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

 It is currently 10 Dec 2018, 02:58

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# At the end of the year 1998, Shepard bought nine dozen goats,

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Jan 2016
Posts: 28
At the end of the year 1998, Shepard bought nine dozen goats,  [#permalink]

### Show Tags

Updated on: 25 Jun 2017, 21:20
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:25) correct 36% (02:24) wrong based on 76 sessions

### HideShow timer Statistics

At the end of the year 1998, Shepard bought nine dozen goats, Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > O. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

(1) p = q
(2) P < q
(3) p> q
(4) P = q/2
(5) P = q/4

Originally posted by theperfectgentleman on 25 Jun 2017, 07:22.
Last edited by Bunuel on 25 Jun 2017, 21:20, edited 1 time in total.
Renamed the topic and edited the question.
Senior Manager
Joined: 28 Jun 2015
Posts: 292
Concentration: Finance
GPA: 3.5
Re: At the end of the year 1998, Shepard bought nine dozen goats,  [#permalink]

### Show Tags

25 Jun 2017, 10:19
1
When some value is increased and decreased by the same percentage, the result is always less than the original. For e.g., profit increased 10% in the first year and decreased 10% in the 2nd year would result in 100 -> 110 -> 99.

So, the increase percentage must be higher than the decrease percentage for the result to be the same. Hence, p > q.
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
At the end of the year 1998, Shepard bought nine dozen goats,  [#permalink]

### Show Tags

27 Jun 2017, 15:52
1
theperfectgentleman wrote:
At the end of the year 1998, Shepard bought nine dozen goats, Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > O. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

(1) p = q
(2) P < q
(3) p> q
(4) P = q/2
(5) P = q/4

Good question.

1. When you increase by a percent, then decrease by that same percent, you do not end up where you began. That's a trap. Eliminate A.

2. In fact, if the original ends up at the same value, p% increase is inversely related to q% decrease. Forget 9 dozen. We just need to watch any quantity increase and decrease by percentages and return to its original value. Use 100.

3. If that 100 increases by p% = 25 at the beginning of the year, there are 100 * 1.25 = 125 goats that, um, Shepard :wink: , must herd. Or feed. Or whatever.

By what percentage q must that 125 decrease in order to return to 100? By 1 - (fractional inverse of the increase).

The increase, from decimal to fraction form, is 1.25 = 1$$\frac{25}{100}$$ = 1$$\frac{1}{4}$$ = $$\frac{5}{4}$$

Because percent increase and percent decrease are inversely proportional when the original quantity is the start and end value, flip the percent increase fraction from $$\frac{5}{4}$$ to $$\frac{4}{5}$$ to get the percent decrease multiplier. ------> 125 *$$\frac{4}{5}$$ = 100

So 1 - $$\frac{4}{5}$$= $$\frac{1}{5}$$ or a 20% decrease. Shepard sells 20% of the goats at the end of the year.

Alternatively, $$\frac{4}{5}$$ = .8 = 80%, which is a 20% decrease.

4. p% increase = 25, q% decrease = 20. p > q

p > q. It doesn't matter that there are four years involved.

It wouldn't matter if there were 40 years involved.

Every year, the number of goats starts at the same value and returns to that same value;
the +25% and -20% just keep getting repeated.

p > q

Non-Human User
Joined: 09 Sep 2013
Posts: 9088
Re: At the end of the year 1998, Shepard bought nine dozen goats,  [#permalink]

### Show Tags

06 Jul 2018, 19:55
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: At the end of the year 1998, Shepard bought nine dozen goats, &nbs [#permalink] 06 Jul 2018, 19:55
Display posts from previous: Sort by