Pigs and sheep

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 31, 2008 2:28 pm

In 2004, the number of sheep on the farm was equal to the number of pigs. In 2005, the population of pigs and sheep each increased 20%.
Which of the following could represent the total number of pigs and sheep on the farm in 2005?

(A) 4832
(B) 5034
(C) 5058
(D) 5076
(E) 5128

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Source: Beat The GMAT — Problem Solving | Wed Dec 31, 2008 2:28 pm

daisy: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Dec 31, 2008 2:20 pm; Location: London

by daisy » Wed Dec 31, 2008 2:44 pm

Answer choices seems to be incorrect. At least one option should be completely divisible by 11.

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by Brent@GMATPrepNow » Wed Dec 31, 2008 3:10 pm

I'm pretty sure the correct answer is there. Having said that, these are questions that I've created I could be wrong.

I'm wondering why the number must be divisible by 11.

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amitabhprasad: Master | Next Rank: 500 Posts; Posts: 259; Joined: Thu Jan 18, 2007 8:30 pm; Thanked: 16 times

by amitabhprasad » Wed Dec 31, 2008 3:24 pm

I am getting "D"
is this correct ?

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: Pigs and sheep

by logitech » Wed Dec 31, 2008 3:28 pm

So the overall number actually increase by 20% , which makes it 120 %, in other words the number needs be divided by 12

It is divisible by 3 and by 4. 324: it is divisible by 3 and by 4.
Subtract the last digit from twice the rest. 324: (32 × 2) − 4 = 60.

5076 fits in.

Enjoy the link below:

https://en.wikipedia.org/wiki/Divisibility_rule

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 31, 2008 3:30 pm

Sheep = Pig 2004

2005 1.2 Sheep = 1.2Pigs

The only value that works is D) 5076

5076 divisible by 12

Good problem Brent!

Last edited by cramya on Wed Dec 31, 2008 3:36 pm, edited 3 times in total.

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daisy: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Dec 31, 2008 2:20 pm; Location: London

by daisy » Wed Dec 31, 2008 3:31 pm

Brent Hanneson wrote:I'm pretty sure the correct answer is there. Having said that, these are questions that I've created I could be wrong.

I'm wondering why the number must be divisible by 11.

Ok I got my mistake. The number should be divisible by 12. Only (D) is the option that is divisible by both 3 and 4. Will choose (D).

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 31, 2008 3:36 pm

The answer is D - nice work.
It's important to note, though, that if the question involved only one animal type, then the resulting population (after the 20% increase) would need to be divisible by 6, not 12.

This is because increasing a number by 20% is the same as multiplying the number by 6/5. The 5 in the denominator would have to cancel out with the original population (or else we would have partial animals).

The reason the resulting number must divisible by 12 is due to the fact that we have 2 equivalent populations.

Brent Hanneson - Creator of GMATPrepNow.com

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brb588: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Nov 17, 2008 11:35 pmFollowed by: 1 member; Thanked: 6 times

by brb588 » Wed Dec 31, 2008 3:37 pm

What's the least it can be? Well, it's 12 (5 pigs, 5 sheep, 20% of the total is 2, which equals 12). Therefore the choice has to be divisible by 12.

Since I know that 12 is divisible by 6, the number has to also be divisible by 6, so now I have to check if the answer choices are divisible by 2 and 3 (as a rule). There is only one choice that is--D.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Wed Dec 31, 2008 3:41 pm

Composite divisors

A number is divisible by a given divisor if it is divisible by the highest power of each of its prime factors. For example, to determine divisibility by 24, check divisibility by 8 and by 3. Note that checking 4 and 6, or 2 and 12, would not be sufficient. A table of prime factors may be useful.

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"DON'T LET ANYONE STEAL YOUR DREAM!"

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Thu Jan 01, 2009 1:56 am

gr8 info logitech....awesm..i was not aware of this rule...

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piyush_nitt: Master | Next Rank: 500 Posts; Posts: 424; Joined: Sun Dec 07, 2008 5:15 pm; Location: Sydney; Thanked: 12 times

by piyush_nitt » Thu Jan 01, 2009 3:50 am

[quote="cramya"]Sheep = Pig 2004

2005 1.2 Sheep = 1.2Pigs

The only value that works is D) 5076

5076 divisible by 12

Good problem Brent![/quote]

Here total combined population would be 1.2Sheep+1.2Pigs

and as Sheep = PIGS

therefore Total population = 2.4 PIGS/Sheeps

Correct me if I am wrong but i guess the figure should be divisible y 24 rather than 12. plz explain ?

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Thu Jan 01, 2009 10:51 am

vivek.kapoor83 wrote:gr8 info logitech....awesm..i was not aware of this rule...

Me neither! But now we all are l!! Beware us GMAT!

LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"

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piyush_nitt: Master | Next Rank: 500 Posts; Posts: 424; Joined: Sun Dec 07, 2008 5:15 pm; Location: Sydney; Thanked: 12 times

by piyush_nitt » Thu Jan 01, 2009 11:30 am

Anyone plz explain?

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brb588: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Nov 17, 2008 11:35 pmFollowed by: 1 member; Thanked: 6 times

by brb588 » Thu Jan 01, 2009 3:09 pm

piyush_nitt wrote:Anyone plz explain?

What should be explained?

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