57+5 = 518 = 7*74

so 7x = 518 => 7x+2 = 520
For 520/16 results into leftover 8 OA D.

HSPA wrote:When a florist makes garlands with 7 flowers each, she is left with 2 flowers.
if she makes garlands with 9 flowers each she is left with 7 flowers.

If the florist has minimum possible number of flowers but above 500
How many flowers are left if she makes garlands with 16 flowers each?

a) 9
b) 5
c) 3
d) 8

Hello maihuna,
I got 79 as the least number that gives remainder of 2 with 7 and remainder of 7 with 9

I havent understood the next part of the question...Answer is with the 4 options.. I got stumped with the answer...

You have missed the portion where it says there are more than 500 flowers, so basically looks for least no above 500 matching the above criterion.

HSPA wrote:Hello maihuna,
I got 79 as the least number that gives remainder of 2 with 7 and remainder of 7 with 9

I havent understood the next part of the question...Answer is with the 4 options.. I got stumped with the answer...

HSPA wrote:When a florist makes garlands with 7 flowers each, she is left with 2 flowers.
if she makes garlands with 9 flowers each she is left with 7 flowers.

If the florist has minimum possible number of flowers but above 500
How many flowers are left if she makes garlands with 16 flowers each?

a) 9
b) 5
c) 3
d) 8

no. of flowers=7k+2, also 9m+7,
as no. of flowers are greater than 500, also we have to look at the minimum possible no. of flowers for which above equations hold true.
now here we can work with any equation, to find the no. of flowers, but lets just work with equation 7k+2,
when k=74 7k+2=518+2=520, 520/9=7 which also satisfy equation 9m+7, hence no. of flowers are 520,

therefore no. of flowers left when a florist makes garland with 16 flowers is =520/16=8 hence D

i forgot to add 2, in final sum corrected in original post...

maihuna wrote:You have missed the portion where it says there are more than 500 flowers, so basically looks for least no above 500 matching the above criterion.

HSPA wrote:Hello maihuna,
I got 79 as the least number that gives remainder of 2 with 7 and remainder of 7 with 9

I havent understood the next part of the question...Answer is with the 4 options.. I got stumped with the answer...

Okay I got it now...
LCM of 7,9 is 63, I was adding 7x+2 or 9y+7 where x,y is natural number to it...

Now I have make 63*7 to have flowers above 500...that gave me 504 Now adding 7x+2 or 9y+7 ie (16)

520/16 ...8 is the remainder...which is the answer...

Source is IIM - CAT exam.. [Med-high rank questions on LCM...]

Manpsingh is a tough guy.. His solution is better than mine... thank you manp
the chapter I was reading corrupted my basic thought...