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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Sep 07, 2015 7:51 am
What is the tens digit of the positive integer r?

1) The tens digit of r/10 is 3
2) The hundreds digit of 10r is 6
Target question: What is the value of n?

Given: What is the tens digit of the positive integer r?

Statement 1: The tens digit of r/10 is 3
Since r is an INTEGER, 10/r will have 1 digit to the right of the decimal place.
So, r/10 = ????3?.? [each ? represents a digit. Notice that 3 is in the tens position of r/10]
Multiply both sides by 10 to get: r = ????3??
We can see that the HUNDREDS digit of r is 3, but we don't know the TENS digit of r
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The hundreds digit of 10r is 6
Since r is an INTEGER, 10r will have a zero in the units position.
So, 10r = ????6?0 [Notice that 6 is in the hundreds position of 10r]
Divide both sides by 10 to get: r = ????6?
Perfect - the TENS digit of r is 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by GMATGuruNY » Mon Sep 07, 2015 8:03 am
What is the tens digit of the positive integer r?

1) The tens digit of r/10 is 3
2) The hundreds digit of 10r is 6
Statement 1:
Make a list of options:
r/10 = 30, 31, 32, 33...
Multiplying both sides by 10, we get:
r = 300, 310, 320, 330
As the values in red illustrate, the tens digit of r can be different values.
INSUFFICIENT.

Statement 2:
Make a list of options:
10r = 600, 610, 620...
Dividing both sides by 10, we get:
r = 60, 61, 62...
As the values in red illustrate, the tens digit of r must be 6.
SUFFICIENT.

The correct answer is B.
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by [email protected] » Mon Sep 07, 2015 9:07 am
Hi anant03,

This DS question is based on pattern-matching with a little bit of "math" thrown in. It's perfect for TESTing VALUES.

We're told that R is a positive integer. We're asked for the TENS DIGIT of R.

Fact 1: The tens digit of R/10 = 3

If....
R = 310, then 310/10 = 31 which fits the given information. In this case, the TENS DIGIT of 310 = 1
R = 320, then 320/10 = 32 which fits the given information. In this case, the TENS DIGIT of 320 = 2
Fact 1 is INSUFFICIENT

Fact 2: The hundreds digit of 10R = 6

If....
R = 61, then 10R = 610, which fits the given information. In this case, the TENS DIGIT of 61 = 6
R = 62, then 10R = 620, which fits the given information. In this case, the TENS DIGIT of 62 = 6
We could TEST additional values, but we have enough information here to prove a pattern: for the hundreds digit of 10R to = 6, the TENS DIGIT of R MUST = 6. The answer to the question will ALWAYS be 6.
Fact 2 is SUFFICIENT

Final Answer: B

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by Max@Math Revolution » Tue Sep 08, 2015 6:09 am
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 equations ensures a solution.


What is the tens digit of the positive integer r?
1) The tens digit of r/10 is 3
2) The hundreds digit of 10r is 6

In the original condition there is 1 variable (r) and we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D is likely the answer.

in case of 1), if r/10 is the tens digit value and is 3, r=300, 310 thus we have multiple answers. The condition is not sufficient.
in case of 2), if 10r is the hundreds digit and is 6, 10r=....,6a0 thus we have r=......6a. Therefore 6 is always the tengs digit, and since the answer is unique the condition is sufficient.

Therefore B is the answer.


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