GMAT Algebra: Challenge
Jeff Sackmann / GMAT HACKS
January 2013
Contents
1 Introduction 2
2 Difficulty Levels 3
3 Problem Solving 4
4 Data Sufficiency 18
5 Answer Key 23
6 Explanations 26
1
, Jeff Sackmann
www.gmathacks.com
1 Introduction
Ready for a challenge? This document contains nothing but difficult GMAT Al-
gebra questions–100 of them, to be exact. They run the gamut from quadratics
and inequalities to symbolism and sequences with several other topics thrown
in for good measure.
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. Another one of my 100-question practice sets, ”Exponents
and Roots,” focuses entirely on those two categories. ”Word Problems: Chal-
lenge” covers much of the same content, but contains only Word Problems, so
you have to take an extra step or two before you even have a chance to do the
algebra.
Also, Total GMAT Math has several chapters (along with focused practice)
on Algebra and related issues, including individual chapters on fractions, deci-
mals, simplifying expressions, linear equations, systems of equations, quadratic
equations, inequalities, absolute value, exponents, roots, and more.
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 Algebra-related.
You’ll find articles at gmathacks.com to help you with your strategic ap-
proach to Algebra questions. Most importantly, 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 Algebra questions waiting inside. Get to
work!
2
Copyright 2008-123 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
004, 007, 009, 013, 014, 015, 016, 017, 019, 035, 049, 050, 059
DS
064, 065, 066, 071, 072, 073, 075, 076, 077, 078, 080, 081, 082, 083, 085, 086,
087, 095, 096, 098, 099, 100
Difficult (6)
PS
002, 005, 006, 010, 011, 012, 018, 021, 024, 025, 026, 027, 028, 029, 030, 032,
033, 034, 036, 037, 038, 044, 045, 046, 047, 048, 051, 052, 056, 060
DS
061, 062, 063, 068, 069, 070, 074, 079, 084, 088, 090, 091, 092, 093, 094, 097
Very Difficult (7)
PS
001, 003, 008, 020, 022, 023, 031, 039, 040, 041, 042, 043, 053, 054, 055, 057,
058
DS
067, 089
3
Copyright 2008-123 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.
1. Which of the following is equal to xk for all positive values of x
and k ?
k 3
(A) (x 4 ) 4
xk
(B) x2k
k k
(C) x2 + x2
k
(D) (x 2 )2
(E) (xk )k
2. For all positive integers m and n, the operation @ is defined by
mˆ2
m@n = n−1 . If z@9 = 2, then z =
(A) 4
(B) 5
(C) 16
(D) 17
(E) 33
3. Hayden began walking from F to G, a distance of 40 miles, at the
same time Ava began walking from G to F on the same road. If
Hayden’s walking speed was x miles per hour and Ava’s was y
miles per hour, how many miles away from F were they, in terms
of x and y, when they met?
40(x−y)
(A) x+y
40x−y
(B) x+y
x−y
(C) x+y
40y
(D) x+y
40x
(E) x+y
4
Copyright 2008-123 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 18
5 Answer Key 23
6 Explanations 26
1
, Jeff Sackmann
www.gmathacks.com
1 Introduction
Ready for a challenge? This document contains nothing but difficult GMAT Al-
gebra questions–100 of them, to be exact. They run the gamut from quadratics
and inequalities to symbolism and sequences with several other topics thrown
in for good measure.
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. Another one of my 100-question practice sets, ”Exponents
and Roots,” focuses entirely on those two categories. ”Word Problems: Chal-
lenge” covers much of the same content, but contains only Word Problems, so
you have to take an extra step or two before you even have a chance to do the
algebra.
Also, Total GMAT Math has several chapters (along with focused practice)
on Algebra and related issues, including individual chapters on fractions, deci-
mals, simplifying expressions, linear equations, systems of equations, quadratic
equations, inequalities, absolute value, exponents, roots, and more.
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 Algebra-related.
You’ll find articles at gmathacks.com to help you with your strategic ap-
proach to Algebra questions. Most importantly, 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 Algebra questions waiting inside. Get to
work!
2
Copyright 2008-123 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
004, 007, 009, 013, 014, 015, 016, 017, 019, 035, 049, 050, 059
DS
064, 065, 066, 071, 072, 073, 075, 076, 077, 078, 080, 081, 082, 083, 085, 086,
087, 095, 096, 098, 099, 100
Difficult (6)
PS
002, 005, 006, 010, 011, 012, 018, 021, 024, 025, 026, 027, 028, 029, 030, 032,
033, 034, 036, 037, 038, 044, 045, 046, 047, 048, 051, 052, 056, 060
DS
061, 062, 063, 068, 069, 070, 074, 079, 084, 088, 090, 091, 092, 093, 094, 097
Very Difficult (7)
PS
001, 003, 008, 020, 022, 023, 031, 039, 040, 041, 042, 043, 053, 054, 055, 057,
058
DS
067, 089
3
Copyright 2008-123 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.
1. Which of the following is equal to xk for all positive values of x
and k ?
k 3
(A) (x 4 ) 4
xk
(B) x2k
k k
(C) x2 + x2
k
(D) (x 2 )2
(E) (xk )k
2. For all positive integers m and n, the operation @ is defined by
mˆ2
m@n = n−1 . If z@9 = 2, then z =
(A) 4
(B) 5
(C) 16
(D) 17
(E) 33
3. Hayden began walking from F to G, a distance of 40 miles, at the
same time Ava began walking from G to F on the same road. If
Hayden’s walking speed was x miles per hour and Ava’s was y
miles per hour, how many miles away from F were they, in terms
of x and y, when they met?
40(x−y)
(A) x+y
40x−y
(B) x+y
x−y
(C) x+y
40y
(D) x+y
40x
(E) x+y
4
Copyright 2008-123 Jeff Sackmann
www.gmathacks.com
