Problem Solving

Q)Santa estimates that 10% of the children in the world have been good this year but do not celebrate Christmas, and that 50% of the children who celebrateChristmas have been good this year. If 40% of the children in theworld have been good, what percentage of children in the world are notgood and do not celebrate Christmas?

How can i do such a problem in less than 2 mins.i hate reading such a long question as it really has bad effect on my speed and flow.need help on this!!

Anurag Sir,

I have a doubt on this question, basically the data that you have taken.

Let us say, x= no. of children who are good and do not celebrate Christmas.
y= no. of children who are good and celebrate Christmas.
z= no. of children who celebrate Christmas and are not good.
and w= no. of children who are not good and do not celebrate christmas.

Now, as per the question,

x = 10
x + y = 40, => hence y = 30

the question says," 50% of the children who celebrate Christmas have been good this year"

So, 50 % of (y + z) = (x + y), => hence z = 50.

Going by this I get w = 100 - (x + y + z) = 10, meaning 10% of children are not good and do not celebrate christmas.

Please tell me the blunder that i just cannot see.

Sir,

Thanks. u r a genius.

Thanks.

Thanks anurag.It was helpful!!

'manpreet singh wrote:Q)Santa estimates that 10% of the children in the world have been good this year but do not celebrate Christmas, and that 50% of the children who celebrateChristmas have been good this year. If 40% of the children in theworld have been good, what percentage of children in the world are notgood and do not celebrate Christmas?

How can i do such a problem in less than 2 mins.i hate reading such a long question as it really has bad effect on my speed and flow.need help on this!!

This is an EITHER/OR group question.
Every child is EITHER good OR not good.
Every child EITHER celebrates Christmas OR does not.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let G = good, NG = not good, C = celebrates, DC = doesn't celebrate.
Here's the grid, with 100 children plugged in for the total.

_______________G______NG_______Total

C:

DC:

total:___________________________100

Now let's use the information in the problem to complete the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

10% of the children in the world have been good this year but do not celebrate Christmas:

_______________G______NG_______Total

C:

DC:____________10

total:____________________________100

50% of the children who celebrate Christmas have been good this year.
Since we don't yet know how many celebrate Christmas, hold onto this information.

40% of the children in the world have been good:

_______________G______NG_______Total

C:_____________30

DC:____________10

total:___________40______60_______100

Now let's return to the information we skipped over:
50% of the children who celebrate Christmas have been good this year.
Since 30 children who celebrate Christmas have been good, the total number who celebrate Christmas = 60:

_______________G______NG________Total

C:_____________30______30_________60

DC:____________10______30_________40

total:___________40______60________100

Now we can answer the question:
Not good and do not celebrate = 30.

Hi Mitch,
As soon as I saw this question, I approached it with the same logic that you have mentioned but it still took me about 4 mins to solve. I think it's because I have encountered and solved a very few questions of similar type before. Can you please post a link where I can find 5-6 similar questions.

Thanks.
Niket

GMATGuruNY wrote:

'manpreet singh wrote:Q)Santa estimates that 10% of the children in the world have been good this year but do not celebrate Christmas, and that 50% of the children who celebrateChristmas have been good this year. If 40% of the children in theworld have been good, what percentage of children in the world are notgood and do not celebrate Christmas?

How can i do such a problem in less than 2 mins.i hate reading such a long question as it really has bad effect on my speed and flow.need help on this!!

This is an EITHER/OR group question.
Every child is EITHER good OR not good.
Every child EITHER celebrates Christmas OR does not.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let G = good, NG = not good, C = celebrates, DC = doesn't celebrate.
Here's the grid, with 100 children plugged in for the total.

_______________G______NG_______Total

C:

DC:

total:___________________________100

Now let's use the information in the problem to complete the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

10% of the children in the world have been good this year but do not celebrate Christmas:

_______________G______NG_______Total

C:

DC:____________10

total:____________________________100

50% of the children who celebrate Christmas have been good this year.
Since we don't yet know how many celebrate Christmas, hold onto this information.

40% of the children in the world have been good:

_______________G______NG_______Total

C:_____________30

DC:____________10

total:___________40______60_______100

Now let's return to the information we skipped over:
50% of the children who celebrate Christmas have been good this year.
Since 30 children who celebrate Christmas have been good, the total number who celebrate Christmas = 60:

_______________G______NG________Total

C:_____________30______30_________60

DC:____________10______30_________40

total:___________40______60________100

Now we can answer the question:
Not good and do not celebrate = 30.

niketdoshi123 wrote:Hi Mitch,
As soon as I saw this question, I approached it with the same logic that you have mentioned but it still took me about 4 mins to solve. I think it's because I have encountered and solved a very few questions of similar type before. Can you please post a link where I can find 5-6 similar questions.

Thanks.
Niket

Here you go:

https://www.beatthegmat.com/applicants-t84647.html
https://www.beatthegmat.com/gmat-test-takers-t88286.html
https://www.beatthegmat.com/avoiding-alg ... 05954.html
https://www.beatthegmat.com/650-800-question-t68610.html
https://www.beatthegmat.com/interns-at-h ... 62065.html
https://www.beatthegmat.com/problem-solving-t84791.html
https://www.beatthegmat.com/probability- ... 66390.html
https://www.beatthegmat.com/700-ds-tough ... 57-15.html
https://www.beatthegmat.com/please-help- ... 86596.html

If you type "group grid" into the search bar, you might find more.

Hi Mitch its a fast method you used here, just saw that in Manhattan book also , but i think we need to read the problem carefully as there is tricky statement(50% of the children who celebrate Christmas have been good this year)...
What i did wrong trying to solve this problem fast was putting 50 in good children and Christmas celebrating

_______________G______NG_______Total

C:_____________50

DC:____________10

total:___________40______60_______100

which was a blunder!!!but tempting thing to do since i was solving it fast...
so one need to understand the statement carefully before going ahead with solution.