GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 22:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59561
If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 09:55
1
13
00:00

Difficulty:

95% (hard)

Question Stats:

44% (02:26) correct 56% (02:22) wrong based on 180 sessions

### HideShow timer Statistics

If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.
Intern
Joined: 19 Sep 2014
Posts: 21
Concentration: Finance, Economics
GMAT Date: 05-05-2015
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 12:44
6
Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.

This was quite a tricky question for me, but I hope that I have been able to crack it! Here's my solution:

Let's assign variables for boys (b), girls (g), sodas (s), juices boxes (j) and the total cents spent as (t). From the information given in the question stem, we also know that boys are greater than girls (b > g). Let's set up some equations:

b*s + g*j = t - 1.... (the total if every boy in the class buys a soda and every girl in the class buys a juice box)

b*j + g*s = t.... (the total if every boy in the class buys a juice box and every girl in the class buys a soda)

We can subtract both equations from each other to cancel out the variable (t). This gives us:

b*j + g*s - (b*s + g*j) = t - (t - 1)..... this gives us: b*j - b*s - g*j + g*s = 1. We can further factorise this equation as b*(j - s) - g*(j - s) = 1........ (b - g)*(j - s) = 1.

From the factorised equation (b - g)*(j - s) = 1, we can say that either (b - g) =1 or (j - s) = 1. This basically means that either the number of boys are one more than the number of girls (b = g + 1) or that the price of a juice box costs 1¢ higher than the price of a soda can (j = s +1). Since we know (from the question stem) that b > g, we could conclude that b = g + 1, and that the prices of both the juices boxes and the sodas are the same!

I think the answer is A.

Please consider giving me KUDOS if you felt this post was helpful and correct! or please enlighten me (in case my answer's incorrect) so that I can learn and improve from my mistakes! Thanks.
##### General Discussion
Manager
Joined: 27 Dec 2013
Posts: 193
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 12:51
I will go with answer E. We need to know the relation between Soda and Juice.

Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.
Intern
Joined: 05 Jan 2015
Posts: 2
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 15:06
4
I will go with A

Here is my solution:

boys (b) , girls (g) , soda (s) , juice box (j) assuming b,g,s,and j are all integers.
Given that b>g
Q: What is b-g ?

Total amount spent ;

Therefore the equation must be

b*s+g*j+1=b*j+g*s

we should try to solve the equation for (b-g) ;
b*s+g*j - b*j-g*s=-1
b(s-j) - g(s-j)=-1
(b-g)(s-j)= -1
Isolate (b-g) to one side of the equation ;
b-g = -1/(s-j)
We know that both b-g and s-j result integers, and b-g must be positive, therefore s-j can only be -1 which makes b-g=1
Intern
Joined: 24 Jan 2014
Posts: 34
Location: France
GMAT 1: 700 Q47 V39
GPA: 3
WE: General Management (Advertising and PR)
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 15:25
1
HI Bunuel,

I will note B the number of boys, G the number of girls, S the number of soda cans and J the number of juice boxes.

We know that B > G and the Q is What is B-G ? ( we don't need to find separately each unknown)

Total amount spent, I note $the TOTAL money spent B x S + G x J =$-1 => B x S + G x J + 1 = $B x J + G x S =$

=> B x S + G x J + 1 = B x J + G x S
=> B X S - B X J + G X J - G X S = -1
=> B(S-J) - G (S-J) = -1
=> (B-G)(S-J) = -1
=> B-G = (-1)/(S-J)

As B-G must be a positive integer, then s-j can only be -1 so that -1/-1 = 1 ( any other number would result in a negative / fraction result)

Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.
Intern
Joined: 19 Sep 2014
Posts: 21
Concentration: Finance, Economics
GMAT Date: 05-05-2015
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 16:57
kdatt1991 wrote:
Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.

This was quite a tricky question for me, but I hope that I have been able to crack it! Here's my solution:

Let's assign variables for boys (b), girls (g), sodas (s), juices boxes (j) and the total cents spent as (t). From the information given in the question stem, we also know that boys are greater than girls (b > g). Let's set up some equations:

b*s + g*j = t - 1.... (the total if every boy in the class buys a soda and every girl in the class buys a juice box)

b*j + g*s = t.... (the total if every boy in the class buys a juice box and every girl in the class buys a soda)

We can subtract both equations from each other to cancel out the variable (t). This gives us:

b*j + g*s - (b*s + g*j) = t - (t - 1)..... this gives us: b*j - b*s - g*j + g*s = 1. We can further factorise this equation as b*(j - s) - g*(j - s) = 1........ (b - g)*(j - s) = 1.

From the factorised equation (b - g)*(j - s) = 1, we can say that either (b - g) =1 or (j - s) = 1. This basically means that either the number of boys are one more than the number of girls (b = g + 1) or that the price of a juice box costs 1¢ higher than the price of a soda can (j = s +1). Since we know (from the question stem) that b > g, we could conclude that b = g + 1, and that the prices of both the juices boxes and the sodas are the same!

I think the answer is A.

Please consider giving me KUDOS if you felt this post was helpful and correct! or please enlighten me (in case my answer's incorrect) so that I can learn and improve from my mistakes! Thanks.

CEZZAR89 - Thanks for the kudos man!

Yeah, after re-reading through the question (and some of the other answer posts) again. I think that I have a made a mistake when reasoning my factorised equation of (b - g)*(j - s) = 1. I think that the number of boys are one more than the number of girls (b = g + 1) AND that the price of a juice box costs 1¢ higher than the price of a soda can (j = s +1). I don't think that this is an 'either and or' situation because we are talking about the relationship between boys and girls (b = g + 1) and between the price of a soda can and a juice box (j = s +1) separately.

I still think that that the answer A, because b = g + 1, but I also think that the j = s +1.
Manager
Joined: 15 Aug 2013
Posts: 50
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 17:21
2
Let, B(no of boys), G(no og girls), S(cost of soda) and J(cost of juice).

Then from the given condition we can safely say -
BS + GJ + 1 = BJ + GS
or B(J-S) - G(J-S) = 1
or (B-G)(J-S) = 1

Here, we know that B and G will be integers (since they represent no of boys and girls in a class).
Hence, in the above equation B-G will be integer.

Now how (B-G) (J-S) will be equal to 1, when B-G is an integer.
This means both the multipliers can be 1 or -1. They cant be -1 since it is given B>G
So we are left with B-G =1 (This is what has been asked)!!

Ans- A
Intern
Joined: 24 Jan 2015
Posts: 15
Location: India
Concentration: General Management, Operations
Schools: Schulich Jan'19
GMAT 1: 700 Q49 V38
GPA: 3.11
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

03 Feb 2015, 23:43
I think answer option E is correct.
Reason - We know b and g are integers but we cannot say the same about j and s. Consider an example - what if b=10, g=8, j=1 and s=1/2. We still get (b-g)*(j-s)=1.

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

04 Feb 2015, 06:37
CEZZAR89 wrote:
I will go with A

Here is my solution:

boys (b) , girls (g) , soda (s) , juice box (j) assuming b,g,s,and j are all integers.
Given that b>g
Q: What is b-g ?

Total amount spent ;

Therefore the equation must be

b*s+g*j+1=b*j+g*s

we should try to solve the equation for (b-g) ;
b*s+g*j - b*j-g*s=-1
b(s-j) - g(s-j)=-1
(b-g)(s-j)= -1
Isolate (b-g) to one side of the equation ;
b-g = -1/(s-j)
We know that both b-g and s-j result integers, and b-g must be positive, therefore s-j can only be -1 which makes b-g=1

hi CEZZAR, kdatt and many others who have given answer as A ie 1..
just one point to ponder..
you all have correctly come down to the final equation, which is
(b-g)(s-j)= 1... but hereon we all are going wrong
b- g can take infinite values depending on the value of (s-j), which can be 1, 1/2,1/3,1/100 and so on..
so ans should be E, depending on values of juice and soda....
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15644
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

04 Feb 2015, 14:43
1
Hi All,

This is a thick, layered question, and would likely take most Test Takers more time than average to solve correctly. 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.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

05 Feb 2015, 22:35
Answer = E. Cannot be uniquely determined

b = The number of boys
g = The number of girls
s = The price of 1 soda
j = The price of 1 juice box

We just reach the point below:

$$b-g = \frac{1}{j-s}$$

To satisfy this equation, j-s has to be 1, means cost of juice has to be greater than cost of soda by 1, however nowhere in the question, this information is given.

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

05 Feb 2015, 22:50
kdatt1991 wrote:
Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.

This was quite a tricky question for me, but I hope that I have been able to crack it! Here's my solution:

Let's assign variables for boys (b), girls (g), sodas (s), juices boxes (j) and the total cents spent as (t). From the information given in the question stem, we also know that boys are greater than girls (b > g). Let's set up some equations:

b*s + g*j = t - 1.... (the total if every boy in the class buys a soda and every girl in the class buys a juice box)

b*j + g*s = t.... (the total if every boy in the class buys a juice box and every girl in the class buys a soda)

We can subtract both equations from each other to cancel out the variable (t). This gives us:

b*j + g*s - (b*s + g*j) = t - (t - 1)..... this gives us: b*j - b*s - g*j + g*s = 1. We can further factorise this equation as b*(j - s) - g*(j - s) = 1........ (b - g)*(j - s) = 1.

From the factorised equation (b - g)*(j - s) = 1, we can say that either (b - g) =1 or (j - s) = 1. This basically means that either the number of boys are one more than the number of girls (b = g + 1) or that the price of a juice box costs 1¢ higher than the price of a soda can (j = s +1). Since we know (from the question stem) that b > g, we could conclude that b = g + 1, and that the prices of both the juices boxes and the sodas are the same!

I think the answer is A.

Please consider giving me KUDOS if you felt this post was helpful and correct! or please enlighten me (in case my answer's incorrect) so that I can learn and improve from my mistakes! Thanks.

Is the factorization correct?

b-g = 1 ONLY WHEN j-s = 1, similarly

j-s = 1 ONLY WHEN b-g = 1

No where in the problem is given that individual difference is 1
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9849
Location: Pune, India
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

06 Feb 2015, 01:55
2
chetan2u wrote:
CEZZAR89 wrote:
I will go with A

Here is my solution:

boys (b) , girls (g) , soda (s) , juice box (j) assuming b,g,s,and j are all integers.
Given that b>g
Q: What is b-g ?

Total amount spent ;

Therefore the equation must be

b*s+g*j+1=b*j+g*s

we should try to solve the equation for (b-g) ;
b*s+g*j - b*j-g*s=-1
b(s-j) - g(s-j)=-1
(b-g)(s-j)= -1
Isolate (b-g) to one side of the equation ;
b-g = -1/(s-j)
We know that both b-g and s-j result integers, and b-g must be positive, therefore s-j can only be -1 which makes b-g=1

hi CEZZAR, kdatt and many others who have given answer as A ie 1..
just one point to ponder..
you all have correctly come down to the final equation, which is
(b-g)(s-j)= 1... but hereon we all are going wrong
b- g can take infinite values depending on the value of (s-j), which can be 1, 1/2,1/3,1/100 and so on..
so ans should be E, depending on values of juice and soda....

Thanks for recapping Chetan, but here is the problem - Everyone agrees that b and g will take integer values but forget that s and j must take integer values too. Note that the cost is given in cents, the smallest monetary unit. The difference between the cost of soda and juice box cannot be less than 1 cent.

When you get the equation (b-g)(s-j)= 1,
b-g can be 4 only if (s-j) is 1/4. But note that prices are defined only up to a cent.
Hence b-g and s-j both must be 1.

Therefore, the difference between the number of boys and number of girls MUST be 1.

_________________
Karishma
Veritas Prep GMAT Instructor

Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

06 Feb 2015, 06:25
1
VeritasPrepKarishma wrote:
chetan2u wrote:
CEZZAR89 wrote:
I will go with A

Here is my solution:

boys (b) , girls (g) , soda (s) , juice box (j) assuming b,g,s,and j are all integers.
Given that b>g
Q: What is b-g ?

Total amount spent ;

Therefore the equation must be

b*s+g*j+1=b*j+g*s

we should try to solve the equation for (b-g) ;
b*s+g*j - b*j-g*s=-1
b(s-j) - g(s-j)=-1
(b-g)(s-j)= -1
Isolate (b-g) to one side of the equation ;
b-g = -1/(s-j)
We know that both b-g and s-j result integers, and b-g must be positive, therefore s-j can only be -1 which makes b-g=1

hi CEZZAR, kdatt and many others who have given answer as A ie 1..
just one point to ponder..
you all have correctly come down to the final equation, which is
(b-g)(s-j)= 1... but hereon we all are going wrong
b- g can take infinite values depending on the value of (s-j), which can be 1, 1/2,1/3,1/100 and so on..
so ans should be E, depending on values of juice and soda....

Thanks for recapping Chetan, but here is the problem - Everyone agrees that b and g will take integer values but forget that s and j must take integer values too. Note that the cost is given in cents, the smallest monetary unit. The difference between the cost of soda and juice box cannot be less than 1 cent.

When you get the equation (b-g)(s-j)= 1,
b-g can be 4 only if (s-j) is 1/4. But note that prices are defined only up to a cent.
Hence b-g and s-j both must be 1.

Therefore, the difference between the number of boys and number of girls MUST be 1.

hi karishma,
this was what i too thought while i answered this Question with whatever knowledge i have on currency. But then there were three points..
1) would the GMAC people test us on knowledge of currency. i may know it but the exam is widely held in different parts of world.
2) if this same question talks of discount of 10% on say both the items, does it mean that .9*juicebox-.9*soda should be an integer. If so, we have to have both these items costing in multiple of 10 cents...
3) if some question talks of some item in terms of dozens, does it mean that it should be costing in multiples of 12.
i know it is logical that the price should be in integer cents, and i dont doubt that for a second.
Ofcourse i know my answer to this question is wrong as it comes from you, the source itself
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9849
Location: Pune, India
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

08 Feb 2015, 22:24
chetan2u wrote:

hi karishma,
this was what i too thought while i answered this Question with whatever knowledge i have on currency. But then there were three points..
1) would the GMAC people test us on knowledge of currency. i may know it but the exam is widely held in different parts of world.
2) if this same question talks of discount of 10% on say both the items, does it mean that .9*juicebox-.9*soda should be an integer. If so, we have to have both these items costing in multiple of 10 cents...
3) if some question talks of some item in terms of dozens, does it mean that it should be costing in multiples of 12.
i know it is logical that the price should be in integer cents, and i dont doubt that for a second.
Ofcourse i know my answer to this question is wrong as it comes from you, the source itself

1) Perhaps not. Note that this question is an experimental question in our question bank. Through it, we are trying to bring across the importance of logic and reasoning in this test. We are forcing you to imagine the situation in the real world. We expect that most people who come across this question would know that 1 cent is the smallest currency denomination. In case we find that it is not so, we may edit the question a bit in the future.

If the discount given is exactly 10%, then it is logical that the cost would be a multiple of 10 cents. As for a dozen items, it depends on how the question is framed. If the items are available only as a closed pack with dozen items, it can cost anything. If items can be sold loose out of the pack, the cost of each item would be specified.

Recall that you do use such logic in Quant questions such as when you deal with integer solutions of equations in 2 variables etc. The number of pens should be an integer etc.
_________________
Karishma
Veritas Prep GMAT Instructor

Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

09 Feb 2015, 04:59
Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

b = # of boys

g = # of girls

s = cost of a soda, in cents

j = cost of a juice, in cents

Here's how we translate the first sentence into math:

sb + jg + 1 = jb + sg

Now we'll subtract sb and jg from both sides, so we can get all of our integers equal to an integer.

1 = jb - jg + sg - sb

1 = j(b-g) + s(g-b)

1 = j(b-g) + s(-1)*(b-g) we do this we can have a common term of (b - g) that we can then factor out

1 = j(b-g) - s(b-g)

1 = (j - s) * (b - g)

At this point we seem stuck, but notice what we have. We know j, s, b, and g are integers, as they represent prices in cents (which must be integers, e.g. 1 cent, 2 cents, 3 cents, etc.) and people, respectively. We know we have more boys than girls, so (b - g) is positive. If we have a positive integer times another integer = 1, then BOTH integers must be 1. Hence (b - g) = 1 and (s - j) = 1, and the answer is A.
Manager
Joined: 21 Apr 2016
Posts: 162
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

02 Apr 2017, 17:20
If the price of 10 candies is 1 cent, price per candy is 1/10th of a cent. 0.1 cent is a perfect denomination, although physically not available.

What makes us think j-s is an integer?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9849
Location: Pune, India
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

02 Apr 2017, 21:50
1
manhasnoname wrote:
If the price of 10 candies is 1 cent, price per candy is 1/10th of a cent. 0.1 cent is a perfect denomination, although physically not available.

What makes us think j-s is an integer?

In that case, since it is physically not available, you would expect the candies to be always sold in multiples of 10 only. The question forces you to think of the real world. Nothing would be priced in non-integer cent terms.
_________________
Karishma
Veritas Prep GMAT Instructor

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

11 Oct 2018, 10:07
Bunuel wrote:
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?

A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined

$$\left. \matrix{ g\,\,\, = \,\,\# \,\,{\rm{of}}\,\,{\rm{girls}} \hfill \cr b\,\,\, = \,\,\# \,\,{\rm{of}}\,\,{\rm{boys}}\,\,{\rm{ = }}\,\,\,g + k\,\, \hfill \cr} \right\}\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,\,k\,\,\,\,,\,\,\,k \ge 1\,\,\,{\mathop{\rm int}} \,\,\,\,\,\left( {b > g} \right)$$

$$\left. \matrix{ s\,\, = \,\,\,{\rm{one}}\,\,{\rm{soda}} \hfill \cr j\,\, = \,\,\,{\rm{one}}\,\,{\rm{juice}}\,\, \hfill \cr} \right\}\,\,\,\,\,{\rm{cost}}\,\,\,\left( {{\rm{in}}\,\,{\rm{cents}}} \right)$$

$$g,j,k,s\,\,\,\, \ge \,\,\,1\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$

$$\left[ {\left( {g + k} \right)\,j\,\, + \,g\,s} \right]\,\, - \,\,\,\left[ {\left( {g + k} \right)\,s\,\, + \,g\,j} \right]\,\,\, = 1\,\,\,\,\,\,\,\,\,\left[ {\,{\rm{cents}}\,} \right]$$

$$k\left( {j - s} \right) = 1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,k\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{positive}}\,\,{\rm{divisor}}\,\,{\rm{of}}\,\,\,1\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = k = 1$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Non-Human User
Joined: 09 Sep 2013
Posts: 13709
Re: If every boy in a kindergarten class buys a soda and every girl in the  [#permalink]

### Show Tags

02 Nov 2019, 10:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If every boy in a kindergarten class buys a soda and every girl in the   [#permalink] 02 Nov 2019, 10:23
Display posts from previous: Sort by