The Sharma family consists of five members: father, mother, two

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 · Accepted 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" GMAT-Club-Forum-psupo97m.png

ManifestDreamMBA · Answer

Let total cookies be T
Son ate - T/5
Remaining cookies - 4T/5
Everyone's share 4T/5 *1/5 = 4T/25
Son's share = T/5 + 4T/25 = 9T/25

The son's total will be a multiple of 9. 27 works which makes T = 75
Other's share therefore is 75 * 4/25 = 12

Bismuth83 · Answer

1. The question asks us to  find a possible combination of the cookies eaten by the son and by the other family members .

2. Since, there doesn't seem to be enough information to figure out exactly the values, we're interested in the ratio between Son and Others.

3. Let the number of cookies eaten by each of the other family members be equal to x. This means the number of cookies left for dinner was 5x.

4. 5x is only  \frac{4}{5}  of the initial amount of cookies since the son ate an extra  \frac{1}{5}  or  \frac{1}{4} * 5x = \frac{5x}{4}  cookies. That means the son ate a total of  x + \frac{5x}{4} = \frac{9x}{4}  cookies.

5. The ratio between Son and Others is  \frac{\frac{9x}{4}}{x} = \frac{9}{4} . The only answer choices that have this ratio are 27 and 12.

6. Our answer will be:   Son - 27 and Others - 12  .

jamiedimonn · Answer

i dont get it . the son first divided into 5 parts meaning x/5 here x meaning total cookies. then his share would be x/25 and family share 4x/25 making ans 4 and 30 could any expert help

Bunuel   KarishmaB

Bunuel · Answer

Have you missed the solutions above?

The first son receives x/5, leaving 4x/5 remaining.

Next, 4x/5 is further divided into 5 parts, so the son will additionally receive 4x/25, and each of the other family members will also get 4x/25.

Thus, the son’s total share is:

x/5 + 4x/25 = 9x/25

The ratio of the son's share to each of the other family members' shares is:

(9x/25) : (4x/25) = 9:4

AbhiS101 · Answer

let's not use any eqns & try to solve using mental math

1. Cookies are divided equally among 5 members so cookies are a multiple of 5 
2. Son ate his cookies share & cookies were divided again, so even after deducting son share cookies are multiple of 5
3. Now, all other 4 members have given equal share to son, basically share given is multiple of 4(4x) & share given is equal to the amount that all 5 members have now
4. Cookies eaten by each other member is multiple of 4 & becomes a multiple of 5 if we consider son share also
5. There are 2 options which are multiple of 4, option 4 & 12. for 5 persons( 4*4 +5, 12*4+12), both options are multiple of 5 if we consider 5 person
6. Although checking the options being multiple of 4 & 5 was an un necessary step, still I did 
7. Now, difference between cookies eaten by son to cookies eaten by each other member will be a multiple of 5, coz when you are deducting the total cookies eaten by son to cookies eaten by each member, you are arriving to a value when son has eaten the cookies at the first time & it will be a multiple of 5 because even after reducing son share which he had eaten, the cookies were divided equally among 5 members which means that the cookies eaten by son at the first time was a multiple of 5 , only the multiple of 5 can be reduced from higher multiple of 5 to get a number which is multiple of
8. So there is no option which which gives difference a multiple of 5 if we reduced 4 from it, but for 12 there is an option 27, 27-12 = multiple of 5

IMO 12 cookies eaten by each member & 27 by Son

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The Sharma family consists of five members: father, mother, two

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