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Hundredth Digit.

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Oct 10, 2014 1:39 pm
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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Brent
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by [email protected] » Fri Oct 10, 2014 3:30 pm
Hi kamalakarthi,

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 Matt@VeritasPrep » Sun Oct 12, 2014 9:37 pm
Let's say that r is the integer abc, where a is the hundreds digit, b is the tens digit, and c is the units digit. We want the value of b.

S1::
r/10 = ab.c
The tens digit of this is 3, so a = 3. NOT SUFFICIENT.

S2::
10r = abc0
The hundreds digit of this is 6, so b = 6. SUFFICIENT.
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