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
tens digit of the positive integer r
This topic has expert replies
- DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
Pick some easy numbers.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
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: What is the tens digit of the positive integer r?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: 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.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
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.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
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
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews