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# If 1 < d < 2, is the tenths’ digit of the decimal representation of d

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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If 1 < d < 2, is the tenths’ digit of the decimal representation of d equal to 9?

(1) d + 0.01 < 2
(2) d + 0.05 > 2

In the original condition, there is 1 variable(d), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), d=1.9 -> yes, 1.8 -> no, which is no and not sufficient.
For 2), if d=1.8..., d+0.05>2 is impossible. So it always has to be d=1.9..., which is yes and sufficient. Therefore, the answer is B.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
The thing to remember here is that Atmost carry in any division is 1
hence B is sufficent
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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
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I am not able to understand how its B. If d=1.90+0.05 then its not greater than 2 . Which make it insufficient.Please explain.
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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
I am not able to understand how its B. If d=1.90+0.05 then its not greater than 2 . Which make it insufficient.Please explain.

When picking numbers you should pick them so that they satisfy the stem and the statement you are testing. Does your example satisfy the second statement, which you are trying to test?
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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
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boomtangboy wrote:
If 1 < d < 2, is the tenths’ digit of the decimal representation of d equal to 9?

(1) d + 0.01 < 2
(2) d + 0.05 > 2
DS97602.01

Given: 1 < d < 2

Target question: Is the tenths’ digit of the decimal representation of d equal to 9?

Statement 1: d + 0.01 < 2
Subtract 0.01 from both sides of the inequality to get: d < 1.99
So, it could be the case that d = 1.93, in which case the answer to the target question is YES, the tenths digit is 9
Or it could be the case that d = 1.77, in which case the answer to the target question is NO, the tenths digit is not 9
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: d + 0.05 > 2
Subtract 0.05 from both sides of the inequality to get: d > 1.95
Since we already know that d < 2, we can combine these inequalities to get: 1.95 < d < 2
So, it MUST be the case that the tenths digit is 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
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Question: If 1 < d < 2, is the tenths’ digit of the decimal representation of d equal to 9?

How can we determine the tenths' digit? We need to have some information about the hundredths' digit. Lets take a look at the choices:

(1) d + 0.01 < 2

d + 0.01 could be 1.91
d + 0.01 could be 1.41

INSUFFICIENT.

(2) d + 0.05 > 2

d + 0.05 is GREATER THAN 2.
We can conclude d must between 1.95 and 2.

for example: 1.96 + 0.05 > 2

SUFFICIENT.

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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
1) just tells us that d < 1.99
But it can be anything 1.98, 1.97 even 1.87, etc, INSUFF

2) tells us that the d>1.95 so either of 1.96, 1.97, 1.98 or 1.99 (since d also has to be < 2)
in each of the 4 cases, tenth digit is 9, so SUFF
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Re: If 1 < d < 2, is the tenths’ digit of the decimal representation of d [#permalink]
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St (1):d + 0.01 < 2

So d <1.99.

If 1.98 <1.99, then with the tenth digit being 9,it is a possibility that the tenths digit of d is 9 and the answer to the question stem is a Yes.

If 1.88 < 1.99, then it is also a possibility that the tenths digit of d is not 9 and the answer to the question stem is a No.

(Insufficient)
With a yes and a No, the statement is insufficient and hence eliminate A,D.

St(2): d + 0.05 > 2

This implies d > 1.95 and since d<2,we can see that 1.95 < d <2 and hence the answer to the question stem is a Yes.
(Sufficient)

(option b)

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Re: If 1 < d < 2, is the tenths digit of the decimal representation of d [#permalink]
boomtangboy wrote:
If 1 < d < 2, is the tenths’ digit of the decimal representation of d equal to 9?

(1) d + 0.01 < 2
(2) d + 0.05 > 2

DS97602.01

Question Stem Analysis:

We are told that d is between 1 and 2, and we must determine whether the tenths digit of d is 9.

Statement One Alone:

$$\Rightarrow$$ d + 0.01 < 2

This means that d < 1.99. If d = 1.1, then the tenths digit of d is 1. If d = 1.98, then the tenths digit of d is 9. Statement one alone is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

$$\Rightarrow$$ d + 0.05 > 2

Thus, d > 1.95. Since 1.95 < d < 2, the tenths digit of d must be equal to 9. Statement two alone is sufficient.

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Re: If 1 < d < 2, is the tenths digit of the decimal representation of d [#permalink]
To determine whether the tenths' digit of the decimal representation of d is equal to 9, we need to analyze the given statements.

Statement (1): d + 0.01 < 2
Statement (2): d + 0.05 > 2

Let's examine these statements step by step:

Statement (1) states that d + 0.01 is less than 2. We can subtract 0.01 from both sides of the inequality to isolate the value of d:

d + 0.01 - 0.01 < 2 - 0.01
d < 1.99

From this inequality, we can conclude that d is less than 1.99.

Now, let's move on to Statement (2), which states that d + 0.05 is greater than 2. Similarly, we can subtract 0.05 from both sides of the inequality to isolate the value of d:

d + 0.05 - 0.05 > 2 - 0.05
d > 1.95

From this inequality, we can conclude that d is greater than 1.95.
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Re: If 1 < d < 2, is the tenths digit of the decimal representation of d [#permalink]
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Re: If 1 < d < 2, is the tenths digit of the decimal representation of d [#permalink]
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