Word problem - II - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Word problem - II

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\'manpreet singh: Master | Next Rank: 500 Posts; Posts: 271; Joined: Tue May 22, 2012 3:22 amFollowed by: 3 members; Thanked: 7 times

by \'manpreet singh » Sat Jun 23, 2012 10:12 am

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!!

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Source: Beat The GMAT — Problem Solving | Sat Jun 23, 2012 10:12 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jun 23, 2012 10:39 am

'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 celebrate Christmas have been good this year. If 40% of the children in the world have been good, what percentage of children in the world are not good and do not celebrate Christmas?

Say, there are 100 children in the world.
Hence, 10 children are good but do not celebrate Christmas.
And 40 children are good.

--> (40 - 10) = 30 children are good and celebrate Christmas.
--> 30 = 50% of number of children who celebrate Christmas.
--> 60 children celebrate Christmas.
--> 40 children do not celebrate Christmas.

Hence, (40 - 10) = 30 children are not good and do not celebrate Christmas.

Therefore, required percentage = 30%

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myselfhari: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Feb 10, 2012 12:52 am

by myselfhari » Sun Jun 24, 2012 5:00 am

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.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Jun 24, 2012 5:11 am

myselfhari wrote: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.

x children do not celebrate Christmas. Hence, they cannot be part of this equation. It should be 50% of (y + z) = y ---> z = y = 30

Therefore, w = 100 = (x + y + z) = 100 - (10 + 30 + 30) = 100 - 70 = 30

Hope that helps.

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myselfhari: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Feb 10, 2012 12:52 am

by myselfhari » Sun Jun 24, 2012 5:13 am

Sir,

Thanks. u r a genius.

Thanks.

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\'manpreet singh: Master | Next Rank: 500 Posts; Posts: 271; Joined: Tue May 22, 2012 3:22 amFollowed by: 3 members; Thanked: 7 times

by \'manpreet singh » Sun Jun 24, 2012 7:14 am

Thanks anurag.It was helpful!!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 25, 2012 1:09 am

'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.

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niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Mon Jun 25, 2012 6:03 am

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.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 25, 2012 6:32 am

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

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\'manpreet singh: Master | Next Rank: 500 Posts; Posts: 271; Joined: Tue May 22, 2012 3:22 amFollowed by: 3 members; Thanked: 7 times

by \'manpreet singh » Mon Jun 25, 2012 8:30 pm

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.

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