It is currently 17 Dec 2017, 08:05

### 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

# Terry holds 12 cards, each of which is red, white, green, or

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42649

Kudos [?]: 135955 [0], given: 12717

Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

11 Sep 2012, 03:52
Expert's post
27
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:24) correct 30% (01:10) wrong based on 1671 sessions

### HideShow timer Statistics

Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

Practice Questions
Question: 39
Page: 278
Difficulty: 650
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135955 [0], given: 12717

Math Expert
Joined: 02 Sep 2009
Posts: 42649

Kudos [?]: 135955 [4], given: 12717

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

11 Sep 2012, 03:52
4
KUDOS
Expert's post
12
This post was
BOOKMARKED
SOLUTION

Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

The question asks whether $$\frac{red+white}{12}<\frac{1}{2}$$ --> is $$red+white<6$$. So, basically we need to know whether the number of red or white cards is less than 6.

(1) The probability that the person will select a blue card is 1/3 --> the number of blue cards is $$\frac{1}{3}*12=4$$. Now, if there is only 1 green card then the number of red or white cards is 12-(4+1)=7 but if there are 3 green cards, then the number of red or white cards is 12-(4+3)=5. Not sufficient.

(2) The probability that the person will select a red card is 1/6 --> the number of red cards is $$\frac{1}{6}*12=2$$. Not sufficient since we don't know the number of white cards.

(1)+(2) We know that there are 4 blue and 2 red cards, but we still don't know how many white cards are there: if there is only one, then the answer is YES but if there are 5 then the answer is NO. Not sufficient.

_________________

Kudos [?]: 135955 [4], given: 12717

Intern
Joined: 12 Jun 2012
Posts: 40

Kudos [?]: 42 [1], given: 28

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

11 Sep 2012, 07:08
1
KUDOS
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

Can we determine if there are less than 6 total R or W's in the pack?

(1) There is 4 blues so 8 other cards. Therefore R+W <8, if 7 no, if 5, yes. INEFF

(2) There is 2 reds so 10 other cards. At least 1B and 1G so there is at most 8 other Whites. So at most 10/12 can be R+W, at least 3 INEFF

Together if we say number of R+W = x (i) says 2<x<8, (ii) says 1<x<10 so both together INEFF

Therefore E
_________________

Kudos [?]: 42 [1], given: 28

Senior Manager
Joined: 15 Jun 2010
Posts: 356

Kudos [?]: 468 [2], given: 50

Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

12 Sep 2012, 03:26
2
KUDOS
Bunuel wrote:
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

ST 1: Insufficient: P(blue) = 1/3, means there are 4 blue cards. So remaining are 8 cards, but don't know exact distribution. If we consider green =1, P(R+W) >1/2, but if we consider green = 4, P(R+W)<1/2. So insufficient.

ST2: Insufficient: P(Red) = 1/6, means there are 2 red cards. So remaining are 10, but don't know exact distribution. If we take white as 5 P(R+W)>1/2, If we take white 2, P(R+W)<1/2. So insufficient.

St 1 + St 2: Insufficient: Red =2, Blue = 4, Remaining 6 cards. If we take white 5, P(R+W) >1/2, But if we take White 2 P(R+W) <1/2. So insufficient.

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Kudos [?]: 468 [2], given: 50

Senior Manager
Joined: 24 Aug 2009
Posts: 493

Kudos [?]: 881 [2], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

12 Sep 2012, 12:38
2
KUDOS
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?
(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

Trick- There is no need to calculate Probability as the question ask about the total no of Red & White cards.
Basically the question can be restated as is the number of Red & White cards less than 6-- Red + White <6

Red+ White + Green + Blue = 12
Statement 1 - Probability of Blue = 1/3 = 4 blue cards are there ---->No info is given regarding Red & White----->Insufficient
Statement 2 - Probability of Red = 1/6 = 2 red cards are there ---->No info is given regarding White cards----->Insufficient
Statement 1 & 2 - Red+ White + Green + Blue = 12
2+ White + Green + 4 = 12 -----> White + Green = 6
Now green can be any number from 0 to 6 i.e. Red + white can be 2,3,4,5,6,7,8----> Insufficient

Hope it helps
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Kudos [?]: 881 [2], given: 276

Director
Joined: 29 Nov 2012
Posts: 862

Kudos [?]: 1492 [0], given: 543

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

01 Feb 2013, 23:32
Bunuel wrote:
SOLUTION

Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

The question asks whether $$\frac{red+white}{12}<\frac{1}{2}$$ --> is $$red+white<6$$. So, basically we need to know whether the number of red or white cards is less than 6.

(1) The probability that the person will select a blue card is 1/3 --> the number of blue cards is $$\frac{1}{3}*12=4$$. Now, if there is only 1 green card then the number of red or white cards is 12-(4+1)=7 but if there are 3 green cards, then the number of red or white cards is 12-(4+3)=5. Not sufficient.

(2) The probability that the person will select a red card is 1/6 --> the number of red cards is $$\frac{1}{6}*12=2$$. Not sufficient since we don't know the number of white cards.

(1)+(2) We know that there are 4 blue and 2 red cards, but we still don't know how many white cards are there: if there is only one, then the answer is YES but if there are 5 then the answer is NO. Not sufficient.

but don't we know that between red and white there are 6 cards remaining so we get red + white < 6 so it will be a NO in all cases or have I missed something over here?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1492 [0], given: 543

Math Expert
Joined: 02 Sep 2009
Posts: 42649

Kudos [?]: 135955 [1], given: 12717

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

01 Feb 2013, 23:48
1
KUDOS
Expert's post
fozzzy wrote:
Bunuel wrote:
SOLUTION

Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

The question asks whether $$\frac{red+white}{12}<\frac{1}{2}$$ --> is $$red+white<6$$. So, basically we need to know whether the number of red or white cards is less than 6.

(1) The probability that the person will select a blue card is 1/3 --> the number of blue cards is $$\frac{1}{3}*12=4$$. Now, if there is only 1 green card then the number of red or white cards is 12-(4+1)=7 but if there are 3 green cards, then the number of red or white cards is 12-(4+3)=5. Not sufficient.

(2) The probability that the person will select a red card is 1/6 --> the number of red cards is $$\frac{1}{6}*12=2$$. Not sufficient since we don't know the number of white cards.

(1)+(2) We know that there are 4 blue and 2 red cards, but we still don't know how many white cards are there: if there is only one, then the answer is YES but if there are 5 then the answer is NO. Not sufficient.

but don't we know that between red and white there are 6 cards remaining so we get red + white < 6 so it will be a NO in all cases or have I missed something over here?

Total = 12
_________
Blue = 4
Red = 2
White = ?

Green = ?

If there is 1 white card and 5 green cards, then red+white=3<6.
If there are 5 white cards and 1 green card, then red+white=6.

Hope it's clear.
_________________

Kudos [?]: 135955 [1], given: 12717

Intern
Joined: 07 Sep 2014
Posts: 4

Kudos [?]: 19 [0], given: 3

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

20 Jul 2015, 12:10
You will ultimately draw the same conclusion as the above methodologies, but my approach was slightly different:

Given: R + W + B + G = 12; prove that either (1) R + W <6 OR (2) B + G > 6.

(1) B = 1/3 * 12 = 4; thus, can simplify (2): (4) + G > 6? G > 2? Since we have not been provided any information pertaining to the value of G, insufficient.

(2) R = 1/6 * 12 = 2; thus, can simplify (1): (2) + W < 6? W < 4? Since we have not been provided any information pertaining to the value of W, insufficient.

Combo: Can we answer either from S1 G > 2 or from S2 W < 4? Using the information provided in both statements, (2) + W + (4) + G = 12; thus, we can deduce that W + G = 6.

W = 2, G = 3 YES
W = 5, G = 1 NO

Hence, (E)

Kudos [?]: 19 [0], given: 3

Intern
Joined: 15 Sep 2015
Posts: 8

Kudos [?]: 6 [0], given: 3

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

02 Oct 2015, 00:45
I guess my approach was a little different.

S1) P(B) ~33% , that leaves roughly 67% for the rest of the probabilities. We're not given any information about R,G,W, so NS. If P(B)>50%, than this would have been sufficient. Since we don't need any information on the number or ratio of the cards to total, to answer if it's less the P(R or W)<50%. Not Sufficient

S2) P(R) ~ 17%. Same logic as S1 Applies, we can have a case where W makes up the majority of the cards, or has minimal representation. One leading to P(R or W)>50%, and the other P(R or W)<50%. Not Sufficient

S1 + S2: Known probability is 50%, leaving the other half to be shared by G or W. We can have a case where W is around 40%, leaving 10% for G, this would put P(R or W)>50%, or we can have a case where W is 10%, and G is 40%, which would mean P(R or W)<50%. Not Sufficient

Kudos [?]: 6 [0], given: 3

Director
Joined: 04 Jun 2016
Posts: 645

Kudos [?]: 390 [0], given: 36

GMAT 1: 750 Q49 V43
Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

05 Aug 2016, 06:22
Bunuel wrote:
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

Practice Questions
Question: 39
Page: 278
Difficulty: 650

From stimulus
Total cards = 12

(1) The probability that the person will select a blue card is 1/3
Blue = 1/3 of 12
Therefore there are 4 blue cards , We dont know anything about Red, white or green
INSUFFICIENT

(2) The probability that the person will select a red card is 1/6
Red = 1/6 of 12
Therefore there are 2 red cards
We don't know anyting about blue green and white cards
INSUFFICIENT

MERGE BOTH STATEMENTS
Blue = 4 ; Red = 2 ; Red and Blue = 6 ; White and Green=6
We still don't know how many WHITE cards are there. There can be 1 or 2 or 3 or 4 or 5 white cards
Therefore our probability with keep changing.
P(Red)*P(White)= 1/2 * {1/12} or {2/12} or {3/12} or {4/12} or {5/12}
NOT SUFFICIENT

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 390 [0], given: 36

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1810

Kudos [?]: 990 [1], given: 5

Re: Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

25 Aug 2016, 15:03
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

We are given that Terry has 12 total cards. The cards are colored red, white, green, or blue. We need to determine whether the probability of selecting a red or a white card is less than ½. Remember, since we are determining the probability of selecting a red or a white card, we must add the probabilities.

Is P(red card) + P(white card) < ½?

Since the sum of all probabilities in a sample set is equal to 1, we also know that:

P(red card) + P(white card) + P(blue card) + P(green card) = 1

P(red card) + P(white card) = 1 – [P(blue card) + P(green card)]

Thus, if we can determine the sum of the probabilities of selecting a red card and of selecting a white card OR the sum of the probabilities of selecting a blue card and of selecting a green card, we also could determine the probability of selecting a red or white card.

Statement One Alone:

The probability that the person will select a blue card is 1/3.

Since we don’t know the probability of selecting a green card, we cannot determine:

1 – [P(blue card) + P(green card)] OR

P(red card) + P(white card)

Thus, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that the person will select a red card is 1/6.

Since we don’t know the probability of selecting a white card, we cannot determine:

P(red card) + P(white card)

Thus, statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using both statements together we know the following:

P(red card) = 1/6

P(blue card) = 1/3

Substituting this into our two expressions we have:

P(red card) + P(white card) = 1/6 + P(white card) = ?

1 – [1/3 + P(green card)] = ?

We see that we still do not have enough information to determine whether the probability of selecting a red card or a white card is less than ½.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 990 [1], given: 5

SVP
Joined: 11 Sep 2015
Posts: 1913

Kudos [?]: 2769 [0], given: 364

Terry holds 12 cards, each of which is red, white, green, or [#permalink]

### Show Tags

03 Aug 2017, 13:37
Expert's post
Top Contributor
Bunuel wrote:
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3
(2) The probability that the person will select a red card is 1/6

Practice Questions
Question: 39
Page: 278
Difficulty: 650

Given: 12 cards - each card is red, white, green, or blue

Target question: Is the probability less than 1/2 that the card selected will be either red or white?
This is a good candidate for rephrasing the target question.
In order for P(selected card is red or white) < 1/2, it must be the case that there are fewer than 6 cards that are either red or white.
Let R = # of red cards in the deck
Let W = # of white cards in the deck
Let G = # of green cards in the deck
Let B = # of blue cards in the deck
REPHRASED target question: Is R + W < 6?

Statement 1: The probability that the person will select a blue card is 1/3
This tells us that B = 4 (since 4/12 = 1/3)
There are several CONFLICTING scenarios that satisfy statement 1. Here are two:
Case a: R = 2, W = 1, G = 5 and B = 4. In this case, R + W = 2 + 1 = 3. So, R + W < 6
Case b: R = 2, W = 6, G = 0 and B = 4. In this case, R + W = 2 + 6 = 8. So, R + W > 6
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The probability that the person will select a red card is 1/6
This tells us that R = 2 (since 2/12 = 1/6)
There are several CONFLICTING scenarios that satisfy statement 2. Here are two:
Case a: R = 2, W = 1, G = 5 and B = 4. In this case, R + W = 2 + 1 = 3. So, R + W < 6
Case b: R = 2, W = 6, G = 0 and B = 4. In this case, R + W = 2 + 6 = 8. So, R + W > 6
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

[Reveal] Spoiler:
E

RELATED VIDEOS

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2769 [0], given: 364

Terry holds 12 cards, each of which is red, white, green, or   [#permalink] 03 Aug 2017, 13:37
Display posts from previous: Sort by