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 Q50+ 24 - 26 correct, your Algebra score is Q49 21 - 23 correct, your Algebra score is Q48 18 - 20 correct, your Algebra score is Q47 15 - 17 correct, your Algebra score is Q46 12 - 14 correct, your Algebra score is Q45 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. Is x = 0 ? (1) xy = x (2) x + y = y B 2. Is Q > 0 ? (1) P*Q^3*R^4 0 C 3. Is |x + y| 0 (2) (-3)^x*y^2 0 (2) x^3*y^2 y ? (1) x + y > 0 (2) y^2 > x^2 C 9. Is |x + 1| y ? (1) x^2 0 (2) x |y| + y ? (1) xy > 0 (2) x + y < 0 C LEVEL 4: 16. Is x^2 < x^3 ? (1) x < x^2 (2) x < 1 B 17. Is ac + \sqrt{(a^2 - 1)(c^2 - 1)} \leq 1 ? (1) a^2 + b^2 = 1 (2) c^2 + d^2 = 1 C 18. If n is an integer such that \frac{1}{6} < \frac{1}{(n-1)} < \frac{1}{3} , what is the value of n? (1) (n - 6)(n - 7) = 0 (2) (n - 5)(n - 3) ≠ 0 D 19. If m and n are positive two-digit integers, what is the value of the tens digit of m minus the tens digit of n ? (1) m - n = 42. (2) The units digit of m minus the units digit of n is not a multiple of 3. E 20. If x + y ≠ 0 , is \frac{1}{(x + y)} < 1 ? (1) x^2 = y^2 (2) \frac{1}{x} < 2 C ------------------- HARD ------------------- LEVEL 5: 21. Is p an odd integer? (1) (p^5)^5 is an odd integer. (2) \sqrt {\sqrt {p is an odd integer. B 22. Does x = y ? (1) \frac{xy}{(x + y)} = 0 (2) xy = 0 A 23. If x and y are integers, m = 3^{x-y}*5^{2y-1}*7^{4-x} and n = 105^y , what is the value of y ? (1) n is NOT a multiple of m . (2) m is a multiple of n . B 24. Is p + q > pq ? (1) p > 0 > q (2) |q| = p C 25. If m and n are positive two-digit integers, what is the value of the tens digit of m minus the tens digit of n ? (1) m - n = 43. (2) The units digit of m minus the units digit of n is not a multiple of 3. C LEVEL 6: 26. If m and n are integers, is mn > 0 ? (1) \frac{m}{n} is an integer. (2) |m| 9 . (2) x = y + 3 . C 28. If s - \frac{1}{s} t ? (1) s > 1 (2) t > 0 A 29. The infinite sequence a_1 , a_2 ,…, a_n , … is such that a_{n} 1. Does the sequence have more than 12 positive numbers ? (1) \frac{a_{14{a_{13=\frac{\sqrt{10{\pi} . (2) The product of any two of the first 14 terms is positive. A 30. If a, b, and c are three-digit positive integers and if a = b + c, is the hundreds digit of a greater than the sum of the hundreds digits of b and c ? (1) The tens digit of a is equal to the sum of the tens digits of b and c. (2) The tens digit of a is equal to the product of the tens digits of b and c. D ------------------- VERY HARD ------------------- LEVEL 7: 31. Positive integers a, b and c are all less than 10. If the sum of all the distinguishable three digit numbers that can be formed by juxtaposing these integers is 3108, is a=b? (1) c = 9 (2) a = 2 D 32. If xy ≠ 0 , is x x B 35. If a and b are single-digit positive numbers and a/b is NOT a recurring decimal, what is the value of a? (1) -\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5} (2) b is equal to the sum of its positive divisors excluding b itself C LEVEL 8: 36. If a + b + c + d = 12 , what is the value of \sqrt{a^2+b^2+c^2+d^2} ? (1) ab = cd = ad (2) |a| = |b| = |c| = |d| C 37. If xy \neq 0 , is x + y |b| > |c| , is a*b^3*c^3 > a*b^4*c^2 ? (1) a > b > c (2) a + b > 0 D 40. If n is an integer such that \frac{1}{9} \frac{1}{(1 - n)} > 1/7 (2) n is not an even integer. A

You cn ignore that question becasue such type of pure algebraic questions are no longer a part of the DS syllabus of the GMAT. DS questions in GMAT Focus encompass various types of word problems, such as: Word Problems Work Problems Distance Problems Mixture Problems Percent and Interest Problems Overlapping Sets Problems Statistics Problems Combination and Probability Problems While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won't encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..." Check GMAT Syllabus for Focus Edition Hope it helps.

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Bunuel

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saswat1987

Bunuel : Where to find the solutions or discussion for all the 40 Questions, I need to know whether my thought process and approach to the solution is okay or not. Probably, I can also learn something new.

Please respond..

We'll be releasing official solutions for all the questions in due course. In the meantime, feel free to share your explanations and insights.

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Bunuel can you explain que 4 why A is wrong

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My 2 cents : Hope this helps.
Statement : (1) (−2)^x∗y^3>0... if you put x=1, (-2)^1 = -2 and y^3 needs to be -ve to hold the statement true... but if y^3 is +ve, then the expression will not hold true..

Now consider, x=2, (-2)^2 = 4 and y^3 needs to be +ve.. if it is -ve then the statement fails..we don't know anything about y. hence not sufficient.

Also, for the time being lets assume x=0, the statement 1 will become (-2)^0 *y^3>0 => 1*y^3>0... a lot will depend on y, hence insufficient. Answer is B.

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Hrishabh07

Bunuel can you explain que 4 why A is wrong

4. If x and y are integers, is \(x = 0\)?

(1) \((-2)^x*y^3 > 0\)

If x is even (including 0), (-2)^x is positive.
If x is odd, (-2)^x is negative.
The sign of y^3 depends on y.

From this, (-2)^x * y^3 > 0 holds when x is even (including 0) and y is positive, as well as when x is odd and y is negative. Thus, x can be either even (including 0) or odd, depending on y's value. Insufficient.

(2) \((-3)^x*y^2 < 0\)

The square of a number is always positive or 0. However, since the product above is not 0, y^2 cannot be 0; hence, y^2 is positive. This implies that (-3)^x must be negative, which further implies that x must be odd. Thus, x cannot be 0. Sufficient.

Answer: B.

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where is x and y = 0 from?

av1901

6. If \(x + y ≠ 0\), is \(\frac{1}{(x + y)} < 2\)?

(1) \(x^3 = y^3\)
(2) \(\frac{1}{x} < 2\)

Solution:

(1) \(x^3 = y^3\)

=> x = y

If x = y = 2: YES
If x = y = 1/10: NO

Not sufficient

(2) \(\frac{1}{x} < 2\)

This does not give us any information about y

Not sufficient

TOGETHER: Both statements combined:

\(x = y\) and \(\frac{1}{x} < 2\) => \(\frac{1}{y} < 2\)

=> \( x = y > \frac{1}{2}\) or \(x = y < 0\)

In any possible case, \(\frac{1}{(x + y)} < 2\) ALWAYS

SUFFICIENT

Answer: C

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Correctness of second half on solving (x-y)(x+y)<0 is correct up to the point where -y < x < y. the second inequality is inconsequential and irrelevant and not attributable to the question. B should be the correct answer.

e.g. (x-3)(x+3)<0. this is only true for -3<x<3.

av1901

8. Is \(x > y\)?

(1) \(x + y > 0\)
(2) \(y^2 > x^2\)

Solution:

(1) \(x + y > 0\)

\(x > -y\)

If \(y = 3: x > -3\): If x = -2 NO, If x = 4 YES

Not sufficient

(2) \(y^2 > x^2\)

\(x^2 - y^2 < 0\)
\((x - y)(x + y) < 0\)

Either \(-y < x < y\) OR \(x > y & x < -y\)

In one case, x > y, in other it is not

Not Sufficient

Together: Both statements combined

From statement 2: Either \(-y < x < y\) OR \(x > y & x < -y\)
From statement 1: \(x > -y\)

=> \(-y < x < y\)

SUFFICIENT

Answer: C

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For question #37, Bunuel, do we have the correct format of statement (1)? I had to skip this question as I could not make out of it. Thanks!

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For question #37, Bunuel, do we have the correct format of statement (1)? I had to skip this question as I could not make out of it. Thanks!

You cn ignore that question becasue such type of pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems
Work Problems
Distance Problems
Mixture Problems
Percent and Interest Problems
Overlapping Sets Problems
Statistics Problems
Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won't encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

Hope it helps.

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Bunuel

hughng92

For question #37, Bunuel, do we have the correct format of statement (1)? I had to skip this question as I could not make out of it. Thanks!

Word Problems
Work Problems
Distance Problems
Mixture Problems
Percent and Interest Problems
Overlapping Sets Problems
Statistics Problems
Combination and Probability Problems

Thank you. I just got the 2024-2025 bundle so I think I will go through those to see the new updated question styles.

Do you recommend the GMAT Official Guide Advanced Question Book (https://www.amazon.com/Official-Advance ... 1119620953) given the question styles have changed in the Focus Edition? Don't want to waste time studying the irrelevant / outdated materials. Thanks, Bunuel.

Bunuel

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hughng92

Bunuel

hughng92

For question #37, Bunuel, do we have the correct format of statement (1)? I had to skip this question as I could not make out of it. Thanks!

Word Problems
Work Problems
Distance Problems
Mixture Problems
Percent and Interest Problems
Overlapping Sets Problems
Statistics Problems
Combination and Probability Problems

I'd check new books from GMAC only.

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Adding this reply to make sure we get more of these insightful diagnostic tests from Bunuel

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My question is, shoudn't statement 2 be enough? because if \(\frac{ 1}{x } <2 \) then no matter what you add as y to x, the fraction \(\frac{1}{(x + y)} < 2\), it will always be lesser than 2

av1901

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sanya511

My question is, shoudn't statement 2 be enough? because if \(\frac{ 1}{x } <2 \) then no matter what you add as y to x, the fraction \(\frac{1}{(x + y)} < 2\), it will always be lesser than 2

av1901

How about x = 3 and y = -2.99? In this case 1/(x + y) = 100.

P.S. You can ignore that question becasue such type of pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems
Work Problems
Distance Problems
Mixture Problems
Percent and Interest Problems
Overlapping Sets Problems
Statistics Problems
Combination and Probability Problems

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Thankyou, I did overlook that aspect : )

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