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tens digit of the positive integer r

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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Sun May 15, 2016 4:42 am
jain2016 wrote: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

OA B
Pick some easy numbers.

S1: If the tens digit of r/10 is 3, that means r/10 can be any number in the 30's. Case 1: r/10 = 31; so r = 310. Tens digit is a 1. Case 2: r/10 = 32; r = 320. Tens digit is a 2. Different results so not sufficient.

S2: 10r can be any number in the 600's. Case 1: 10r = 600. r = 60. So tens digit is 6. Case 2: 10r = 610. r = 61. So tens digit is 6. No matter what we pick the tens digit will be 6. Sufficient. (Put another way, the hundreds digit of 10r is, by definition, the tens digit of r.)

Answer is B
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tens digit of the positive integer r

by Brent@GMATPrepNow » Sun May 15, 2016 6:50 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 tens digit of the positive integer r?

Given: r is a positive integer

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

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Tue Mar 06, 2018 7:07 am, edited 1 time in total.
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by [email protected] » Sun May 15, 2016 9:22 am
Hi jain2016,

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 Jeff@TargetTestPrep » Mon Dec 11, 2017 11:31 am
jain2016 wrote: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
We need to determine the tens digit of a positive integer r. Although we don't know how many digits r has, we can let r be a three-digit number. That is, we can let r = ABC, in which A = the hundreds digit, B = the tens digit, and C = the units digit. We need to determine the value of B.

Statement One Alone:

The tens digit of r/10 is 3.

We see that ABC/10 = AB.C and thus A = 3. Since we do not have a value for B, statement one alone is not sufficient to answer the question.

Statement Two Alone:

The hundreds digit of 10r is 6.

We see that ABC x 10 = ABC0 and thus B = 3. Since we have a value for B, statement two alone is sufficient to answer the question.

Answer: B

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