NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 22:16 It is currently 23 Apr 2024, 22:16
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Math Revolution and GMAT Club Contest! If a, b, and c are the tenths

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618637 [11]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   28 Nov 2015, 09:54
2
Kudos
9
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

61% (01:57) correct 39% (02:02) wrong based on 326 sessions
Hide Show timer Statistics

Math Revolution and GMAT Club Contest Starts!



QUESTION #2:

If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

(1) a + b > 14
(2) a + c > 15


Check conditions below:


Show Spoiler

Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum


We are happy to announce a Math Revolution and GMAT Club Contest

For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize:

PS + DS course with 502 videos that is worth $299!



All announcements and winnings are final and no whining :-) GMAT Club reserves the rights to modify the terms of this offer at any time.


NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!

ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
divya06
Intern
Intern
Joined: 04 Sep 2015
Posts: 3
Own Kudos [?]: 21 [9]
Given Kudos: 4
Location: Singapore
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 09:27
7
Kudos
2
Bookmarks
If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

Statement 1 - a + b > 14
Statement 2 - a + c > 15

ANSWER - OPTION D, both statements alone are sufficient

From question - Max value that a, b or c can have is 9. We have to check if 0.abc > 0.666...

a+b >14, min possible value of 'a' is 6 (by substituting b=9) making min value of term 0.69x
a+c >15, min possible value of 'a' is 7 (by substituting c=9) making min value of term 0.7X9

Thus both options independently can help us answer question
General Discussion
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [2]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   Updated on: 29 Nov 2015, 08:43
1
Kudos
1
Bookmarks
If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?
the question really asks if a>6 and b>6 since 2/3 = ~0.66

(1) a + b > 14
to check whether a<=6, we need to maximize the value of b, which can only be 9, since 9 is the highest digit. in this case, a minimal value of a would be 6, because we need to satisfy the condition a+b>14.
in this case, we have 0.69c. Regardless of what C is, 0.abc is definitely greater than 2/3
note that we cannot put a<6, since a+b would not yield a number greater than 14, and since a and b can take values from 0 to 9, there is no such possibilities to make a<6.

A is sufficient, and we can clearly cross B, C, and E.

We are left with A and D, and the chances of getting the correct answer is 50% ! :)

(2) a + c > 15
now, again trying to maximize one value and minimize the other one, so that to see whether our number is greater than 2/3.
suppose that a=7 and c=9 -> this is the smallest possible combination with the minimum value of a, but which satisfies the condition a+c>15.
we have 0.7b9. this number is definitely greater than 2/3.

we can cross A, and select confidently D as the correct answer!

Originally posted by mvictor on 28 Nov 2015, 10:23.
Last edited by mvictor on 29 Nov 2015, 08:43, edited 1 time in total.
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11161
Own Kudos [?]: 31872 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   28 Nov 2015, 12:24
Expert Reply
hi mvictor,
there is a typo in your answer..
you have ofcourse nailed the question but marked the answer as B, whereas i am sure you meant D..
avatar
kingjamesrules
Intern
Intern
Joined: 09 Jul 2015
Posts: 42
Own Kudos [?]: 61 [1]
Given Kudos: 63
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   28 Nov 2015, 13:04
1
Kudos
The answer is D

To simply the statement, is 0.abc>0.666666.. or in other words is any one of a or b or c >6. Even if one of the digits is great than 6, then 0.abc can turn out to be greater than 2/3.

1) a+b>14, in this case, the possible values of a/b are (9/6, 6/9, 8/7, 7/8, 9/8, 8/9, 9/9). In all cases either a or b is greater than 6. The lowest number is 0.69 which is still greater than 0.6666. so 0.abc > 2/3. SUFFICIENT

2) a+C>15, in this case, the possible values of a/c are (7/9, 9/7, 8/8, 9/8, 8/9, 9/9). In all cases a or c is greater than 6. This is clearly SUFFICIENT.

Hence answer is D

PS: (note that we cannot round of decimals, If you do round off then, 2/3 can be 0.7 & the answer will be B as option 1 will turn our insufficient. But this should not be the case as the question has clearly mentioned 2/3 and not the decimals itself which means 2/3=0.666666666 and not 0.7)
avatar
roym
Intern
Intern
Joined: 01 Nov 2015
Posts: 7
Own Kudos [?]: 10 [1]
Given Kudos: 14
Concentration: General Management
GMAT 1: 720 Q48 V41
Send PM
Reviews Badge
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   28 Nov 2015, 21:15
1
Kudos
We have to check if 0.abc>0.667
Option A: If a+b>14 then taking a+b=15 we get max value of b can be 9 which makes a=6 thus Yes 0.69>0.67
A sufficient
Option B: If a+c> 15 then taking a+c=16 we get max value of c can be 9 which makes a=7 thus Yes 0.709>0.667
B sufficient
Thus each stmnt sufficient on a ta own
Ans: D
User avatar
asethi
Manager
Manager
Joined: 08 Sep 2015
Status:tough ... ? Naaahhh !!!!
Posts: 58
Own Kudos [?]: 37 [1]
Given Kudos: 6
Location: India
Concentration: Marketing, Strategy
WE:Marketing (Computer Hardware)
Send PM
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 00:17
1
Kudos
is 0.abc > 2/3 or 0.66

1. a+b>14, that means, 18>a+b>14, so the min digit value combinations could be 9+6, 8+7, 7+8, 6+9, 8+7 and 8+7. In any case 0.abc will be greater than 0.66 ... Sufficient
2. a+c>14, In all the cominations the minimum digit value of 'a' will be 7, So 0.7bc will be greater than 0.66. Sufficient

Ans: D
User avatar
S
zmtalha
Intern
Intern
Joined: 27 Mar 2014
Status:Current Student
Posts: 25
Own Kudos [?]: 56 [1]
Given Kudos: 14
Location: United States (IL)
Concentration: Statistics, Marketing
GPA: 3.44
WE:Consulting (Advertising and PR)
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 04:16
1
Kudos
2/3=0.66666.....
Statement 1:
a+b>14
so, a>14-b or, a>5 [Highest value of b=9 is taken so that the least value of a can be derived]
Therefore, when least a=6 then b=9. [since value must be integer]
From here, we know that the number is at least 0.69 irrespective of C [Sufficient]
Statement 2:
a>15-c
Similarly, a>6 and hence sufficient.
Ans is D
User avatar
L
HKD1710
Retired Moderator
Joined: 22 Jun 2014
Posts: 971
Own Kudos [?]: 3801 [2]
Given Kudos: 182
Location: India
Concentration: General Management, Technology
Schools: IIMB IIMA ISB PGP Pro '19
GMAT 1: 540 Q45 V20
GPA: 2.49
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 06:30
2
Kudos
If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

is 0.abc > 2/3 (0.666) ?
i.e. is abc > 666?

if a < 6 then NO
if a > 6 then YES
But if a = 6 then check the value of b which if equal to 6 then check the value of c.

(1) a + b > 14
if a + b = 15 then 6 + 9 = 15 OR 7 + 8 = 15 OR 8 + 7 = 15 OR 9 + 6 = 15, let us say abc = 69c
if the value of c is 0 to 9 and respectively abc = 690 to 699
in all cases abc > 666
Definite answer. Hence Sufficient.

(2) a + c > 15
if a + c = 16 then 7 + 9 = 16 OR 8 + 8 = 16 OR 9 + 7 = 16
in all cases a > 6, hence abc > 666.

Definite answer. Hence Sufficient.

Both (1) & (2) are individually sufficient. Hence "D" is the final answer!
avatar
druday
Intern
Intern
Joined: 17 Oct 2015
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 06:54
A..OPTION A IS SUFFICIENT TO ANSWER THE QUESTION
User avatar
swanidhi
Manager
Manager
Joined: 11 Oct 2013
Posts: 70
Own Kudos [?]: 286 [2]
Given Kudos: 137
Concentration: Marketing, General Management
Schools: Tepper MISM '17 (A) SPJ PGPM"16 (A)
GMAT 1: 600 Q41 V31
Send PM
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 09:18
2
Kudos
My answer to this Question is D

If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

(1) \(a + b > 14\)
(2) \(a + c > 15\)

\(\frac{2}{3}= 0.666..\)
Is \(0.abc > 0.666\)?

1) \(a + b > 14\)
We know that these are digits => their sum cannot be a decimal. So take \(a + b = 15\)
a and b have to be single digits from 0 to 9. To form \(15\), possible values of a and b are -
\((9, 6)\) and\((8, 7)\)

Considering (9, 6), \(0.abc = 0.96c\) or\(0.69c\) -- Both are greater than \(0.666..\)
Considering (8, 7), \(0.abc = 0.87c\) or \(0.78c\) -- Both are greater than \(0.666..\)
Note - a + b cannot exceed 18, or else values of a and b will exceed 9 each. Any value of a + b> 15 will result in higher values of a and b, still resulting in \(0.abc > 0.666\)
Hence, Sufficient!

2) \(a + c > 15\)
Like (1), Lets take \(a + c = 16\)
To form \(16\), possible values of a and b are -
\((9, 7)\) and \((8, 8)\)
Considering (9, 7), \(0.abc = 0.9b7\) or \(0.7b9\). -- Both are greater than \(0.666..\)
Considering (8, 8), \(0.abc = 0.8b7\). -- Greater than \(0.666..\)
Note - a + c cannot exceed 18, or else values of a and c will exceed 9 each. Any value of a + c> 16 will result in higher values of a and b, still resulting in \(0.abc > 0.666\)
HHence Sufficient!
User avatar
Beat720
Intern
Intern
Joined: 22 Dec 2014
Posts: 26
Own Kudos [?]: 47 [2]
Given Kudos: 182
Send PM
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 10:04
2
Kudos
QUESTION #2:

If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

(1) a + b > 14
(2) a + c > 15

Solution:

0.abc = abc/1000
2/3 = 667/1000 (approximately)

(1) a+b > 14 --> min (a+b) = 15 --> min a = 6 --> min abc/1000 = 690/1000 > 667/1000 - Sufficient
(2) a+c > 15 --> min (a+c) = 16 --> min a = 7 --> min abc/1000 = 709/1000 > 667/1000 - Sufficient

Answer D
User avatar
B
Icecream87
Senior Manager
Senior Manager
Joined: 23 Sep 2015
Posts: 333
Own Kudos [?]: 325 [1]
Given Kudos: 72
Location: France
Schools: Insead Sept '17 (M$)
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE:Real Estate (Mutual Funds and Brokerage)
Send PM
Reviews Badge
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 10:42
1
Kudos
2/3 = 0,667
We want to know if abc is greater than 667

1) a+b > 14: for A and B to be greater than 14, the minimum value for A would have to be 6, and B will have a maximum value of 9. So 0.69_ > 0.667. Statement 1 is sufficient.
2) a+c > 15: for A and C to be greater than 15, the minimum value for A has to be 7 and maximum c 9. So 0.7_9 is also greater than 0.667. Statement 2 is sufficient.
Answer D
User avatar
B
tarunk31
Manager
Manager
Joined: 25 Feb 2014
Posts: 183
Own Kudos [?]: 448 [1]
Given Kudos: 147
GMAT 1: 720 Q50 V38
Send PM
Reviews Badge
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 11:09
1
Kudos
We have
If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

(1) a + b > 14
(2) a + c > 15

for 0.abc > 2/3 to be true, the minimum value of 0.abc should be 0.667

1) a+b > 14
let's take a+b = 15, then for a=6 and b = 9 and assume c=0, we can conclude that 0.690 > 2/3. For all other possible values of a and b, 0.abc will be greater than 0.690. Sufficient.
2) a+c > 15
Let's take a+c = 16, the minimum value of 0.abc,assuming b = 0, will be 0.709. again we can conclude that 0.709>2/3. Sufficient.

Ans. D
avatar
jamesav
Intern
Intern
Joined: 26 Sep 2014
Posts: 6
Own Kudos [?]: 6 [1]
Given Kudos: 10
Location: India
Schools: IIMB (A)
GMAT 1: 700 Q50 V34
GPA: 3.2
Send PM
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 11:12
1
Kudos
we need to find if 0.abc> 0.666

1. a+b> 14 => a +b is atleast 15.
the least that a can be is 6 and in this case, b will be 9.
hence regardless of the value of c, 0.abc will be greater than .666

2. a+c> 15 => a + c is atleast 16.
the least that a can be is 7 and in this case, c will be 9.
hence regardless of the value of b, 0.abc will be greater than .666

Hence Ans.: D
User avatar
pooja3017
Intern
Intern
Joined: 12 Aug 2015
Posts: 7
Own Kudos [?]: 8 [0]
Given Kudos: 17
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 11:34
The answer to this question must be D. Both the statements are themselves sufficient to tell.
User avatar
B
shapla
Intern
Intern
Joined: 29 Aug 2013
Posts: 34
Own Kudos [?]: 82 [0]
Given Kudos: 48
Location: Bangladesh
GPA: 3.76
WE:Supply Chain Management (Transportation)
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 11:48
Answer: (C).
Solution: Only by (I), we cant guess the value of c, whereas by only (II), we cant guess the value of B. Since we have to find whether 0.abc > 2/3 or not, hereby we need to know a, b, c all value. (I) and (II) together gave us the sufficient answer to the question. so the answer choice will be (C).
User avatar
B
Nightfury14
Manager
Manager
Joined: 13 Sep 2015
Status:In the realms of Chaos & Night
Posts: 125
Own Kudos [?]: 623 [1]
Given Kudos: 98
Schools: ISB '20 INSEAD Jan '19
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 11:48
1
Kudos
Question says : 0.abc > 2/3 => 0.abc > 0.66

Case 1 : a+b>14 i.e minimum a+b=15,
consider smallest value of a=6, hence b=9 => 0.ab=0.69 > 0.66 True Sufficient

Case 2 : a+c>15 i.e minimum a+b=16,
consider smallest value of a=7, hence b=9 => 0.ab=0.79 > 0.66 True Sufficient

Sol. D. Both are sufficient separately.

---------------------------------------------------------------------------
You know the importance of Kudos, be generous.
User avatar
B
shapla
Intern
Intern
Joined: 29 Aug 2013
Posts: 34
Own Kudos [?]: 82 [0]
Given Kudos: 48
Location: Bangladesh
GPA: 3.76
WE:Supply Chain Management (Transportation)
Send PM
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 11:49
Answer: (C).
Solution: Only by (I), we cant guess the value of c, whereas by only (II), we cant guess the value of B. Since we have to find whether 0.abc > 2/3 or not, hereby we need to know a, b, c all value. (I) and (II) together gave us the sufficient answer to the question. so the answer choice will be (C).
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1436
Own Kudos [?]: 4543 [1]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink] New post   29 Nov 2015, 22:06
1
Kudos
is 0.abc > 0.667?

St1: a + b > 14
Minimum value of a + b = 15;
Minimum value of a is possible when b is maximum --> b = 9 and a = 6 --> 0.abc = 0.69c > 0.667
Statement 1 alone is sufficient.

(2) a + c > 15
Minimum value of a + c = 16;
Minimum value of a is possible when c is maximum --> c = 9 and a = 7 --> 0.abc = 0.7b9 > 0.667
Statement 2 alone is sufficient.

Answer: D
GMAT Club Bot
gmatclubot
Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths [#permalink]
29 Nov 2015, 22:06
 1   2   
Moderator:
Bunuel
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions