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

Question

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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

Check conditions below:

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Official Answer

D

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divya06 · Accepted Answer

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

mvictor · Answer

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!

(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!

chetan2u · Answer

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..

kingjamesrules · Answer

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)

roym · Answer

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

asethi · Answer

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

zmtalha · Answer

2/3=0.66666.....
Statement 1:
a+b>14
so, a>14-b or, a>5  
Therefore, when least a=6 then b=9.  
From here, we know that the number is at least 0.69 irrespective of C  
Statement 2:
a>15-c
Similarly, a>6 and hence sufficient.
Ans is D

HKD1710 · Answer

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!

druday · Answer

A..OPTION A IS SUFFICIENT TO ANSWER THE QUESTION

swanidhi · Answer

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  
 H Hence Sufficient!

Beat720 · Answer

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

Icecream87 · Answer

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

tarunk31 · Answer

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

jamesav · Answer

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

pooja3017 · Answer

The answer to this question must be D. Both the statements are themselves sufficient to tell.

shapla · Answer

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).

Nightfury14 · Answer

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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shapla · Answer

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).

Kurtosis · Answer

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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