Each of the families participating in a bake sale brought 6 muffins

Question

Each of the families participating in a bake sale brought 6 muffins, but 45 of the muffins were eaten before the sale. All of the remaining muffins were sold in boxes of 5. How many families participated in the bake sale? 
 
(1) Between 180 and 200 muffins were sold at the bake sale. 
 
(2) Between 190 and 210 muffins were sold at the bake sale.

Redmaster2 · Answer

Each family brings 6 muffins, so if there are f families, they bring a total of 6f muffins.

45 muffins were eaten before the sale, so the number sold, S, is
S = 6f – 45.

All remaining muffins were sold in boxes of 5, so S must be a positive multiple of 5. 
 We want to find f. Once we know S,
f = (S + 45) / 6,
and f must be an integer.
 
  Statement (1): “Between 180 and 200 muffins were sold.” 
  This means 180 ≤ S ≤ 200, and S is a multiple of 5. The possible values are
180, 185, 190, 195, 200.
Compute f for each: 
 • S = 180 → f = (180 + 45) / 6 = 225 / 6 = 37.5, not an integer
• S = 185 → f = (185 + 45) / 6 = 230 / 6 ≈ 38.3, not an integer
• S = 190 → f = (190 + 45) / 6 = 235 / 6 ≈ 39.2, not an integer
• S = 195 → f = (195 + 45) / 6 = 240 / 6 = 40, an integer
• S = 200 → f = (200 + 45) / 6 = 245 / 6 ≈ 40.8, not an integer 
 Only S = 195 yields an integer f = 40. Statement (1) alone is sufficient. 
 
 Statement (2): “Between 190 and 210 muffins were sold.”  
 This means 190 ≤ S ≤ 210, and S is a multiple of 5. The possible values are
190, 195, 200, 205, 210.
Compute f for each: 
 • S = 190 → f = (190 + 45) / 6 = 235 / 6 ≈ 39.2, not an integer
• S = 195 → f = (195 + 45) / 6 = 240 / 6 = 40, an integer
• S = 200 → f = (200 + 45) / 6 = 245 / 6 ≈ 40.8, not an integer
• S = 205 → f = (205 + 45) / 6 = 250 / 6 ≈ 41.7, not an integer
• S = 210 → f = (210 + 45) / 6 = 255 / 6 ≈ 42.5, not an integer 
 Again, only S = 195 yields f = 40. Statement (2) alone is sufficient.
 
  Conclusion: Each statement alone is sufficient to determine that 40 families participated. The correct answer is D.

ravi1522 · Answer

Hello,
Each of the families participating in a bake sale brought 6 muffins, but 45 of the muffins were eaten before the sale. All of the remaining muffins were sold in boxes of 5. How many families participated in the bake sale?

Let the total family be N 
(N*6-45)/5 = Total sold muffins

It means that the total shall be mutiple of 6 and 5 logically

Statement 1
(1) Between 180 and 200 muffins were sold at the bake sale
only number which are multiple of 5 will be 185,190,195 but in this only 195 is multiple of 5 and 6 
 we can calculate the no of families 
Hence it sufficient

statement

(2) Between 190 and 210 muffins were sold at the bake sale

so the option will be 195 200 and 205 which are multiple of 5

but only 195 will be multiple of 5 and 6

we can calculate the no of families

Hence sufficient

both statement is sufficient

Option D is correct

Each of the families participating in a bake sale brought 6 muffins

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