GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Jul 2020, 22:55

### 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

# In a national park, there are only Hippopotamus or Peacocks. When the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64939
In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

### Show Tags

17 Apr 2020, 02:27
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:36) correct 21% (01:57) wrong based on 42 sessions

### HideShow timer Statistics

In a national park, there are only Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it comes out to be 336. What is the number of peacocks in the park?

A. 24
B. 48
C. 60
D. 72
E. 80

Project PS Butler

_________________
Intern
Joined: 13 Apr 2020
Posts: 24
Location: United Kingdom
Schools: LBS '16 (A\$)
Re: In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

### Show Tags

17 Apr 2020, 02:53
1
Let's note h the number of hippos and p the number of peacocks.

Each animal has only one head (assuming there is no genetic engineering going on!) so the number of heads give us the following equation:
(1) h + p = 96

A hippo has 4 legs and a peacock has 2 legs. Therefor, the "leg count" gives us:
(2) 4h+2p = 336 that can also be simplified to 2h+p = 168 (by dividing both sides by 2)

Subtracting equation (1) from equation (2) give us:
2h+p - (h + p) = 168-96

which is equivalent to:
h = 72

The easy mistake here is to go and click (D) straight away !!!!! , but let's remember that we're looking for the number of peacocks rather than hippos!
Using (1) we have p = 96 - h = 96 - 72 = 24

The answer is (B) 24 peacocks
_________________
Graeme
Founder of MBA Backstage
http://www.mbabackstage.com/guides/
GMATWhiz Representative
Joined: 07 May 2019
Posts: 796
Location: India
Re: In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

### Show Tags

17 Apr 2020, 03:21
1
Bunuel wrote:
In a national park, there are only Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it comes out to be 336. What is the number of peacocks in the park?

A. 24
B. 48
C. 60
D. 72
E. 80

Project PS Butler

Solution:

Each peacock will have one head and two legs, and each Hippopotamus will have one head and four legs.
Let x and y be the number of peacock and hippopotamus respectively.
o $$x + y = 96$$ …(i)
• legs of peacock + legs of hippopotamus = total legs
o $$2x + 4y = 336$$
 $$x + 2y = 168$$…(ii)
• Equation (i), can be written as;
o $$y = 96 – x$$
• On substituting above value in equation (ii), we get
o $$x +2(96-x) = 168$$
o $$x + 192 – 2x = 168$$
o $$192-168 = x$$
o $$x = 24$$
Hence, the correct answer is Option A.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Director
Joined: 04 Dec 2015
Posts: 723
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

### Show Tags

17 Apr 2020, 17:37
1
Bunuel wrote:
In a national park, there are only Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it comes out to be 336. What is the number of peacocks in the park?

A. 24
B. 48
C. 60
D. 72
E. 80

Project PS Butler

Let Hippopotamus be $$H$$ and Peacock be $$P$$ . Each Hippopotamus will have $$1$$ head and $$4$$ legs, and each Peacock will have $$1$$ head and $$2$$ legs.

Total number of heads $$=>$$

$$H + P = 96 ----- (i)$$

$$H = 96 - P ----- (ii)$$

Total number of legs $$=>$$

$$4 H + 2 P = 336 ----- (iii)$$

Substituting value of $$H$$ in equation $$(iii)$$, we get;

$$4 (96-P) + 2 P = 336$$

$$384 - 4P + 2P = 336$$

$$384 - 2P = 336$$

$$2P = 384 - 336 = 48$$

$$P = \frac{48}{2} = 24$$

Total number of Peacocks $$= 24$$

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3410
In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

### Show Tags

31 May 2020, 06:41

Solution

Given
• Total count of Heads = 96. Total count of Legs = 336.

To Find
• Number of peacocks.

Approach and Working Out
The question can be solved using the process skill of ‘translation’. Let’s see how.
(Conceptual knowledge needed = Solving linear equations)
• Let the numbers of hippopotamus be H and that of Peacocks be P.
• Translating the first statement as H + P =96. Since both H and P have one head each. Thus the number of heads = number of both hippopotamus and peacocks taken together.
• Using translation again for second statement: 4H + 2P = 336. Since each hippopotamus has 4 legs and each peacock has 2 legs, thus the number of legs of hippopotamus = 4H and number of legs of peacocks = 2P.
• Solving the two equations gives us H = 72 and P = 24.

_________________
In a national park, there are only Hippopotamus or Peacocks. When the   [#permalink] 31 May 2020, 06:41