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

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.

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

(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.

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.

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..

A..OPTION A IS SUFFICIENT TO ANSWER THE QUESTION

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

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).

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).

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

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

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.

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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