p, q, and r are positive integers. If p, q, and r are assembled into the six-digit number pqrpqr, which one of the following must be a factor of pqrpqr?
(A) 23
(B) 19
(C) 17
(D) 7
(E) none of the above
[spoiler]D[spoiler][/spoiler]
p, q, and r are positive
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 468
- Joined: Mon Jul 25, 2011 10:20 pm
- Thanked: 29 times
- Followed by:4 members
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
It implies that p, q, r are digits only, say 2, 3, and 4; and then look for the factors by dividing 234234 by 234, and we get 234234 = 234 × 1001, where the factor 234 is optional but the factor 1001 is a must.vipulgoyal wrote:p, q, and r are positive integers. If p, q, and r are assembled into the six-digit number pqrpqr, which one of the following must be a factor of pqrpqr?
(A) 23
(B) 19
(C) 17
(D) 7
(E) none of the above
[spoiler]D[spoiler][/spoiler]
Since 1001 = 7 × 11 × 13, out of which, only [spoiler]7 is in the options, hence (D)[/spoiler].
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Integer PQRPQR can be rephrased as follows:vipulgoyal wrote:p, q, and r are positive integers. If p, q, and r are assembled into the six-digit number pqrpqr, which one of the following must be a factor of pqrpqr?
(A) 23
(B) 19
(C) 17
(D) 7
(E) none of the above
P(10�) + Q(10�) + R(10³) + P(10²) + Q(10) + R
= P(10�) + P(10²) + Q(10�) + Q(10) + R(10³) + R
= 10²P(10³ + 1) + 10Q(10³ + 1) + R(10³ + 1)
= (10³ + 1)(10²P + 10Q + R)
= (1001)(10²P + 10Q + R)
= (7*11*13)(10²P + 10Q + R).
Thus, 7 must be a factor of PQRPQR.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3