Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 30 Mar 2015, 08:16

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# John has 7 bananas and 3 kiwis .he needs to divide the 10 in

Author Message
TAGS:
Manager
Joined: 30 Jul 2004
Posts: 102
Followers: 1

Kudos [?]: 0 [0], given: 0

John has 7 bananas and 3 kiwis .he needs to divide the 10 in [#permalink]  30 Nov 2004, 19:02
John has 7 bananas and 3 kiwis .he needs to divide the 10 in 2 parcels
so that there is an equal total number of fruit in either parcel and so that there is at least one kiwi in each parcel.
How many ways ?

a) 21
b) 35
c) 60
d) 105
e) 120

Director
Joined: 16 Jun 2004
Posts: 893
Followers: 1

Kudos [?]: 18 [0], given: 0

Anyways, I think..

a) There has to be 5 in each parcel with atleast 1 kiwi in each of them.
b) In such case, it would be to choose the first 5 in the first parcel and the parcel 2 will only have what is left automatically.
c) So, ways to choose the first parcel would be

3C1*7C4 + 3C2*7C3 = 210.

3C1 (one kiwi out of 3) * 7C4 (because remaning 4 fruits from the 7 bannas) OR 2 kiwis and 3 bananas. There cant be a 3 kiwi situation as the restraint is that there got to be atleast one kiwi in a parcel.

Am I missing anything here..?
Manager
Joined: 30 Jul 2004
Posts: 102
Followers: 1

Kudos [?]: 0 [0], given: 0

-- No , it is 120 as given.

Nothing is missing in the question..........
Director
Joined: 16 Jun 2004
Posts: 893
Followers: 1

Kudos [?]: 18 [0], given: 0

If we choose 3C1*7C4 in one of the parcels, the other parcel will naturally have what is left and since it does not matter which parcel has the combination above, it will simply be 105.
Manager
Joined: 30 Jul 2004
Posts: 102
Followers: 1

Kudos [?]: 0 [0], given: 0

OA is D) ..You are right 105.

Your explanation is easier to understand as compared to the explanation in original source....

But don't we take into account the combinations for other parcel...pls. elaborate little more...

Thanks !
CIO
Joined: 09 Mar 2003
Posts: 465
Followers: 2

Kudos [?]: 33 [0], given: 0

venksune wrote:

If we choose 3C1*7C4 in one of the parcels, the other parcel will naturally have what is left and since it does not matter which parcel has the combination above, it will simply be 105.

Not 100% on this one, but I think I agree with venksune.

Notice that if you work out the combination in the other direction, meaning, if you work out how many ways to have 2 kiwi and 3 bananas, it also comes out to 105.

where is this question from?
Manager
Joined: 30 Jul 2004
Posts: 102
Followers: 1

Kudos [?]: 0 [0], given: 0

got it from gmat club...bought some questions from gmat club.....
Director
Joined: 21 Sep 2004
Posts: 618
Followers: 1

Kudos [?]: 6 [0], given: 0

it would be either 3c2 * 7c3 ways or 3c1 * 7c4 ways which is the same.
105.
Director
Joined: 31 Aug 2004
Posts: 606
Followers: 3

Kudos [?]: 40 [0], given: 0

My first answer was 1... as there is no clue that these fruits are dinstinct...

Since we having only 2 parcels, allocating fruits to the first one will lead to the same number of ways as allocating fruits to the second one.

1st one (2K, 3B) = 3C2.7C3 = 3.35 = 105
or
2nd one (1K, 4B) = 3C1.7C4 = 3.35 = 105
Similar topics Replies Last post
Similar
Topics:
8 John has 10 pairs of matched socks. If he loses 7 individual 8 11 Sep 2012, 03:41
1 John has 12 clients and he wants to use color coding to iden 4 03 Jan 2011, 17:02
John has to paint a wall with seven horizontal stripes. He 4 26 Oct 2008, 02:05
John has 12 clients and he wants to use color coding to 4 26 Aug 2008, 16:27
John has 7 bananas and 3 kiwis. In how many ways can John 3 06 Feb 2007, 09:17
Display posts from previous: Sort by