Hundredth Digit.
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Target question: What is the value of n?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
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
Cheers,
Brent
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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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.
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.