Bunuel's Algebra PS Diagnostic Test : Problem Solving (PS)

Bunuel · 2022-10-02T04:59:00-07:00

Bunuel's Algebra Diagnostic Test Absolute Values/Modulus, Algebra, Arithmetic, Exponents/Powers, Fractions/Ratios/Decimals, Functions and Custom Characters, Inequalities, Min/Max Problems, Must or Could be True Questions, Percent and Interest Problems. https://gmatclub.com/forum/download/file.php?id=68660 Please note that the questions are ranked in ascending level of difficulty according to the timer stats. Grading & How to use this test: Please time yourself and allocate 2 mins per question 27 or more correct, your Algebra score is Q90 24 - 26 correct, your Algebra score is Q86 21 - 23 correct, your Algebra score is Q83 18 - 20 correct, your Algebra score is Q80 15 - 17 correct, your Algebra score is Q78 12 - 14 correct, your Algebra score is Q76 Note that levels 7 and 8 are very hard questions. These questions are well within the GMAT parameters but their difficulty is driven by the amount of time you will need to spend to solve each of the questions. Do not be discouraged if you are not able to solve any of the Level 7 or 8 questions. ------------------- EASY ------------------- LEVEL 1: 1. If the average of a, b, c, 14 and 15 is 12. What is the average value of a, b, c and 29 ? A. 12 B. 13 C. 14 D. 15 E. 16 D 2. If 22 - |y + 14| = 20, what is the sum of all possible values of y ? A. -28 B. -16 C. -12 D. -4 E. 4 A 3. Jeeves prepares a hangover cure using four identical cocktail shakers. The first shaker is 1/2 full, the second shaker is 1/3 full, the third shaker is 1/4 full and the last one is empty. If Jeeves redistributes all the content of the shakers equally into the four shakers, what fraction of each shaker will be filled? A. 13/48 B. 4/13 C. 13/36 D. 9/13 E. 35/48 A 4. If 7^8 = m and 8^7 = n , then what is the value of 56^{56} in terms of m and n ? A. mn B. m^7*n^8 C. m^8*n^7 D. (mn)^{56} E. 56^{mn} B 5. If ab^2 > 0 and ac 0 II. b^2c 0 A. I only B. II only C. III only D. II and III only E. I, II, and III D LEVEL 2: 6. What is the value of \sqrt{(49\%)} - \frac{7}{100} ? A. 0 B. 0.63% C. 0.063 D. 63% E. 6.3 D 7. What is the value of (12\%)^2 ? A. 0.144\% B. 1.44\% C. 0.144 D. 144\% E. 14.4 B 8. If \sqrt{2+\sqrt{2+x} } +\sqrt{2-\sqrt{2+x} }=\sqrt{2x} , what is the value of x ? A. -2 B. -\sqrt{2} C. 1 D. \sqrt{2} E. 2 E 9. If x > 0 and \sqrt{17^{\sqrt{x} } } = 17^{\frac{1}{\sqrt{x} } } , what is the value of x ? A. \frac{1}{2} B. \frac{1}{\sqrt{2 C. \sqrt{2} D. 2 E. 4 D 10. If m is a positive number and n is a negative number, and |m| > |n|, then which of the following has the greatest value ? A. |\frac{m - n}{n}| B. |\frac{m - n}{m}| C. |\frac{m + n}{m - n}| D. |\frac{m + n}{n}| E. |\frac{m + n}{m}| A ------------------- MEDIUM ------------------- LEVEL 3: 11. Jeeves prepares a hangover cure using four identical cocktail shakers. The first shaker is 1/2 full, the second shaker is 4/5 full, the third shaker is 1/k full and the last one is empty. After Jeeves redistributed all the content of the shakers equally into the four shakers, each shaker became 31/80 full. What is the value of k? A. 2 B. 3 C. 4 D. 5 E. 6 C 12. If the sum of all 21 terms of an arithmetic progression is zero, then which of the following MUST be true ? (An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant) I. 11th smallest term is zero II. 11th largest term is zero III. The range of the numbers is 20 A. I B. II C. III D. I and II E. None of the above D 13. What is the value of \sqrt {2.7\%}-\sqrt {0.16\%} ? A. 0.001 B. 10\% C. 1 D. 1000\% E. 100 B 14. x_1+x_2+...+x_{100} = 1 ; x_1+x_2+...+x_{99} = 2 ; x_1+x_2+...+x_{98} = 3 ; ... x_1= 100 . What is the value of x_1*x_2*...*x_{100} ? A. -100 B. -1 C. 0 D. 1 E. 100 A 15. What is the value of (\sqrt {800\%})^2 A. 0.04\% B. 0.4 C. 100\% D. 2 E. 400\% E LEVEL 4: 16. A merchant offers a discount of 30% on her list price and ends up making a profit of 19% on her cost price. By what percentage was her list price more than the cost price? A. 76% B. 70% C. 57% D. 55% E. 49% B 17. If (x + y)^2 0 . What is the sum of the first 11 terms of the sequence? A. 43954414 B. 43954588 C. 43954675 D. 43954713 E. 43954780 D 19. What is the value of |\sqrt{3} - |\sqrt{5}-\sqrt{7}|| - ||\sqrt{3} - \sqrt{5}|-\sqrt{7}| ? A. 2\sqrt{5}-2\sqrt{7}-2\sqrt{3} B. 2\sqrt{5}-2\sqrt{7} C. 2\sqrt{7}-2\sqrt{5} D. 2\sqrt{5}-2\sqrt{7}+2\sqrt{3} E. 2\sqrt{7}+2\sqrt{5} B 20. If x > 0 and x^{(3*x^{12})}=4 , what is the value of x ? A. \sqrt {2} B. \sqrt {2} C. \sqrt {2} D. \sqrt{3} E. \sqrt{2} B ------------------- HARD ------------------- LEVEL 5: 21. If a > b > c > d > e and abcde > 0 , then which of the following must be true ? I. ab > 0 II. bc > 0 III. de > 0 A. I only B. II only C. III only D. II and III only E. I, II, and III D 22. If the sum of the first 31 terms of an arithmetic progression consisting 46 terms is zero, then which of the following MUST be true ? (An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant) I. 31st smallest term is zero II. 16th largest term is zero III. The sum of the largest and smallest terms of the sequence is positive A. I only B. II only C. III only D. I and II only E. None of the above E 23. What is the value of 4^{3^{2^{1^{2^{3^4} } } } } ? A. 2,144 B. 262,142 C. 262,144 D. 262,146 E. 262,148 C 24. If x is an integer and \frac{(x^2 - 2)!}{x^2-2}=33! , what is the range of all possible values of x ? A. 0 B. 2 C. 6 D. 11 E. 12 E 25. If 9^x + 9^{-x} = 62 , then what is the value of 3^x + 3^{-x} ? A. 1/64 B. 1/8 C. 8 D. 62 E. 64 C LEVEL 6: 26. If x^x=\sqrt{\frac{\sqrt{2} }{2} } , which of the following could be a value of x ? A. \frac{1}{16} B. \frac{1}{4} C. \frac{1}{\sqrt{2 D. \frac{1}{2} E. \sqrt{2} A 27. A cloth merchant professes to sell at a loss of 5%. However, the merchant falsifies the meter scale and gains 25%. What is the measure of the scale that he uses when measuring 1 meter of cloth? A. 70 B. 72 C. 75 D. 76 E. 77 D 28. If 45x = 121y, which of the following must be true? I. x > y II. x^2 > y^2 III. x/11 is an integer (A) I only (B) II only (C) III only (D) I and III only (E) None of the above E 29. If x and y are integers 35x = 69y, which of the following must be true? I. x > y II. y/7 is an integer III. x/23 is an integer (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III D 30. What is the value of (\sqrt{4-\sqrt{15}})(4 + \sqrt{15})(\sqrt{6} - \sqrt{10}) ? A. -4 B. -2 C. -1 D. 1 E. 2 B ------------------- VERY HARD ------------------- LEVEL 7: 31. If is the greatest integer less than or equal to x, and = 5 and = 6, where x and y are positive integers, what is the greatest possible value of x + y ? A. 61 B. 81 C. 82 D. 83 E. 85 D 32. If \frac{|x| - 2}{|x - 2|}= 1 , then which of the following must be true? I. |x| > 2 II. x^2 0 A. I only B. II only C. III only D. I and III only E. None D 33. {x, y, z} is an increasing sequence of numbers such that the ratio between the consecutive terms is constant. {x + 2y, 2x + y + z, x + 3y + z} is an increasing sequence of numbers such that the difference between the consecutive terms is constant. What is the value of x/z ? A. 1/4 B. 1/2 C. 1 D. 2 E. 4 A 34. Mbappe withdraws \frac{100}{x}% of the amount in his account each time he visits the bank, where x is an integer greater than 1. If, after 5 visits, he has less than \frac{1}{x}^{th} of the initial amount left in the bank, what is the range of possible values for x ? A. 1 B. 2 C. 3 D. 4 E. 5 B 35. If the sum of the first 11 terms of an arithmetic progression consisting 16 terms is zero, then which of the following COULD be true ? (An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant) I. 11th smallest term is zero II. 6th largest term is zero III. All terms are non negative A. I only B. II only C. III only D. I and II only E. I, II, and III E LEVEL 8: 36. If \frac{x+500}{510}+\frac{x+510}{515} + \frac{x+520}{520} + \frac{x+530}{525}+ \frac{x+540}{530}=10 , what is the value of x ? A. 515 B. 520 C. 525 D. 530 E. 535 B 37. If x and y are consecutive integers, x > y, and x^2 - 1 > y^2 - 4y + x - 1, then which of the following must be true? A. x -1 D. y ≠ 1 E. x + y > 3 C 38. If \frac{m^4}{|m|} -8 A. I only B. II only C. III only D. I and II only E. I, II, and III E 39. The infinite sequence of integers a_1 , a_2 , ..., a_n , ... is such that a_1 = -17 and a_{n-1} - 7 1 . If a_x=-53 , then how many different values can x take? A. 1 B. 4 C. 5 D. 6 E. 7 E 40. If n is an integer greater than 1, what is the value of 10*\sqrt {10*\sqrt {10*\sqrt {10*\sqrt {...}}}} , where the given expression extends to an infinite number of roots? A. 10 B. 10^{\frac{1}{n}} C. 10^{\frac{n-1}{n}} D. 10^{\frac{n}{n-1}} E. 10^{n} D Check Word Problems Diagnostic set HERE . algebra.jpg

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 28 March 2025

Posts: 100,124

Own Kudos:

711,481

Given Kudos: 92,748

Products:

Expert

Expert reply

Posts: 100,124

Kudos: 711,481

03 Oct 2022, 01:30

Kudos

Bookmarks

dabrien3

Where are the answers to these questions

Answer will be posted in a week or so, after we get solutions here.

bb

Founder

Joined: 04 Dec 2002

Last visit: 27 Mar 2025

Posts: 40,333

Own Kudos:

78,472

[1]

Given Kudos: 22,319

Location: United States

GMAT 1: 750 Q49 V42 Verified score

GPA: 3

Products:

Expert

Expert reply

GMAT 1: 750 Q49 V42 Verified score

Posts: 40,333

Kudos: 78,472

[1]

05 Oct 2022, 22:16

1

Kudos

Bookmarks

Thank you! We may need the OA's to make this test work since I can't really get much past level 6 with confidence 😂

P.S. Really liked the questions - each one I can learn something new! All have a special touch to them! Thank you for this. I have enjoyed taking the test and I don't even need to take the GMAT - you sucked me into it!
Great question #23 by the way! It has 2 great tricks (one with powers of 1 and the other with 4). I really liked it!

singhaz

Joined: 20 Feb 2021

Last visit: 23 May 2023

Posts: 53

Own Kudos:

31

Given Kudos: 24

Location: India

Concentration: Entrepreneurship, Technology

GPA: 2.8

Posts: 53

Kudos: 31

05 Oct 2022, 23:57

Kudos

Bookmarks

Hi @bunnel
For Q8 I am getting two values of x which is 1 & 2, can u pls tell me where i am getting wrong.
I solved the ques by squaring both sides and then solved for x

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 28 March 2025

Posts: 100,124

Own Kudos:

711,481

[1]

Given Kudos: 92,748

Products:

Expert

Expert reply

Posts: 100,124

Kudos: 711,481

[1]

06 Oct 2022, 00:58

1

Kudos

Bookmarks

Hi,

OA's are added in the original post under the spoilers.

Happy solving!

sampathgelam

Joined: 02 Jul 2021

Last visit: 29 Aug 2024

Posts: 138

Own Kudos:

148

Given Kudos: 50

Location: India

Schools: IIM (A) IIMA '25 (A)

GMAT Focus 1: 665 Q87 V82 DI80 Verified score

GPA: 3

Products:

Schools: IIM (A) IIMA '25 (A)

GMAT Focus 1: 665 Q87 V82 DI80 Verified score

Posts: 138

Kudos: 148

06 Oct 2022, 11:25

Kudos

Bookmarks

Bunuel

Hi,

OA's are added in the original post under the spoilers.

Happy solving!

Q23 Answer is 262144,Please recheck and if the OA is correct, then kindly explain

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 28 March 2025

Posts: 100,124

Own Kudos:

711,481

Given Kudos: 92,748

Products:

Expert

Expert reply

Posts: 100,124

Kudos: 711,481

06 Oct 2022, 11:35

Kudos

Bookmarks

sampathgelam

Bunuel

Hi,

OA's are added in the original post under the spoilers.

Happy solving!

Q23 Answer is 262144,Please recheck and if the OA is correct, then kindly explain

_____________________
Typo. Edited. Thank you.

jonNNNNNy

Joined: 09 Jan 2022

Last visit: 19 Dec 2022

Posts: 11

Own Kudos:

1

Given Kudos: 11

Posts: 11

Kudos: 1

06 Oct 2022, 12:59

Kudos

Bookmarks

Thank you so much for this Bunuel !!
Please do some others for other topics

)

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 28 March 2025

Posts: 100,124

Own Kudos:

711,481

[6]

Given Kudos: 92,748

Products:

Expert

Expert reply

Posts: 100,124

Kudos: 711,481

[6]

06 Oct 2022, 13:00

4

Kudos

2

Bookmarks

jonNNNNNy

Thank you so much for this Bunuel !!
Please do some others for other topics

)

Word problems will include:

Distance/Rate Problems
Mixture Problems
Overlapping Sets
Work/Rate Problems
Word problems

Number properties will include:

Divisibility/Multiples/Factors
Remainders
Number properties

Combinations/probability/statistics will include:

Combinations
Probability
Statistics and Sets Problems

Geometry will include:

Coordinate Geometry
Geometry

OK. Here is a deal: if both Algebra: PS Diagnostic Test and Algebra: DS Diagnostic Test get 100 replies, I'll do ALL these topic for PS as well as DS!

How does this sound?

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

06 Oct 2022, 14:22

Kudos

Bookmarks

Hey Bunuel,

Answer to Q36 should be B) 520, I guess there might have been a typo

kungfury42

Joined: 07 Jan 2022

Last visit: 31 May 2023

Posts: 583

Own Kudos:

480

[2]

Given Kudos: 725

Schools: NUS '25 (A)

GMAT 1: 740 Q51 V38 Verified score

GPA: 4

Products:

Schools: NUS '25 (A)

GMAT 1: 740 Q51 V38 Verified score

Posts: 583

Kudos: 480

[2]

06 Oct 2022, 16:22

2

Kudos

Bookmarks

Time taken: 60 minutes
Verdict: Q50+ (37 Correct, 3 Incorrect)

Thank you so much for the amazing test Bunuel

Level 1: 3 minutes, 5/5 correct
Level 2: 4 minutes, 5/5 correct
Level 3: 3 minutes, 5/5 correct
Level 4: 6 minutes, 5/5 correct
Level 5: 7 minutes, 4/5 correct
Level 6: 10 minutes, 4/5 correct
Level 7: 14 minutes, 5/5 correct
Level 8: 13 minutes, 4/5 correct

Incorrect analysis:
Q24: Silly error, arrived at ±6 but ignored -6 value for some reason
Q30: Calculation intensive, couldn't find a shortcut, took a guess
Q37: Used smart POE, but got it wrong somewhere, will have to recheck

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

06 Oct 2022, 16:39

Kudos

Bookmarks

av1901

Hey Bunuel,

Answer to Q36 should be B) 520, I guess there might have been a typo

Also for Q37: Both A and C seem to satisfy the criteria for MUST BE TRUE. Anywhere I'm going particularly wrong?
This is my reasoning:
If y > -1, then because x and y are consecutive integers and x > y, then that would imply that x > 0 as well

kungfury42

Joined: 07 Jan 2022

Last visit: 31 May 2023

Posts: 583

Own Kudos:

480

Given Kudos: 725

Schools: NUS '25 (A)

GMAT 1: 740 Q51 V38 Verified score

GPA: 4

Products:

Schools: NUS '25 (A)

GMAT 1: 740 Q51 V38 Verified score

Posts: 583

Kudos: 480

06 Oct 2022, 16:45

Kudos

Bookmarks

av1901

Hey Bunuel,

Answer to Q36 should be B) 520, I guess there might have been a typo

Also for Q37: Both A and C seem to satisfy the criteria for MUST BE TRUE. Anywhere I'm going particularly wrong?
This is my reasoning:
If y > -1, then because x and y are consecutive integers and x > y, then that would imply that x > 0 as well

Yes that's the same POE I used. AC are paired options, similarly BD are paired options, and since we can only have one correct answer, it should be E.

Posted from my mobile device

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

[1]

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

[1]

06 Oct 2022, 17:43

1

Kudos

Bookmarks

1. If the average of a, b, c, 14 and 15 is 12. What is the average value of a, b, c and 29 ?

A. 12
B. 13
C. 14
D. 15
E. 16

Solution:

\(\frac{a+b+c+14+15}{5} = 12\)
\(a+b+c+29 = 60\)

We need to find average of a, b, c, and 29
Sum of these four numbers = 60 (Above)
Average = Sum/Number = \(\frac{60}{4} = 15\)

Answer: D

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

[1]

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

[1]

06 Oct 2022, 17:48

1

Kudos

Bookmarks

2. If 22 - |y + 14| = 20, what is the sum of all possible values of y ?

A. -28
B. -16
C. -12
D. -4
E. 4

With modulus, we take two cases: Negative and Non-Negative

Negative: \(22 - (- y - 14) = 20\) => \(y = -16\)
Non-negative: \(22 - y - 14 = 20\) => \(y = -12\)

Sum of all values \(= -16 - 12 = -28\)

Answer: A

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

[1]

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

[1]

06 Oct 2022, 18:46

1

Kudos

Bookmarks

3. Jeeves prepares a hangover cure using four identical cocktail shakers. The first shaker is 1/2 full, the second shaker is 1/3 full, the third shaker is 1/4 full and the last one is empty. If Jeeves redistributes all the content of the shakers equally into the four shakers, what fraction of each shaker will be filled?

A. 13/48
B. 4/13
C. 13/36
D. 9/13
E. 35/48

When fractions are involved, best way is to take LCM of the denominators so that we have easier numbers to work with

First shaker: 1/2 full
Second shaker: 1/3 full
Third shaker: 1/4 full
Fourth shaker: Empty

Let capacity of each individual shaker = LCM (2,3,4) = 12
Total shaker capacity = 12*4 = 48

First shaker = 1/2 * 12 = 6
Second shaker = 1/3 * 12 = 4
Third shaker = 1/4 * 12 = 3
Fourth shaker = 0

Filled capacity = 13
Total capacity = 48

Fraction filled = 13/48

Answer: A

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

[2]

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

[2]

06 Oct 2022, 18:51

1

Kudos

1

Bookmarks

4. If \(7^8 = m\) and \(8^7 = n\), then what is the value of \(56^{56}\) in terms of m and n ?

A. \(mn\)

B. \(m^7*n^8\)

C. \(m^8*n^7\)

D. \((mn)^{56}\)

E. \(56^{mn}\)

Solution:

\(56^{56} = 7^{56} * 8^{56} = (7^8)^7 * (8^7)^8 = m^7 * n^8\)

Answer: B

av1901

Joined: 28 May 2022

Last visit: 19 Dec 2024

Posts: 429

Own Kudos:

432

[1]

Given Kudos: 83

Status:Dreaming and Working

Affiliations: None

WE:Brand Management (Manufacturing)

Products:

Posts: 429

Kudos: 432

[1]

06 Oct 2022, 18:56

1

Kudos

Bookmarks

5. If \(ab^2 > 0\) and \(ac < 0\), then which of the following must be true?

I. \(ab >0\)

II. \(b^2c < 0\)

III. \(a*c^2 > 0\)

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Solution:

\(ab^2 > 0\) => \(a > 0\) & \(b\) could either be positive or negative

\(ac < 0\) => We already deduced \(a > 0\) from the previous inequality so here \(c < 0\)

So, we have \(a > 0, c < 0\) and \(b\) is inconclusive

I. \(ab >0\)

\(a > 0\) but \(b\) could either be + or - , so this CANNOT BE MUST BE TRUE

II. \(b^2c < 0\)

We already know that \(c < 0\) and \(b^2\) will always be positive so expression will always be < 0. MUST BE TRUE

III. \(a*c^2 > 0\)

We already know that \(a > 0, c < 0\) so \(c^2 > 0\), since both parts of the product are > 0, expression will always be > 0. MUST BE TRUE

II and III MUST BE TRUE

Answer: D

Bunuel's Algebra PS Diagnostic Test

Prep Toolkit

My Rewards

GMAT Problem Solving (PS) Questions

Bunuel's Algebra PS Diagnostic Test

Prep Toolkit

My Rewards