BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Probability

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Mon Feb 08, 2010 8:19 am
Location: Norway
Thanked: 1 times

Probability

by C » Wed Apr 14, 2010 9:30 pm
A zoo has w wildebeests, y yaks, z zebras, and no other animals. If an animal is chosen at random from the zoo, is the probability of choosing a yak greater than the probability of choosing a zebra?

(1) y/w+z > 1/2

(2) z/w+y < 1/2

OA is C

Source is MGMAT Word Translations.

Hope someone can explain. Thanks.
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pm
Thanked: 97 times
Followed by:1 members

by liferocks » Wed Apr 14, 2010 9:51 pm
A zoo has w wildebeests, y yaks, z zebras, and no other animals. If an animal is chosen at random from the zoo, is the probability of choosing a yak greater than the probability of choosing a zebra?

(1) y/w+z > 1/2

(2) z/w+y < 1/2

probability of choosing a yak =y/(W+y+z)
probability of choosing a zebra =z/(W+y+z)

from 1 we get y/(w+z)>1/2 or y/(w+y+z)>1/3-->not sufficient
from 2 we get z/(w+y)<1/2 or z/(w+y+z)<1/3-->not sufficient

together we can say z/(w+y+z)<y/(w+y+z) -->sufficient ans C

note: I have assumed that condition is like y/(w+z)>1/2 and z/(w+y)<1/2 if this is not correct than above logic does not hold good.
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Thu Apr 15, 2010 12:22 am
liferocks wrote:A zoo has w wildebeests, y yaks, z zebras, and no other animals. If an animal is chosen at random from the zoo, is the probability of choosing a yak greater than the probability of choosing a zebra?

(1) y/w+z > 1/2

(2) z/w+y < 1/2

probability of choosing a yak =y/(W+y+z)
probability of choosing a zebra =z/(W+y+z)

from 1 we get y/(w+z)>1/2 or y/(w+y+z)>1/3-->not sufficient
from 2 we get z/(w+y)<1/2 or z/(w+y+z)<1/3-->not sufficient

together we can say z/(w+y+z)<y/(w+y+z) -->sufficient ans C

note: I have assumed that condition is like y/(w+z)>1/2 and z/(w+y)<1/2 if this is not correct than above logic does not hold good.
great explanation

For those who can be misled by the bold part in the above post must know that w, y, and z are positive integers and:

when y/ (w + z) > 1/2; (w + z)/y < 2,

or [(w + z)/y] + 1 < 2 + 1,

or (w + y + z)/y < 3,

or y/(w + y + z) > 1/3; and

when z/ (w + y) < 1/2; (w + y)/z > 2,

or [(w + y)/z] + 1 > 2 + 1,

or (w + y + z)/z > 3,

or z/(w + y + z) < 1/3.

Therefore comparison is possible.

[spoiler]C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Fri Aug 02, 2013 12:34 am
Location: New Delhi, India

by digvijay.rajput » Fri Aug 02, 2013 1:00 am
In the above example, can you please explain these steps....

when y/ (w + z) > 1/2; (w + z)/y < 2,

or [(w + z)/y] + 1 < 2 + 1,

or (w + y + z)/y < 3,

Thanks in advance
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Fri Aug 02, 2013 4:16 am
digvijay.rajput wrote:In the above example, can you please explain these steps....

when y/ (w + z) > 1/2; (w + z)/y < 2,

or [(w + z)/y] + 1 < 2 + 1,

or (w + y + z)/y < 3,

Thanks in advance
Take suitable numbers for the variables when you are in fix.

E.g. if 3/4 > 1/2, then 4/3 < 2 RIGHT!

OR

If 5 > 1/2, then 1/5 < 2; the statement would consistently remain true. Do the remaining math likewise.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Aug 02, 2013 3:48 pm
Hi C,

This DS question can be beaten by TESTing values and a bit of logic:

The question asks if the probability of picking a yak is greater than the probability of picking a zebra.

Since we're dealing with a certain number of animals (and positive integers only), this question can be rewritten as: "Is Y > Z"?

Fact 1 tells us that Y/(W+Z) > 1/2

We could have
Y = 4
W = 1
Z = 1
The answer to the question is YES

We could also have
Y = 4
W = 1
Z = 5
The answer to the question is NO
Inconsistent = INSUFFICIENT

Fact 2 tells us that Z/(W+Y) < 1/2

We could have
Y = 4
W =1
Z = 1
The answer to the question is YES

We could also have
Y = 4
W = 10
Z = 5
The answer to the question is NO
Inconsistent = INSUFFICIENT

Now, we have to COMBINE Facts (and we get a number property shortcut). Since the W is a "fixed" value in both inequalities, it's the Y and Z that have to change to fit the > or <. In this scenario, by definition, the Y would have to be greater than the Z.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Aug 02, 2013 4:31 pm
Maybe an easier way:

(If I'm reading this right, the original statements are y/(w+z) > 1/2 ... not (y/w) + z > 1/2. If I'm mistaken, ignore this post.)

The question is really "Are there more yaks than zebras?" or "is y > z?"

S1::
y/(w+z) > 1/2
2y > w + z
y + y > w + z

So y > w or y > z, but we don't know which. (Both could be true, for that matter.)

S2::
1/2 > z/(w+y)
w + y > 2z
w + y > z + z

Much like the above: w > z or y > z, but we don't know which.

Combining the two statements, we have two options:

Either y > z ... or y > w and w > z, implying y > z. So y > z.
Top
Post new topic Post Reply
• Page 1 of 1