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d = 0.7abc In the decimal representation of d above, is a +

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by conquistador » Tue Apr 14, 2015 9:25 am
d = 0.7abc
In the decimal representation of d above, is a + b + c > 15?
(1) When d is rounded to the nearest thousandth, the result would be 0.765
(2) When d is rounded to the nearest hundredth, the result would be 0.77
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Source: — Data Sufficiency |

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by [email protected] » Tue Apr 14, 2015 4:32 pm
Hi Mechmeera,

This DS question is based on rounding "rules"; you can TEST VALUES to prove the correct answer (although you have to be thorough).

We're given that D = 0.7ABC (where A, B and C represent digits). We're asked if A+B+C > 15. This is a YES/NO question.

Fact 1: When D is rounded to the nearest thousandth, the result would be 0.765

This means that D could be 'rounded up' or 'rounded down'

IF....
D = .7649
Then 6+4+9 = 19 and the answer to the question is YES

IF....
D = .7651
Then 6+5+1 = 12 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: When d is rounded to the nearest hundredth, the result would be 0.77

This too can be the result of 'rounding up' or 'rounding down'

IF...
D = .7650
6+5+0 = 11 and the answer to the question is NO

IF...
D = .7749
7+4+9 = 20 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know...
When D is rounded to the nearest thousandth, the result would be 0.765
When D is rounded to the nearest hundredth, the result would be 0.77

This limits down the possibilities. D must begin with .765 (so that when D is 'rounded up' it becomes .77). It's the missing "C" digit that impacts the question here. Note, that .765 has to be the result from rounding to the nearest thousandth, so "C" MUST be one of the digits from 0-4, inclusive (if it was 5-9, then D would = .766).

IF....
D = .7650
6+5+0 = 11 and the answer to the question is NO

IF....
D = .7654
6+5+4 = 15 and the answer to the question is NO

The other 3 possibilities would fall 'in between' these two TESTS and would also give us NO answers.
Combined, SUFFICIENT

Final Answer: C

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by conquistador » Tue Apr 14, 2015 9:37 pm
[email protected] wrote:Hi Mechmeera,

This DS question is based on rounding "rules"; you can TEST VALUES to prove the correct answer (although you have to be thorough).

We're given that D = 0.7ABC (where A, B and C represent digits). We're asked if A+B+C > 15. This is a YES/NO question.

Fact 1: When D is rounded to the nearest thousandth, the result would be 0.765

This means that D could be 'rounded up' or 'rounded down'

IF....
D = .7649
Then 6+4+9 = 19 and the answer to the question is YES

IF....
D = .7651
Then 6+5+1 = 12 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: When d is rounded to the nearest hundredth, the result would be 0.77

This too can be the result of 'rounding up' or 'rounding down'

IF...
D = .7650
6+5+0 = 11 and the answer to the question is NO

IF...
D = .7749
7+4+9 = 20 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know...
When D is rounded to the nearest thousandth, the result would be 0.765
When D is rounded to the nearest hundredth, the result would be 0.77

This limits down the possibilities. D must begin with .765 (so that when D is 'rounded up' it becomes .77). It's the missing "C" digit that impacts the question here. Note, that .765 has to be the result from rounding to the nearest thousandth, so "C" MUST be one of the digits from 0-4, inclusive (if it was 5-9, then D would = .766).

IF....
D = .7650
6+5+0 = 11 and the answer to the question is NO

IF....
D = .7654
6+5+4 = 15 and the answer to the question is NO

The other 3 possibilities would fall 'in between' these two TESTS and would also give us NO answers.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

since it said in Fact 1: When D is rounded to the nearest thousandth, the result would be 0.765.
it is not compulsory that b=5 c=0-4
we can also consider b=4 and c=5-9 in this case sum will be more than 15.
then how can we conclude c.
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by DavidG@VeritasPrep » Wed Apr 15, 2015 3:41 am
since it said in Fact 1: When D is rounded to the nearest thousandth, the result would be 0.765.
it is not compulsory that b=5 c=0-4
we can also consider b=4 and c=5-9 in this case sum will be more than 15.
then how can we conclude c.
Give Rich's explanation another read. He considers D = .7649 when evaluating statement 1 alone. When testing the statements together, we have to incorporate the information from statement 2, "when d is rounded to the nearest hundredth, the result would be 0.77." Consequently, we can no longer consider .7649, because this value, rounded to the nearest hundredth, would be .76. This would violate statement 2.
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by conquistador » Wed Apr 15, 2015 3:53 am
DavidG@VeritasPrep wrote:
since it said in Fact 1: When D is rounded to the nearest thousandth, the result would be 0.765.
it is not compulsory that b=5 c=0-4
we can also consider b=4 and c=5-9 in this case sum will be more than 15.
then how can we conclude c.
Give Rich's explanation another read. He considers D = .7649 when evaluating statement 1 alone. When testing the statements together, we have to incorporate the information from statement 2, "when d is rounded to the nearest hundredth, the result would be 0.77." Consequently, we can no longer consider .7649, because this value, rounded to the nearest hundredth, would be .76. This would violate statement 2.
Thanks David
I just missed this point.
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by GMATGuruNY » Wed Apr 15, 2015 5:08 am
Mechmeera wrote:d = 0.7abc
In the decimal representation of d above, is a + b + c > 15?
(1) When d is rounded to the nearest thousandth, the result would be 0.765
(2) When d is rounded to the nearest hundredth, the result would be 0.77
Statement 1: When d is rounded to the nearest thousandth, the result would be 0.765.
Here, the range for d is as follows:
0.7645 ≤ d < 0.7655.
If d = 0.7645, then a+b+c = 15.
If d = 0.7646, then a+b+c > 15.
INSUFFICIENT.

Statement 2: When d is rounded to the nearest hundredth, the result would be 0.77.
Here, the range for d is as follows:
0.765 ≤ d < 0.775.
If d = 0.7650, then a+b+c < 15.
If d = 0.7659, then a+b+c > 15.
INSUFFICIENT.

Statements combined:
Statement 1: 0.7645 ≤ d < 0.7655.
Statement 2: 0.765 ≤ d < 0.775.
OVERLAP between the two ranges:
0.765 ≤ d < 0.7655.
Options for d:
0.7650, 0.7651, 0.7652, 0.7653, 0.7654.
In every case, a+b+c ≤ 15.
SUFFICIENT.

The correct answer is C.
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