Is the tens digit of a threedigit positive integer p divisible by 3?
(1) p7 is a multiple of 3
(2) p13 is a multiple of 3
Divisible by 3
This topic has expert replies
 akhilsuhag
 Master  Next Rank: 500 Posts
 Posts: 351
 Joined: 04 Jul 2011
 Thanked: 57 times
 Followed by:4 members
 GMATGuruNY
 GMAT Instructor
 Posts: 15533
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1898 members
 GMAT Score:790
Note:akhilsuhag wrote:Is the tens digit of a threedigit positive integer p divisible by 3?
(1) p7 is a multiple of 3
(2) p13 is a multiple of 3
0 is considered divisible by EVERY POSITIVE INTEGER.
Statement 1: p7 is a multiple of 3
Make a list of options for p7:
p7 = 93, 96, 99, 102, 105...
Adding 7 to each value in the list, we get the following options for p:
p = 100, 103, 106, 109, 112...
If p=100, then its tens digit is 0, which is divisible by 3.
If p=112, then its tens digit is 1, which is NOT divisible by 3.
INSUFFICIENT.
Statement 2: p13 is a multiple of 3
Make a list of options for p13:
p13 = 87, 90, 93, 96, 99...
Adding 13 to each value in the list, we get the following options for p:
p = 100, 103, 106, 109, 112...
Both statements yield the same list of options for p.
Implication:
Even when the two statements are combined, it's possible that p=100 (in which case its tens digit is divisible by 3) or that p=112 (in which case its tens digit is NOT divisible by 3).
Thus, the the two statements combined are INSUFFICIENT.
The correct answer is E.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15564
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
Target question: Is the tens digit of a threedigit positive integer p divisible by 3?akhilsuhag wrote:Is the tens digit of a threedigit positive integer p divisible by 3?
(1) p7 is a multiple of 3
(2) p13 is a multiple of 3
IMPORTANT: When I scan the two statements, I see that they both tell me the SAME THING.
There's a rule that says: If N and K are both divisible by d, then N+K and NK are also divisible by d.
OBSERVE: p13 is 6 less than p7. In other words, (p7)  6 = p13
Statement 1 tells us that p7 is divisible by 3, and we know that 6 is divisible by 3. So, by the above rule, p13 must be divisible by 3.
When two statements provide the SAME information, we can conclude that the correct answer will be either D or E.
Statement 1: p7 is a multiple of 3
There are several values of p that satisfy this condition. Here are two:
Case a: p = 139, in which case p7 = 132, and 132 is divisible by 3. In this case, the tens digit of p (3) IS divisible by 3
Case b: p = 118, in which case p7 = 111, and 111 is divisible by 3. In this case, the tens digit of p (1) is NOT divisible by 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: p13 is a multiple of 3
We already learned that statements 1 and 2 provide the SAME information. So, if statement 1 is NOT SUFFICIENT, we know that statement 2 is NOT SUFFICIENT
If you're not convinced, check out these two conflicting cases:
Case a: p = 139, in which case p13 = 126, and 126 is divisible by 3. In this case, the tens digit of p (3) IS divisible by 3
Case b: p = 118, in which case p13 = 105, and 105 is divisible by 3. In this case, the tens digit of p (1) is NOT divisible by 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Since both statements are not sufficient, and since both statements provide the SAME information, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent

 Master  Next Rank: 500 Posts
 Posts: 447
 Joined: 08 Nov 2013
 Thanked: 25 times
 Followed by:1 members
Consider the value p = ABC where A,B,C are the three digits.
Working backwards, firstly, for B to be a multiple of 3, it can only be 3, 6 or 9.
So, these are possibilities:
p = A3C, A6C, A9C
If we subtract 7 (= 10 + 3)we get:
p = A2C+3, A5C+3, A8C+3
For p to be a multiple of 3, then the sum of all digits must be a multiple of 3
As A and C are both undefined, then Statement A is NOT SUFFICIENT
Instead if we subtract 13 (= 10  3)we get:
p = A2C3, A5C3, A8C3
For p to be a multiple of 3, then the sum of all digits must be a multiple of 3
As A and C are both undefined, then Statement A is NOT SUFFICIENT
Combined statements will still leave A and C undefined. NOT SUFFICIENT>
Answer = (E)
Working backwards, firstly, for B to be a multiple of 3, it can only be 3, 6 or 9.
So, these are possibilities:
p = A3C, A6C, A9C
If we subtract 7 (= 10 + 3)we get:
p = A2C+3, A5C+3, A8C+3
For p to be a multiple of 3, then the sum of all digits must be a multiple of 3
As A and C are both undefined, then Statement A is NOT SUFFICIENT
Instead if we subtract 13 (= 10  3)we get:
p = A2C3, A5C3, A8C3
For p to be a multiple of 3, then the sum of all digits must be a multiple of 3
As A and C are both undefined, then Statement A is NOT SUFFICIENT
Combined statements will still leave A and C undefined. NOT SUFFICIENT>
Answer = (E)
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15564
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
Hey Mathsbuddy,Mathsbuddy wrote: Working backwards, firstly, for B to be a multiple of 3, it can only be 3, 6 or 9.
You're absolutely right about the answer being E, but be careful. If B is a multiple of 3, then B can equal 0, 3, 6 or 9
Zero is a multiple of all integers. Likewise, zero is divisible by all integers.
Cheers,
Brent

 Master  Next Rank: 500 Posts
 Posts: 447
 Joined: 08 Nov 2013
 Thanked: 25 times
 Followed by:1 members
Thanks Brent, I did wonder if I should have included zero![email protected] wrote:Hey Mathsbuddy,Mathsbuddy wrote: Working backwards, firstly, for B to be a multiple of 3, it can only be 3, 6 or 9.
You're absolutely right about the answer being E, but be careful. If B is a multiple of 3, then B can equal 0, 3, 6 or 9
Zero is a multiple of all integers. Likewise, zero is divisible by all integers.
Cheers,
Brent
However, as it is not sufficient for the other values, it's sufficiency for zero becomes obsolete.
Nonetheless, I haven't totally convinced myself if 'working backwards' is 100% valid!