I12-29

Question

The Sharma family consists of five members: father, mother, two daughters, and a son. The father got cookies and gave them to the son to keep. Tempted, the son divided them into five equal parts and ate his share.
 
At dinner, the remaining cookies were again redistributed equally among all five and eaten.
 
Select for  Son  a value for the total number of cookies the son could have eaten and select for  Others  a value for the number of cookies each of the other members could have eaten that would be jointly consistent with the given information. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

The initial number of cookies was first divided into five parts and then divided into five parts again. For simplicity, let's assume the initial number of cookies was 25 (a multiple of 5 * 5). In this case, the son first ate 5 cookies, leaving 20 cookies, which were then divided into five parts of 4 cookies each. Thus, the son ate a total of 5 + 4 = 9 cookies, while each of the other family members ate 4 cookies. This makes the ratio of cookies eaten by the son to each of the others 9:4. Among the options, only 27 to 12 maintains this ratio: 27/12 = 9/4.

Correct answer:

Son  "27"

Others  "12"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

AryakiSekera · Answer

I don’t quite agree with the solution. The question does not specify if its asking for total amt of cookies the son could have eaten, or the amt he ate before distributing to the family.

Bunuel · Answer

The question asks how many cookies the son could have eaten, that means total, not just the first share. The son ate twice. Ignoring that is just wrong.

ccarson · Answer

I like the solution - it’s helpful. It's a very difficult question that definitely is more deceiving than it looks

BinodBhai · Answer

I like the solution - it’s helpful. clever ques, one that will make you go wrong most of the times

KRNSW · Answer

"  Select for    Son    a value for the total number of cookies the son could have eaten and select for    Others    a value for the number of cookies each of the other members could have eaten that would be jointly consistent with the given information. Make only two selections, one in each column."

The question is asking the total number fo cookies eaten by Son and each of the rest of the family members. Nowhere it asks the ratio of cookie eaten by son to ookie eaten by other member. What am I missing here?

Bunuel · Answer

The question indeed asks for totals. The ratio is not the answer itself but the check: whatever the initial number of cookies, the son’s total and each other member’s total will always be in the ratio 9:4. That’s why the solution tested the options against that ratio. Among the listed choices, only 27 and 12 satisfy it, so those are the actual totals.

NikunjC · Answer

I like the solution - it’s helpful. Hello,|I have a question,
I assumed the cookies got by dad was X.

Since the son at a fifth of it,
Son at x/5
left for others 4x/5

Then at dinner, the 4x/5 was further divided by a 5.

giving us 4x/25

so son ate x/5 + 4x/25 and the rest ate 4*4x/25 = 16x/25.

And none of the option was fulfilling the 9:16 ratio.

Why was my approch wrong ?

Bunuel · Answer

Your math setup is fine, but the interpretation is off.

When you say the others together ate 16x/25, you’re mixing total eaten by  all four  others with the amount eaten  per person . The question asks for the number eaten  by each  other member, not the total eaten by all of them.

Each of the other four gets 4x/25, while the son eats x/5 + 4x/25 = 9x/25. So the correct ratio is (9x/25) : (4x/25) = 9:4 (son :  each  other), not 9:16 (son :  all  others). That’s why your ratio didn’t match the options.

Hope it's clear.

agrasan · Answer

I like the solution - it’s helpful.

nicklemieux · Answer

I like the solution - it’s helpful.

I12-29

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