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Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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28 Nov 2015, 08:54
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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 ContestThe 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 6months 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.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 08:27
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




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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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Updated on: 29 Nov 2015, 07:43
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, 09:23.
Last edited by mvictor on 29 Nov 2015, 07:43, edited 1 time in total.



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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28 Nov 2015, 11:24
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..
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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28 Nov 2015, 12:04
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)



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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28 Nov 2015, 20:15
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



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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28 Nov 2015, 23:17
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



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 03:16
2/3=0.66666..... Statement 1: a+b>14 so, a>14b 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>15c Similarly, a>6 and hence sufficient. Ans is D



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 05:30
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!
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 05:54
A..OPTION A IS SUFFICIENT TO ANSWER THE QUESTION



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 08:18
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!
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 09:04
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



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 09:42
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
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 10:09
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



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 10:12
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



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 10:34
The answer to this question must be D. Both the statements are themselves sufficient to tell.



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 10:48
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).



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 10:48
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.
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 10:49
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).



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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths
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29 Nov 2015, 21:06
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




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