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

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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post Updated on: 05 Dec 2015, 00:16
1
My take is D.

(1) a+b>14 ; Say a+b = 15 ; then only possible combination is 0.96c or 0.69c. In any case its greater than 2/3= 0667 or 0.67. You can check any condition like a+b =18 etc. Hence sufficient.
(2) a+c> 15 ; Say a+c = 16; then only possible combination is 0.8b8 or 0.7b9 or 0.9b7. Hence sufficient.

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Originally posted by FightToSurvive on 30 Nov 2015, 01:14.
Last edited by FightToSurvive on 05 Dec 2015, 00:16, edited 1 time in total.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 30 Nov 2015, 07:07
Answer is B

From statement 2, we get that the smallest value of 'a' will be greater than 6

From statement 1, we get the smallest value of "a" to be greater than 5. So we don't know whether the value of 0.abc > 2/3
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 30 Nov 2015, 08:51
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D. Each statement alone is sufficient.

Is 0.abc>2/3?
2/3 is nothing but 0.6666

(i) Given a+b>14
The possible set of digits for a and b is (6,7,8,9); anything below 6 cannot add up to a sum greater than 14.
Now the minimum value for a is 6.
Hence the minimum value for 0.abc=0.69c, which will always be greater than 0.666
Therefore sufficient.

(ii) a+c>15
The possible set of digits for a and c is (7,8,9); anything below 7 cannot add up to a sum greater than 15.
The minimum value for a is 7.
And for 0.abc=0.7bc, which will always be greater than 0.666
Sufficient.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 30 Nov 2015, 11:03
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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

st1) a+b is atleast 15
(7,8), (8,7), (9,6),(6,9)
so minimum is .69 which is >2/3

st2) a+c is minimum 16
(8,8), (9,7), (7,9)
So minimum is .79 > 2/3

Ans D
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 30 Nov 2015, 18:55
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Ans: D (Either)
2/3 = 0.667. So the question simply wants us to find out if a, b, c > 6

1. a+b> 14.
a few ways of getting a 14 using single digit numbers only - 7+7, 6+8, 8+6, 5+9 ....
The smallest number a can take is 5 and largest that b can take is 9 to get 14. With this combination, 0.abc<2/3. with others it is >2/3 and hence sufficient.

2. c+a>15. Same logic as 1 and hence sufficient.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 01 Dec 2015, 10:10
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We need to prove if 0.abc>0.667 or not.

Statement 1- Since a+b>14, a should be minimum 6 (5+9=14). Sufficient.
Statement 2- Since a+c>15, a should be minimum 7 (6+9=15). Sufficient.

Answer is D.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 02 Dec 2015, 00:01
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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

Question is if 0.abc>2/3
-> 0.abc > 0.66666


Stmt 1:

a+b>14
The lease value a+b can have is 15
in this scenario max b can be equal to 9, hence a=6

we have 0.69c which is greater than 0.66667 irrespective of value of c
trying any other scenarios will lead to 0.abc being greater than 0.66667

Hence suff

Stmt 2:


a+c>15
The least value a+c can have is 16
in this scenario max c can be equal to 9, hence a=7

we have 0.7b9 which is greater than 0.66667 irrespective of value of b
trying any other scenarios will lead to 0.abc being greater than 0.66667

Hence suff


Hence ans: D
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 03 Dec 2015, 11:59
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Question asks if 0.abc > 0.666...

Statement (1): a + b > 14
possible values a and b are 6 and 9 (see if min possible value for a > 6 or a&b > 6&6)
so substituting values of a and b
0.69c > 0.666.. TRUE for any value of c
Statement (1) is Sufficient

Statement (2): a + c > 15
possible values a and c are 7 and 9
so substituting values of a and c
0.7b9 > 0.666.. TRUE for any value of b
Statement (2) is Sufficient

Answer (D)
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 03 Dec 2015, 13:12
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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


Soln: First, let's express \(\frac{2}{3}\) in the decimal form for ease of comparison: \(\frac{2}{3}\) = 0.6666666...
Now, we need to compare a,b, and c with the digit 6 in order to determine whether \(0.abc\) > \(\frac{2}{3}\)

1. \(a+b > 14.\) Suppose, \(a=7, b=8, c=1,\) So, \(0.abc = 0.781 > 0.666..\) YES, condition holds. (Pls note, c can take any value, no restriction at all)
Suppose, \(a=6, b=9, c=2. So, 0.abc = 0.692 > 0.666..\) YES, cond. holds.
Now, a cannot be less than 6, as b can't be greater than 9. So, \(0.abc\) > \(\frac{2}{3}\) for all a, b and c. SUFFICIENT.

2. \(a+c > 15.\) Suppose, \(a = 7, c = 9 and b = 1.\) So, \(0.abc = 0.719 > 0.666..\) YES, condition holds. (Pls note, b can take any value, no restriction at all)

Now, a cannot be less than 7, as c can't be greater than 9. So, \(0.abc\) > \(\frac{2}{3}\) for all a, b and c. SUFFICIENT.
Answer: D.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 04 Dec 2015, 05:58
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Answer is D
Asked is whether 0.abc>0.666

So 0.667>0.666, therefore minimum values of a,b and c should be 6, 6, and 7 respectively to provide concrete solution in YES or NO.

S1 : a+b>14, therefore a cannot be less than 6 as that would make equation impossible, i.e. if a=5, than b has to be 10 or more which is impossible. if a is considered minimum 6, than b has to be 9 which makes 0.abc =0.69c which is sufficient to say that 0.abc>2/3.

S2 : a+c>15, in order to qualify this equation a has to be 7 or more. Which makes 0.abc =0.7bc. that is sufficient to provide concrete answer.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 04 Dec 2015, 11:01
This question is asking if 0.abc > 2/3 ; let's rephrase this.
For this statement to be true:
a>=7 or a=6, b>=6 AND c>=6

Evaluating statement 1:
if a + b = 14, we can make a "Yes" response by choosing a to be 7 and b to be 7. Alternatively, we can make a "No" response by choosing a to be 5 and b to 9.
Not Sufficient.

Evaluating statement 2:
if a + c = 15, the smallest possible value for a is 6, but without knowing if b is also greater or equal to 6, this is not sufficient.
Not Sufficient

Together:
With the 2nd statement, the smallest possible value of a is 6, and given this situation, b would have to be 8, which would provide a "Yes". For any larger value of a, the statement directly is true. So all situations provide a "Yes".
Sufficient

Answer: C
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 04 Dec 2015, 23:37
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If a, b, and c are the tenths digit, the hundredths digit, and the thousandths digit of 0.abc, is 0.abc > 2/3?

0.abc>2/3 or > 0.6666

(1) a + b > 14

When a + b> 14, a+b can be 15,16,17,18 for both a and b to be single-digits.
For a +b = 15, ab can be 69, 78, 87, 96 . All values greater than 0.666
For a +b = 16, ab can be 79, 88, 97. All values greater than 0.666.
For a+b= 17, ab can be 89,98.All values greater than 0.666.
For a+b= 18, ab can be 99. All values greater than 0.666
a+b cannot be greater than 18.
Since all values are greater than 0.666, choice A is sufficient.

(2) a + c > 15

For a +c = 16, ac can be 79, 88, 97. All values greater than 0.666.
For a+c= 17, ac can be 89,98.All values greater than 0.666.
For a+c= 18, ac can be 99. All values greater than 0.666

a+c cannot be greater than 18.
Since all values are greater than 0.666, choice B is sufficient.

Hence each choice alone is sufficient. Hence answer is choice D
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 06 Dec 2015, 09:33
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(1) a + b > 14 then min a >=6. If a > 6 => 0.abc > 0.67 > 2/3.
If a = 6 then b = 9, 0.abc = 0.69c > 2/3
-> Sufficient
(2) a + c > 15 then a >= 7 => 0.abc > 2/3 -> Sufficient

Hence D.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 14 Dec 2015, 09:00
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Bunuel wrote:

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:



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:

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


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MATH REVOLUTION OFFICIAL SOLUTION:

This type of question appears within a score range of 49 to 51. There are 3 variables in the original condition. E is likely be an answer. Generally, when the question asks if a value is bigger than a certain number - just like the question 0.abc>2/3? -, we have to find the smallest possible value. This is because if the smallest possible value is bigger than 2/3, the rest would also be bigger than 2/3. So, if we solve for the smallest possible value of 0.abc, the answer comes out to be: a=7, b=8 and c=9. So, because 0.789 is bigger than 2/3, which means yes, this is sufficient. The answer is likely to be C.

However, we can apply the Mistake Type 4 for this problem because it is an integer question, which is one of key questions.

When applied with the mistake type 4,
in a case of 1), you have to find a minimum. When a=6, b=9, it should be 0.69n>2/3 yes(n is a positive 1-digit integer), this is sufficient.

In a case of 2), you also have to find a minimum value. When a=7, c=9, it should be 0.7m9>2/3 yes (m is a positive 1-digit integer), this is also sufficient. Therefore, the actually correct answer is D.

This is a Mistake Type that appears frequently in Integers and Statistics section. Students have to take extra caution because this is a case where, if C and D are both correct answers, then D becomes the final answer choice. You can solve this question in less than 2 minutes while conventional way of solving takes 4-5 minutes.

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 15 Dec 2015, 07:27
from question stem 0.abc=abc/1000>2/3
cross multiply both are positive.
abc>2000/3
abc>666.

from statment 1

a+b>14
possible values are 15,16, 17and 18.

last value only 18 because single maximum digit is 9 only.

take" a" as minimum value. if b=9, then a=6, b=8, then a=7
if a=6, b=9. then value is 69 take minimum value for c=0. then value starts from 690. minimum value is greater >666.
statement 1 itself sufficient.
statment 2

a+c>15 possible values are 16,17 and 18.
take minimum value a=7, c=9. value starts form 709 onwards . it is greater than 666
so statment 2 itself sufficient.


so option D is correct.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths  [#permalink]

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New post 11 Oct 2018, 09:14
Quote:
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



So the question precisely asks if 0.abc is greater than 0.(666)
For 0.abc to be bigger than 0.(666) a MUST BE MINIMUM 6.
With this in mind, lets check the provided information in the given statements.

1.Statement: a+b > 14. So since a and b NEED TO BE one digit numbers, the maximum for each one is 9.
Remember: For the statement to be true, the least value for a must be 6.
With statement 1 we can say a must be either 6 and b 9 (to be bigger than 14. Both are integers so to be bigger than 14, the both must be at least 15 ;) ) So the statement tells aus 0.abc is minimum 0.69c
SUFFICIENT alone.

2.Statement: a+c > 15
Here we use the same technique as we used for statement 1. So the minimum for a will be 7 here, since a+c must be at least 16 (again, remember that a and c are integers and they must be bigger than 15 combined.
So they must be at least 16 because two integers cannot form a number like 15,1 etc. Just whole numbers need to be considered) Therefore, the lowest value for a will be 7 and thus the minimum value for .abc will be 0.7b9, which is bigger than 0,(666) and thus SUFFICIENT alone, again.

Hence, the correct answer for this question will be D.

(Note that the prompt has told us that A,B,C are integers. Without this hint, we would neither be able to say that a+b has to be at least 15 (which gave us a=6 minimum and b=7 minimum, that combined lead us to 0.abc = 0.69c > 0.(666)) nor be able to say that a+c must be at least 16 (which gave us a=7 minimum)
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths &nbs [#permalink] 11 Oct 2018, 09:14

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