GMAT Number Properties: Challenge
Jeff Sackmann / GMAT HACKS
January 2013
Contents
1 Introduction 2
2 Difficulty Levels 3
3 Problem Solving 4
4 Data Sufficiency 15
5 Answer Key 21
6 Explanations 24
1
, Jeff Sackmann
www.gmathacks.com
1 Introduction
This document contains nothing but difficult GMAT Number Properties questions–
100 of them, to be exact. Number Properties is one of the most challenging
topics on the test, since many questions can’t be solved algebraically. There
are plenty of techniques you can learn to make these questions more clear-cut
(and those are discussed in the explanations), but most test-takers never learn
them.
As in all of my GMAT preparation resources, you’ll find these questions
indexed by difficulty. That doesn’t mean you should skip straight to the hardest
questions, or even that you should start with the easier ones. On the GMAT
itself, questions won’t come labeled with their difficulty level, and despite the
intent of the adaptive algorithm, they won’t be precisely consistent in terms
of difficulty either. Each question presents its own unique challenges, and the
sooner you get accustomed to changing gears with every single question, the
more time you’ll have to prepare for that particular challenge of the exam.
For further, more specific practice, I have produced several other resources
that may help you. I’ve also created a 100-question set called ”Exponents and
Roots,” which covers exactly that material, including dozens of questions that
force you to master every last exponent-related rule the GMAT will test you
on. You’ll also find many Number Properties questions in my general sets,
”Problem Solving: Challenge” and ”Data Sufficiency: Challenge.”
Also, Total GMAT Math has several chapters (along with focused practice)
on Number Properties and related issues, including individual chapters on prime
numbers, factors, multiples, evens and odds, consecutive numbers, and more. If
you find you are struggling with the mechanics of these problems, your time is
probably better spent with Total GMAT Math than in doing dozens and dozens
of practice problems, hoping to pick up those skills along the way.
If you find yourself having problems with only the most difficult questions,
you might try my ”Extreme Challenge” set, which contains only 720 and higher
level questions, many of which are Number Properties-related.
As far as strategy is concerned, there are dozens of articles at gmathacks.com
to help you with your strategic approach to Arithmetic questions. Most impor-
tantly, you should make sure you understand every practice problem you do. It
doesn’t matter if you get it right the first time–what matters is whether you’ll
get it right the next time you see it, because the next time you see it could be
on the GMAT.
With that in mind, carefully analyze the explanations. Redo questions that
took you too long the first time around. Review questions over multiple sessions,
rather than cramming for eight hours straight each Saturday. These basic study
skills may not feel like the key to GMAT preparation, but they are the difference
between those people who reach their score goals and those who never do.
Enough talking; there are 100 Number Properties questions waiting inside.
Get to work!
2
Copyright 2007-13 Jeff Sackmann
www.gmathacks.com
, Jeff Sackmann
www.gmathacks.com
2 Difficulty Levels
In general, the level 5 questions in this guide are 560- to 620-level questions.
The level 6 questions representing a broad range of difficulty from about 620 to
720, while the level 7 questions are higher still.
Moderately Difficult (5)
PS
001, 002, 010, 035, 043
DS
051, 052, 053, 062, 067, 068, 070, 071, 073, 074, 075, 081, 083, 084, 086, 087,
090, 092, 094, 096, 097
Difficult (6)
PS
003, 005, 007, 009, 011, 012, 013, 014, 015, 016, 020, 021, 022, 024, 026, 027,
029, 032, 033, 034, 037, 038, 039, 040, 042, 044, 045, 046, 048
DS
049, 050, 054, 055, 056, 057, 058, 059, 061, 063, 064, 065, 066, 069, 072, 076,
077, 078, 079, 082, 085, 088, 089, 093, 095, 098, 099, 100
Very Difficult (7)
PS
004, 006, 008, 017, 018, 019, 023, 025, 028, 030, 031, 036, 041, 047
DS
060, 080, 091
3
Copyright 2007-13 Jeff Sackmann
www.gmathacks.com
, Jeff Sackmann
www.gmathacks.com
3 Problem Solving
Note: this guide contains both an answer key (so you can quickly check your
answers) and full explanations.
n+78
1. For which of the following values of n is n an integer?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
2. What is the probability that a random number selected from the
set of integers 101 through 300, inclusive, has a units digit of 6?
20
(A) 299
20
(B) 199
3
(C) 20
2
(D) 15
1
(E) 10
243
3. (62 )(42 )(22 )
(A) 2
(B) 3
(C) 6
(D) 9
(E) 12
4. If p is a positive integer and p2 is divisible by 12, then the largest
positive integer that must divide p3 is
(A) 23
(B) 26
(C) 33
(D) 63
(E) 122
5. What is the least positive integer that is divisible by each of the
integers 1 through 6, inclusive?
(A) 60
(B) 120
(C) 180
(D) 240
(E) 360
4
Copyright 2007-13 Jeff Sackmann
www.gmathacks.com
Jeff Sackmann / GMAT HACKS
January 2013
Contents
1 Introduction 2
2 Difficulty Levels 3
3 Problem Solving 4
4 Data Sufficiency 15
5 Answer Key 21
6 Explanations 24
1
, Jeff Sackmann
www.gmathacks.com
1 Introduction
This document contains nothing but difficult GMAT Number Properties questions–
100 of them, to be exact. Number Properties is one of the most challenging
topics on the test, since many questions can’t be solved algebraically. There
are plenty of techniques you can learn to make these questions more clear-cut
(and those are discussed in the explanations), but most test-takers never learn
them.
As in all of my GMAT preparation resources, you’ll find these questions
indexed by difficulty. That doesn’t mean you should skip straight to the hardest
questions, or even that you should start with the easier ones. On the GMAT
itself, questions won’t come labeled with their difficulty level, and despite the
intent of the adaptive algorithm, they won’t be precisely consistent in terms
of difficulty either. Each question presents its own unique challenges, and the
sooner you get accustomed to changing gears with every single question, the
more time you’ll have to prepare for that particular challenge of the exam.
For further, more specific practice, I have produced several other resources
that may help you. I’ve also created a 100-question set called ”Exponents and
Roots,” which covers exactly that material, including dozens of questions that
force you to master every last exponent-related rule the GMAT will test you
on. You’ll also find many Number Properties questions in my general sets,
”Problem Solving: Challenge” and ”Data Sufficiency: Challenge.”
Also, Total GMAT Math has several chapters (along with focused practice)
on Number Properties and related issues, including individual chapters on prime
numbers, factors, multiples, evens and odds, consecutive numbers, and more. If
you find you are struggling with the mechanics of these problems, your time is
probably better spent with Total GMAT Math than in doing dozens and dozens
of practice problems, hoping to pick up those skills along the way.
If you find yourself having problems with only the most difficult questions,
you might try my ”Extreme Challenge” set, which contains only 720 and higher
level questions, many of which are Number Properties-related.
As far as strategy is concerned, there are dozens of articles at gmathacks.com
to help you with your strategic approach to Arithmetic questions. Most impor-
tantly, you should make sure you understand every practice problem you do. It
doesn’t matter if you get it right the first time–what matters is whether you’ll
get it right the next time you see it, because the next time you see it could be
on the GMAT.
With that in mind, carefully analyze the explanations. Redo questions that
took you too long the first time around. Review questions over multiple sessions,
rather than cramming for eight hours straight each Saturday. These basic study
skills may not feel like the key to GMAT preparation, but they are the difference
between those people who reach their score goals and those who never do.
Enough talking; there are 100 Number Properties questions waiting inside.
Get to work!
2
Copyright 2007-13 Jeff Sackmann
www.gmathacks.com
, Jeff Sackmann
www.gmathacks.com
2 Difficulty Levels
In general, the level 5 questions in this guide are 560- to 620-level questions.
The level 6 questions representing a broad range of difficulty from about 620 to
720, while the level 7 questions are higher still.
Moderately Difficult (5)
PS
001, 002, 010, 035, 043
DS
051, 052, 053, 062, 067, 068, 070, 071, 073, 074, 075, 081, 083, 084, 086, 087,
090, 092, 094, 096, 097
Difficult (6)
PS
003, 005, 007, 009, 011, 012, 013, 014, 015, 016, 020, 021, 022, 024, 026, 027,
029, 032, 033, 034, 037, 038, 039, 040, 042, 044, 045, 046, 048
DS
049, 050, 054, 055, 056, 057, 058, 059, 061, 063, 064, 065, 066, 069, 072, 076,
077, 078, 079, 082, 085, 088, 089, 093, 095, 098, 099, 100
Very Difficult (7)
PS
004, 006, 008, 017, 018, 019, 023, 025, 028, 030, 031, 036, 041, 047
DS
060, 080, 091
3
Copyright 2007-13 Jeff Sackmann
www.gmathacks.com
, Jeff Sackmann
www.gmathacks.com
3 Problem Solving
Note: this guide contains both an answer key (so you can quickly check your
answers) and full explanations.
n+78
1. For which of the following values of n is n an integer?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
2. What is the probability that a random number selected from the
set of integers 101 through 300, inclusive, has a units digit of 6?
20
(A) 299
20
(B) 199
3
(C) 20
2
(D) 15
1
(E) 10
243
3. (62 )(42 )(22 )
(A) 2
(B) 3
(C) 6
(D) 9
(E) 12
4. If p is a positive integer and p2 is divisible by 12, then the largest
positive integer that must divide p3 is
(A) 23
(B) 26
(C) 33
(D) 63
(E) 122
5. What is the least positive integer that is divisible by each of the
integers 1 through 6, inclusive?
(A) 60
(B) 120
(C) 180
(D) 240
(E) 360
4
Copyright 2007-13 Jeff Sackmann
www.gmathacks.com
