If every boy in a kindergarten class buys a soda and every girl in the

Hi Nityanshu1990,

You bring up a really important point in regards to this question - and the key to solving it is to realize that we don't know the prices of each soda and each juice box - they MIGHT be integers, but they MIGHT NOT. Also, we don't know the relative prices (so one might be more expensive than the other, or vice-versa).

From the given prompt, we have 4 variables:

B = The number of boys
G = The number of girls
S = The price of 1 soda
J = The price of 1 juice box

From the prompt, we can create just 1 equation:

(B)(S) + (G)(J) = (B)(J) + (G)(S) - 1

Here's how we can TEST VALUES to prove that there's more than one answer. Since this IS such a thick question, the key to doing the work quickly is to keep the values SMALL.

We do have a couple of 'restrictions' that we have to work with:
1) B and G are both INTEGERS (since you cannot have a 'fraction' of a boy or girl)
2) We're told that there are MORE boys than girls, so B > G

IF....
B=2
G=1
S=1
J=2
(2)(1) + (1)(2) = (2)(2) + (1)(1) - 1
2 + 2 = 4 + 1 - 1
4 = 4
Here, we have 2 boys and 1 girl, so the difference is 1.

In the above example, both S and J are INTEGERS and S < J. What happens if we make one of those variables a fraction......

IF....
B=3
G=1
S=1/2
J=1
(3)(1/2) + (1)(1) = (3)(1) + (1)(1/2) - 1
1.5 + 1 = 3 + 0.5 - 1
2.5 = 2.5
Here, we have 3 boys and 1 girl, so the difference is 2.

Thus, there's no exact answer....

GMAT assassins aren't born, they're made,
Rich

Bunuel : The OA needs correction. Correct answer is Option E

Answer: Option E

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chetan2u -

It has nothing to do with natives vs non natives. Anyone who takes GMAT pays his/her fees in dollars and is aware of the currency. This is very basic general awareness for people intending to go for MBA. In any case, the only time such a question may need tweaking is if in its experimental stage, it shows unexpected results.

We do need to take into account the unwritten constraints as per what is possible and what is not. When we deal with questions containing buying of pencils, we know that we cannot buy 1.5 pencils. Similarly, note here what the question says - Every boy buys a soda (no packs of 2 for 3 cents etc). Hence it SHOULD be possible for every boy to buy a soda. Hence, the cost of soda cannot be 0.25 cents. The question you quote from GMAT Prep is an old, retired question in which the actual cost of shares has no relevance since you are required to calculate a percentage. How much thought was actually put into it is unknown.

But most importantly, the intent of this practice question is to make you realise a pitfall. We know that (B - G) is an integer but we ignore that (S - J) needs to be an integer too. That is the reason the question gives you 1 cent (not 1 dollar). We can keep arguing about what is acceptable and what is not and miss the whole point the question is making. The idea is to make test takers realise that they always need to take a step back and evaluate the unwritten constraints.
We cannot change the official answer given as per our different understanding.

VeritasKarishma

I will respond taking this as a healthy discussion, which in the end should benefit a student.
If the question and the logic for the solution of the prep institute is correct, students and many of us who have responded otherwise on top would realize that cents mean integer values on GMAT.
If otherwise, many will get saved from a wrong notion presented by this question.


When I pay my fees, I pay it in dollars and would know that 100 cents make 1 $. But knowing cents is lowest measure of currency may not be a requirement for intending to go to MBA or for that matter even for appearing in GMAT.


The time I read this question, I did realize each boy/girl is buying the given item, so he/she should be able to buy it himself/herself. But if someone in Australia or HK reads it, he may take this to mean something else. If my knowledge and the resources available on net serves me right, 5 cents coin is the smallest coin in Australia, and 10 cents in Hong kong. Why would some one in Australia believe the difference can be 1 cent when the minimum there is 5 cent coins. So a boy buying a soda in Australia has to do it in multiples of 5 only.


I agree and appreciate the fact that the intent is noble, but hopefully we do not end up teaching something that may act in a totally opposite way.
A question from Veritasprep, giving the value of a certain item as 7.3xy7 may conflict with the logic used to arrive at the solution here
https://gmatclub.com/forum/the-exact-cost-price-to-make-each-unit-of-a-widget-is-7-6xy7-where-x-196044.html#p2581121
Yes, the intent in the question is to teach rounding off but the amount becomes 761.27 cents, which just gives an impression to the test takers that there can be decimals in cents.


I could not have agreed more. I would add a bit more - We cannot change our explanations to suit an answer. This question or the one posted in the link above is surely wrong and both are by same prep institute.
Please do not take this to do anything with any institute. I find very knowledgeable person from the institute on the forum.

Bunuel, since the answer has been changed back from E to A, there are many questions posted on the forum which go against this very concept. I'll post one such question where almost all the options are in decimals, 1.2 cents etc. There will be many more.
https://gmatclub.com/forum/a-company-manufactures-nails-that-are-meant-to-be-precisely-10-cm-long-355160.html#p2766300

I would step back now and leave this here, but would love to see some official question testing cents as integers only. I know I could be wrong if there is some official question testing cents vs integer values, but then would surely learn something new.

GMAT tests reasoning and logic (more and more as time goes by). From the context of each question, we derive what is logical in that situation and that is what we intend to teach our students too.

When I ask someone that each boy buys 1 soda so what can the possible cost of soda be in cents, the answer will be 1 cent or 2 cents or 3 cents etc. At any store, you will not find an item priced in fractions of a cent because you cannot buy it using currency.
It is not something that many will catch because we think of currency as fractional. But the question talks about currency in cents which need to be integral units if we are to buy 1 item. The question and the explanation are made to help test takers understand this. To think rationally in the given context. If geographical differences change the rationale behind the question, data will tell that once the question is tested in different geographies and is not something we need to worry about.

This does not mean that the concept of fractional cost in cents cannot occur. As mentioned previously, we can have a pack of 2 sodas for 3 cents (in which effectively each soda is for 1.5 cents but they are not available for individual buying). That is not possible in our question as per the given constraints.
Similarly, when we manufacture N widgets, our cost price for each can come out to be $7.1278... (to as many digits as we wish) when we take into account our fixed cost and variable cost and divide it all by N. No logical issues in that. Hence there is absolutely nothing wrong with the other question mentioned either. Both questions are correct.

No one writes explanations to suit any particular answer, especially when we are the ones providing the answer in the first place. We have given the answer as (A) because the question demands it.
The takeaway from the question is not that you cannot have fractional currency but that be aware of logical constraints. In some cases, fractional values may not be acceptable and one needs to be aware of that. In this question, fractional values of cents does not make sense and the whole question revolves around that point only. That does not mean that any question presenting a fractional value is wrong. As we see above, in some cases it is a calculated value and makes all the sense. What we intend to teach is making this distinction based on the context of the given question.

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