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

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

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New post 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


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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 29 Nov 2015, 08:27
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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?

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  [#permalink]

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New post Updated on: 29 Nov 2015, 07:43
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1
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  [#permalink]

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New post 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  [#permalink]

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New post 28 Nov 2015, 12:04
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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  [#permalink]

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New post 28 Nov 2015, 20:15
1
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  [#permalink]

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New post 28 Nov 2015, 23:17
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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  [#permalink]

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New post 29 Nov 2015, 03:16
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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
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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 29 Nov 2015, 05:30
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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?

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  [#permalink]

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New post 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  [#permalink]

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New post 29 Nov 2015, 08:18
2
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  [#permalink]

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New post 29 Nov 2015, 09:04
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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

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  [#permalink]

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New post 29 Nov 2015, 09:42
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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  [#permalink]

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New post 29 Nov 2015, 10:09
1
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  [#permalink]

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New post 29 Nov 2015, 10:12
1
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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 29 Nov 2015, 10:48
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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  [#permalink]

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New post 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  [#permalink]

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New post 29 Nov 2015, 21:06
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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
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Re: Math Revolution and GMAT Club Contest! If a, b, and c are the tenths   [#permalink] 29 Nov 2015, 21:06

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