Bunuel's Algebra Diagnostic TestAbsolute 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.
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) \(x + y = y\)
2. Is \(Q > 0\) ?(1) \(P*Q^3*R^4 < 0\)
(2) \(P*Q^2*S^6 > 0\)
3. Is \(|x + y| < |x| + |y|\) ?(1) \(xy < 0\)
(2) \(x < y\)
4. If x and y are integers, is \(x = 0\)?(1) \((-2)^x*y^3 > 0\)
(2) \((-3)^x*y^2 < 0\)
5. If m and n are positive integers, is \(4^m*(\frac{1}{3})^n < 1\)?(1) n = 2m
(2) n = 4
LEVEL 2:
6. If \(x + y ≠ 0\), is \(\frac{1}{(x + y)} < 2\)?(1) \(x^3 = y^3\)
(2) \(\frac{1}{x} < 2\)
7. Is \(x = 0\) ?(1) \(x^2*y^3 > 0\)
(2) \(x^3*y^2 < 0\)
8. Is \(x > y\)? (1) \(x + y > 0\)
(2) \(y^2 > x^2\)
9. Is \(|x + 1| < 2\) ?(1) \((x - 1)^2 < 1\)
(2) \(x^2 - 2 < 0\)
10. Is \(x > y\) ?(1) \(x^2 < y^2\)
(2) \(y < 0\)
------------------- MEDIUM -------------------
LEVEL 3:
11. Is \(|x - y| = ||x| - |y||\) ?(1) \(xy > 0\)
(2) \(x < y < 0\)
12. What is the value of positive integer n ?(1) \(n^{5!} = 1\)
(2) \(n^5 = n!\)
13. If m and n are positive integers, and \(x = 2^m3^n\), is m < n ?(1) x is divisible by 144
(2) x is not divisible by 648
14. Is \(xy < 0\) ?(1) \(x^2 = y^2\)
(2) \(\frac{1}{(x + y)} < 1\)
15. Is \(|x| + x > |y| + y\) ?(1) \(xy > 0\)
(2) \(x + y < 0\)
LEVEL 4:
16. Is \(x^2 < x^3\)?(1) \(x < x^2\)
(2) \(x < 1\)
17. Is \(ac + \sqrt{(a^2 - 1)(c^2 - 1)} \leq 1\) ?(1) \(a^2 + b^2 = 1\)
(2) \(c^2 + d^2 = 1\)
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) \((n - 5)(n - 3) ≠ 0\)
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.
20. If \(x + y ≠ 0\), is \(\frac{1}{(x + y)} < 1\)?(1) \(x^2 = y^2\)
(2) \(\frac{1}{x} < 2\)
------------------- HARD -------------------
LEVEL 5:
21. Is p an odd integer?(1) \((p^5)^5\) is an odd integer.
(2) \(\sqrt[5]{\sqrt[5]{p\) is an odd integer.
22. Does \(x = \)y ?(1) \(\frac{xy}{(x + y)} = 0\)
(2) \(xy = 0\)
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 \(n\).
24. Is \(p + q > pq\) ?(1) \(p > 0 > q\)
(2) \(|q| = p\)
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.
LEVEL 6:
26. If m and n are integers, is [b]mn > 0 ?[/b]
(1) \(\frac{m}{n}\) is an integer.
(2) \(|m| < |n|\)
27. If \(x^2 +y^2 \leq 25\), is \(x^2 < x\) ?(1) \(y^2 > 9\).
(2) \(x = y + 3\).
28. If \(s - \frac{1}{s} < \frac{1}{t} - t\), then is \(s > t\) ?(1) \(s > 1\)
(2) \(t > 0\)
29. The infinite sequence \(a_1\), \(a_2\),…, \(a_n\), … is such that \(a_{n} < a_{n-1}\), for all 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.
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.
------------------- 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
32. If \(xy ≠ 0\), is \(x < y\)?(1) \(x^8 < y^8\)
(2) \(x^{(-9)} < y^{(-9)}\)
33. If \(x ≠ 0\), is \(x < |x|\) ?(1) \(|x|< 1\)
(2) \(\frac{x}{|x|} < x\)
34. If x is an integer and \(|x - 3| + |x + 4| \leq |x + 8|\), what is the value of x ?(1) \(x < 1\)
(2) \(|x| > x\)
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
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) \(|a| = |b| = |c| = |d|\)
37. If \(xy \neq 0\), is \(x + y < 0\)?(1) \(\frac{x}{\sqrt{x^2-\sqrt{-y*|y|}=y-1\)
(2) \((x+3)^2+(y+4)^2<15\)
38. 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 1332, is a = b?(1) c = 3
(2) b = 2
39. If \(|a| > |b| > |c|\), is \(a*b^3*c^3 > a*b^4*c^2\) ?(1) \(a > b > c\)
(2) \(a + b > 0\)
40. If n is an integer such that \(\frac{1}{9} < \frac{1}{(n^2-1)} < \frac{1}{2}\), what is the value of n?(1) \(\frac{1}{3} > \frac{1}{(1 - n)} > 1/7\)
(2) n is not an even integer.
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