1
Is the sequence 15, 7, 10, 0, ... arithmetic, geometric, or neither?
Algebra - Functions and Sequences (including word…
Medium
A
Cannot be determined
B
Geometric
C
Neither
D
Arithmetic
Explanation There is no constant common difference or common ratio between terms, so this sequence is neither arithmetic nor geometric.
2
A shop offers successive discounts of 25% and 2% on an item marked at Rs. 4200. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
3051
B
3015
C
3087
D
3183
Explanation Final price = 4200 × (1 − 25/100) × (1 − 2/100) = Rs. 3087.
3
A sequence is defined by a₁ = -17 and aₙ = aₙ₋₁ − 8 for n > 1. What is a11?
Algebra - Functions and Sequences (including word…
Medium
A
-89
B
-87
C
-97
D
-92
Explanation Each term adds -8 to the previous one, so a11 = a₁ + (11−1)(-8) = -97.
4
What is the value of 8x^2 − 5x when x = -3?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
78
B
94
C
89
D
87
Explanation 8(-3)^2 + (-5)(-3) + (0) = (72) + (15) + (0) = 87.
5
In an arithmetic sequence, the 4th term is -51 and the 10th term is -93. What is the 17th term?
Algebra - Functions and Sequences (including word…
Medium
A
-126
B
-142
C
-141
D
-139
Explanation d = (-93 − (-51))/(10−4) = -7. Then the 17th term = -51 + (17−4)(-7) = -142.
6
How many digits does 5^32 have?
Arithmetic - Number Properties
Medium
A
25
B
23
C
22
D
21
Explanation The number of digits of 5^32 is floor(32 × log10(5)) + 1 = 23.
7
What is 4/5 × 1/3?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
13/30
B
12/5
C
17/15
D
4/15
Explanation Multiply numerators and denominators: (4×1)/(5×3) = 4/15.
8
Express 5,300 in scientific notation.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
5.3 × 10^3
B
53.0 × 10^2
C
5.3 × 10^4
D
5.3 × 10^2
Explanation Move the decimal point so only one nonzero digit remains before it: 5,300 = 5.3 × 10^3.
9
What is the ratio of 340 to 20, expressed in lowest terms?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
17:1
B
18:1
C
1:17
D
17:2
Explanation 340:20 reduces by dividing both terms by their GCD (20), giving 17:1.
10
How many multiples of 3 are there between 165 and 234, inclusive?
Arithmetic - Number Properties
Medium
A
27
B
24
C
21
D
23
Explanation The multiples of 3 in this range run from 165 to 234, giving 24 multiples.
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11
What is the compound interest on Rs. 12500 at 16% per annum, compounded annually, for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
4375
B
4320
C
4305
D
4266
Explanation Amount = P(1 + R/100)^2 = 12500 × (1 + 16/100)^2 = Rs. 16820, so CI = Rs. 16820 − Rs. 12500 = Rs. 4320.
12
Does the parabola y = -2x^2 + 7x − 19 open upward or downward?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
Cannot be determined
B
Downward
C
Upward
D
It is a straight line
Explanation Since a = -2 is negative, the parabola opens downward.
13
For the function f(x) = 1/(x − (-68)), which value of x must be excluded from the domain?
Algebra - Functions and Sequences (including word…
Medium
A
-71
B
-64
C
-68
D
-66
Explanation The denominator x − (-68) cannot equal 0, so x = -68 must be excluded from the domain.
14
Which equation has roots 8 and -10?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
x^2 + 4x − 80 = 0
B
x^2 − 2x − 80 = 0
C
x^2 + 2x − 80 = 0
D
x^2 + 2x + 80 = 0
Explanation Sum of roots = -2, product of roots = -80, giving x^2 − (-2)x + (-80) = 0, i.e. x^2 + 2x − 80 = 0.
15
A shopkeeper marks up an item costing Rs. 83 by 44%. What is the markup amount (in Rs.)?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
35.52
B
36.52
C
42.52
D
39.52
Explanation Markup amount = CP × 44/100 = 83 × 0.4400 = Rs. 36.52.
16
The digits of 5636 sum to 20. Based on this, is 5636 divisible by 3?
Arithmetic - Number Properties
Medium
A
Yes
B
Cannot be determined
C
No
D
Only if n is even
Explanation A number is divisible by 3 if and only if its digit sum is divisible by 3. Here the digit sum is 20, which is not divisible by 3.
17
What is (3.3 × 10^4) ÷ (2.6 × 10^3) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
1.27 × 10^2
B
1.27 × 10^1
C
1.77 × 10^1
D
1.27 × 10^7
Explanation Divide the mantissas (3.3 ÷ 2.6 ≈ 1.27) and subtract the exponents (4 − 3 = 1), adjusting the mantissa as needed: 1.27 × 10^1.
18
What is the vertex of the parabola y = 3x^2 + 22?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
(0, 22)
B
(0, 23)
C
(1, 22)
D
(2, 22)
Explanation The vertex x-coordinate is −b/(2a) = −(0)/(2×3) = 0. Substituting gives y = 22, so the vertex is (0, 22).
19
What is the vertex of the parabola y = -2x^2 + 32x + 3?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
(8, 131)
B
(8, 132)
C
(-8, 131)
D
(9, 131)
Explanation The vertex x-coordinate is −b/(2a) = −(32)/(2×-2) = 8. Substituting gives y = 131, so the vertex is (8, 131).
20
What is (6/11)^3 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
6/11
B
216/11
C
216/1331
D
6/1331
Explanation (6/11)^3 = 6^3/11^3 = 216/1331.
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21
Solve the system for x: -6x + 2y = 50, -2x + 4y = 40
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
-3
B
-6
C
-9
D
-10
Explanation Solving the system by elimination or substitution gives x = -6 (and y = 7).
22
Solve for x: -11x + 19 < -212
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
x < 21
B
x > 20
C
x > 21
D
x > 22
Explanation Dividing both sides by the negative coefficient -11 reverses the inequality sign, giving x > 21.
23
Simplify √90 to its simplest radical form.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
4√10
B
2√10
C
3√10
D
6√10
Explanation 90 = 3^2 × 10, so √90 = 3√10.
24
Simplify: 5^3 × 5^3
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
5^9
B
10^6
C
5^6
D
5^0
Explanation When multiplying powers with the same base, add the exponents: 5^3 × 5^3 = 5^(3+3) = 5^6.
25
How many digits does 3^50 have?
Arithmetic - Number Properties
Medium
A
25
B
22
C
24
D
23
Explanation The number of digits of 3^50 is floor(50 × log10(3)) + 1 = 24.
26
What is 3/10 of 250?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
77
B
81
C
75
D
79
Explanation 3/10 of 250 = (3 × 250) / 10 = 75.
27
What is (3.3 × 10^8) ÷ (1.7 × 10^4) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
1.94 × 10^12
B
1.94 × 10^4
C
2.44 × 10^4
D
1.94 × 10^5
Explanation Divide the mantissas (3.3 ÷ 1.7 ≈ 1.94) and subtract the exponents (8 − 4 = 4), adjusting the mantissa as needed: 1.94 × 10^4.
28
What are the solutions to x^2 − 196 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
x = -14 or x = 13
B
x = -15 or x = 15
C
x = 14 or x = -14
D
x = -14 or x = 14
Explanation x^2 − 196 = (x + 14)(x - 14), so x = -14 or x = 14.
29
The ratio of boys to girls in a class is 13:11. If there are 416 boys, how many girls are there?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
360
B
320
C
352
D
386
Explanation Since boys:girls = 13:11 and there are 416 boys, each 'part' = 416/13 = 32, so girls = 11 × 32 = 352.
30
What is the smallest number that must be subtracted from 1016 so that the result is exactly divisible by 20?
Arithmetic - Number Properties
Medium
A
19
B
12
C
13
D
16
Explanation 1016 divided by 20 leaves remainder 16, so subtracting 16 makes it exactly divisible by 20.
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31
What is the difference between the compound interest and simple interest on Rs. 3750 at 4% per annum for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
6
B
5
C
2
D
3
Explanation For 2 years, the difference between CI and SI is always P × (R/100)^2 = 3750 × (4/100)^2 = Rs. 6.
32
Simplify: 5^6 × 5^3
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
5^9
B
5^18
C
5^3
D
10^9
Explanation When multiplying powers with the same base, add the exponents: 5^6 × 5^3 = 5^(6+3) = 5^9.
33
Is 449 a prime number?
Arithmetic - Number Properties
Medium
A
Cannot be determined without a calculator
B
Yes
C
No
D
Only if n is odd
Explanation 449 is not divisible by any integer other than 1 and itself, so it is prime.
34
What is (5.3 × 10^5) × (1.3 × 10^5) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
6.89 × 10^11
B
7.89 × 10^10
C
6.89 × 10^25
D
6.89 × 10^10
Explanation Multiply the mantissas (5.3 × 1.3 = 6.89) and add the exponents (5 + 5 = 10), adjusting so the mantissa stays between 1 and 10: 6.89 × 10^10.
35
What is 13/6 − 3/2?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
5/6
B
11/3
C
2/3
D
5/2
Explanation Using a common denominator, 13/6 − 3/2 = 2/3.
36
In an arithmetic sequence, the 14th term is -176 and the 15th term is -189. What is the common difference?
Algebra - Functions and Sequences (including word…
Medium
A
-15
B
-13
C
-19
D
-12
Explanation d = (aⱼ − aᵢ)/(j−i) = (-189 − (-176))/(15−14) = -13.
37
Is x^2 − 18x + 83 a perfect square trinomial?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
Cannot be determined
B
Yes
C
No
D
Only if x is positive
Explanation A trinomial x^2 + bx + c is a perfect square exactly when c = (b/2)^2. Here (b/2)^2 = (-9)^2 = 81, which does not match c = 83, so it is not a perfect square trinomial.
38
Among 75, 39, 77, and 36, which is closest to 0 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
A
75
B
36
C
39
D
77
Explanation The number closest to 0 has the smallest absolute value. |36| = 36, which is the smallest among the options.
39
After a discount of 20%, an item sells for Rs. 1028. What was the marked price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
1300
B
1299
C
1285
D
1248
Explanation Marked price = SP / (1 − 20/100) = 1028 / 0.8000 = Rs. 1285.
40
What is |20| − |-35|?
Artithmetic - Absolute Value and Number Lines
Medium
A
-20
B
-19
C
-10
D
-15
Explanation |20| − |-35| = 20 − 35 = -15. (Note this is generally different from |20 − (-35)|.)
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41
Does the fraction 6/479 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
A
Repeats (does not terminate)
B
Terminates
C
It equals exactly 0
D
Cannot be determined without long division
Explanation In lowest terms, 6/479 = 6/479. A fraction terminates only if its denominator (in lowest terms) has no prime factors other than 2 and 5. Here that is not the case, so it repeats (does not terminate).
42
What is the solution set of |x − 21| < 29?
Artithmetic - Absolute Value and Number Lines
Medium
A
x < 50
B
-10 < x < 52
C
-8 < x < 50
D
x < -8 or x > 50
Explanation |x − 21| < 29 means x is within 29 of 21, giving -8 < x < 50.
43
In an arithmetic sequence, the 12th term is 1 and the 22nd term is -39. What is the common difference?
Algebra - Functions and Sequences (including word…
Medium
A
-4
B
-2
C
-3
D
-7
Explanation d = (aⱼ − aᵢ)/(j−i) = (-39 − 1)/(22−12) = -4.
44
What are the solutions to x^2 + 13x + 40 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
x = -9 or x = -4
B
x = -8 or x = -5
C
x = 8 or x = 5
D
x = -8 or x = -6
Explanation x^2 + 13x + 40 = (x + 8)(x + 5), so x = -8 or x = -5.
45
What is the midpoint between 55 and 27 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
A
40
B
42
C
41
D
14
Explanation The midpoint of 55 and 27 is (55 + 27) / 2 = 82/2 = 41.
46
If f(x) = 3x + 16, what is f(12) + f(-10)?
Algebra - Functions and Sequences (including word…
Medium
A
40
B
43
C
39
D
38
Explanation f(12) = 52 and f(-10) = -14, so f(12) + f(-10) = 38.
47
How many integers satisfy |x + 10| < 7?
Artithmetic - Absolute Value and Number Lines
Medium
A
16
B
13
C
10
D
14
Explanation |x + 10| < 7 means -17 < x < -3. The integers strictly between -17 and -3 number 13.
48
What is the value of 9x^2 + 19x − 13 when x = -5?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
121
B
109
C
125
D
117
Explanation 9(-5)^2 + (19)(-5) + (-13) = (225) + (-95) + (-13) = 117.
49
A geometric sequence has first term -15 and second term 60. What is the common ratio?
Algebra - Functions and Sequences (including word…
Medium
A
-1/4
B
-4
C
-3
D
4
Explanation Common ratio = a₂/a₁ = 60/-15 = -4.
50
What is the simple interest on Rs. 8137 at 6% per annum for 5 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
2441.1
B
2354.1
C
2343.1
D
2404.1
Explanation Simple Interest = (P × R × T) / 100 = (8137 × 6 × 5) / 100 = Rs. 2441.1.
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51
What is |12 × -6|?
Artithmetic - Absolute Value and Number Lines
Medium
A
72
B
70
C
77
D
75
Explanation |12 × -6| = |12| × |-6| = 12 × 6 = 72.
52
What is the compound interest on Rs. 10625 at 4% per annum, compounded annually, for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
906
B
867
C
880
D
830
Explanation Amount = P(1 + R/100)^2 = 10625 × (1 + 4/100)^2 = Rs. 11492, so CI = Rs. 11492 − Rs. 10625 = Rs. 867.
53
How many distinct prime factors does 348 have?
Arithmetic - Number Properties
Medium
A
2
B
3
C
5
D
4
Explanation The prime factorization of 348 is 2^2 × 3^1 × 29^1, which includes 3 distinct prime(s).
54
What are the solutions to |x − 32| = 1?
Artithmetic - Absolute Value and Number Lines
Medium
A
x = -31 or x = -33
B
x = 32 only
C
x = 30 or x = 34
D
x = 31 or x = 33
Explanation |x − 32| = 1 means x is 1 away from 32, so x = 32 + 1 = 33 or x = 32 − 1 = 31.
55
Solve for x: -9x + 1 < -188
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
x > 22
B
x > 20
C
x < 21
D
x > 21
Explanation Dividing both sides by the negative coefficient -9 reverses the inequality sign, giving x > 21.
56
What is (6.0 × 10^2) × (1.5 × 10^6) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
9.0 × 10^9
B
9.0 × 10^12
C
9.0 × 10^8
D
10.0 × 10^8
Explanation Multiply the mantissas (6.0 × 1.5 = 9.0) and add the exponents (2 + 6 = 8), adjusting so the mantissa stays between 1 and 10: 9.0 × 10^8.
57
If f(x) = -x^2 − 14x + 12, what is f(-4)?
Algebra - Functions and Sequences (including word…
Medium
A
58
B
52
C
56
D
57
Explanation f(-4) = -1(-4)^2 + (-14)(-4) + (12) = 52.
58
A shop offers successive discounts of 45% and 60% on an item marked at Rs. 1650. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
373
B
363
C
385
D
347
Explanation Final price = 1650 × (1 − 45/100) × (1 − 60/100) = Rs. 363.
59
If f(x) = 11x − 7, what is f(-3)?
Algebra - Functions and Sequences (including word…
Medium
A
-44
B
-42
C
-36
D
-40
Explanation f(-3) = (11)(-3) − 7 = -40.
60
Which is farther from 10 on the number line: -78 or 77?
Artithmetic - Absolute Value and Number Lines
Medium
A
77
B
-78
C
They are equally far
D
Cannot be determined
Explanation Distance from 10: |-78 − 10| = 88, and |77 − 10| = 67. So -78 is farther.
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61
What are the solutions to x^2 − 3x − 10 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
x = -2 or x = 5
B
x = 2 or x = -5
C
x = -3 or x = 6
D
x = -2 or x = 4
Explanation x^2 − 3x − 10 = (x + 2)(x - 5), so x = -2 or x = 5.
62
If f(x) = 6x − 2 and g(x) = -2x − 6, what is g(f(-4))?
Algebra - Functions and Sequences (including word…
Medium
A
43
B
52
C
46
D
48
Explanation f(-4) = -26, so g(f(-4)) = g(-26) = -2(-26) − 6 = 46.
63
An arithmetic sequence has first term -15 and common difference -5. What is the 34th term?
Algebra - Functions and Sequences (including word…
Medium
A
-180
B
-165
C
-161
D
-162
Explanation aₙ = a₁ + (n−1)d = -15 + (34−1)(-5) = -180.
64
What is the product of the roots of 4x^2 + 3x − 28 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
-7
B
-9
C
-6
D
-8
Explanation By Vieta's formulas, the product of the roots equals c/a = -28/4 = -7.
65
How many trailing zeros are in 49! (49 factorial)?
Arithmetic - Number Properties
Medium
A
10
B
8
C
13
D
9
Explanation Trailing zeros come from factors of 5 in 49!. Counting multiples of 5, 25, 125, ... gives 10 trailing zeros.
66
Solve the system for y: 7x + 7y = 0, -6x − 3y = 57
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
19
B
17
C
21
D
22
Explanation Solving the system by elimination or substitution gives y = 19 (and x = -19).
67
How many integers satisfy |x + 15| < 12?
Artithmetic - Absolute Value and Number Lines
Medium
A
23
B
24
C
19
D
20
Explanation |x + 15| < 12 means -27 < x < -3. The integers strictly between -27 and -3 number 23.
68
If f(x) = -2x + 21, what is f(14) − f(-3)?
Algebra - Functions and Sequences (including word…
Medium
A
-34
B
-30
C
-31
D
-35
Explanation f(14) = -7 and f(-3) = 27, so f(14) − f(-3) = -34.
69
What is 16^(2/2) equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
15
B
14
C
16
D
13
Explanation 16^(2/2) means take the 2-th root of 16 (which is 4), then raise it to the 2 power: 4^2 = 16.
70
What is the sum of all positive divisors of 108 (including 108 itself)?
Arithmetic - Number Properties
Medium
A
294
B
281
C
280
D
264
Explanation The divisors of 108 are [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108], which sum to 280.
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71
What is 1/2 + 8/5?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
11/5
B
21/10
C
9/7
D
-11/10
Explanation Using a common denominator, 1/2 + 8/5 = 21/10.
72
How many multiples of 7 are there between 39 and 129, inclusive?
Arithmetic - Number Properties
Medium
A
13
B
17
C
12
D
11
Explanation The multiples of 7 in this range run from 42 to 126, giving 13 multiples.
73
Simplify: 2^15 ÷ 2^11
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
2^4
B
2^26
C
2^-4
D
2^165
Explanation When dividing powers with the same base, subtract the exponents: 2^15 ÷ 2^11 = 2^(15-11) = 2^4.
74
A value is first increased by 6% and then increased by 22%. What is the overall net percentage change?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
+24.32%
B
+34.32%
C
-29.32%
D
+29.32%
Explanation Starting with 100: after the first change it becomes 106.00, and after the second change it becomes 129.32 — a net change of +29.32% from the original 100.
75
Solve for x: -13x − 24 < -258
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
x > 17
B
x > 18
C
x < 18
D
x > 19
Explanation Dividing both sides by the negative coefficient -13 reverses the inequality sign, giving x > 18.
76
What is the axis of symmetry of the parabola y = -x^2 − 8x − 28?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
x = 4
B
x = -5
C
x = -4
D
x = -3
Explanation The axis of symmetry is x = −b/(2a) = −(-8)/(2×-1) = -4.
77
If an integer n leaves a remainder of 13 when divided by 15, what is the remainder when n^2 is divided by 15?
Arithmetic - Number Properties
Medium
A
4
B
8
C
2
D
12
Explanation n = 15q + 13 for some integer q, so n^2 ≡ 13^2 = 169 (mod 15), which leaves remainder 4 when divided by 15.
78
What is 215^0 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
1
B
-1
C
215
Explanation Any nonzero number raised to the power 0 equals 1, by definition.
79
At 15% simple interest per annum, a sum earns Rs. 6549 in 5 years. What is the principal?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
8751
B
8732
C
8755
D
8799
Explanation Principal = (SI × 100) / (R × T) = (6549 × 100) / (15 × 5) = Rs. 8732.
80
A shopkeeper marks up an item costing Rs. 208 by 48%. What is the markup amount (in Rs.)?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
103.84
B
98.84
C
99.84
D
100.84
Explanation Markup amount = CP × 48/100 = 208 × 0.4800 = Rs. 99.84.
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81
Factor: x^2 − 19x + 70
Algebra - Quadratic equations (factoring, roots, …
Medium
A
(x + 14)(x - 5)
B
(x - 14)(x - 5)
C
(x + 14)(x + 5)
D
(x - 14)(x + 5)
Explanation x^2 − 19x + 70 factors as the product of (x − r) for each root: (x - 14)(x - 5).
82
An interest rate rises from 17% to 24%. By how many percentage points did it increase?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
11 points
B
9 points
C
7 points
D
8 points
Explanation A percentage-point increase is a simple subtraction: 24% − 17% = 7 percentage points.
83
How many distinct prime factors does 266 have?
Arithmetic - Number Properties
Medium
A
1
B
3
C
2
D
5
Explanation The prime factorization of 266 is 2^1 × 7^1 × 19^1, which includes 3 distinct prime(s).
84
A shop offers successive discounts of 8% and 5% on an item marked at Rs. 1000. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
892
B
862
C
820
D
874
Explanation Final price = 1000 × (1 − 8/100) × (1 − 5/100) = Rs. 874.
85
A sum of Rs. 1620 earns Rs. 1296 in simple interest over 4 years. What is the annual interest rate?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
20%
B
22%
C
21%
D
16%
Explanation Rate = (SI × 100) / (P × T) = (1296 × 100) / (1620 × 4) = 20%.
86
If -8x − 4y = -28 and x − 2y = 16, what is x + y?
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
-3
B
-2
C
1
D
-1
Explanation Solving the system gives x = 6 and y = -5, so x + y = 1.
87
What is the sum to infinity of a geometric sequence with first term -16 and common ratio -2/3?
Algebra - Functions and Sequences (including word…
Medium
A
-53/5
B
-43/5
C
-80/3
D
-48/5
Explanation Sum to infinity = a₁/(1 − r) = -16/(1 − (-2)/3) = -48/5.
88
If f(x) = -5x^2 + x − 19, what is f(-2)?
Algebra - Functions and Sequences (including word…
Medium
A
-43
B
-38
C
-35
D
-41
Explanation f(-2) = -5(-2)^2 + (1)(-2) + (-19) = -41.
89
Solve the system for x: -6x − 9y = 123, 6x − 8y = -72
Algebra - Linear equations (1 and 2 variables) an…
Medium
A
-19
B
-12
C
-16
D
-13
Explanation Solving the system by elimination or substitution gives x = -16 (and y = -3).
90
Express 42,000,000 in scientific notation.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
4.2 × 10^8
B
4.2 × 10^6
C
4.2 × 10^7
D
42.0 × 10^6
Explanation Move the decimal point so only one nonzero digit remains before it: 42,000,000 = 4.2 × 10^7.
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91
What is the length of the solution interval for |x − 10| < 23?
Artithmetic - Absolute Value and Number Lines
Medium
A
46
B
49
C
40
D
50
Explanation |x − 10| < 23 describes the interval (-13, 33), which has length 33 − (-13) = 46.
92
Solve for x: 9/14 = 216/x
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
360
B
349
C
353
D
336
Explanation Cross-multiplying: 9 × x = 14 × 216, so x = 3024/9 = 336.
93
What is 5/3 × 8/5?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
49/15
B
17/6
C
25/24
D
8/3
Explanation Multiply numerators and denominators: (5×8)/(3×5) = 8/3.
94
Which equation has roots -3 and 13?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
x^2 − 10x − 39 = 0
B
x^2 − 8x − 39 = 0
C
x^2 − 10x + 39 = 0
D
x^2 + 10x − 39 = 0
Explanation Sum of roots = 10, product of roots = -39, giving x^2 − (10)x + (-39) = 0, i.e. x^2 − 10x − 39 = 0.
95
Which is greater: 6^6 or 6^5?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
A
6^6
B
6^5
C
Cannot be determined without a calculator
D
They are equal
Explanation 6^6 = 46656 and 6^5 = 7776, so 6^6 is greater.
96
Rs. 18516 is invested at 7.5% simple interest per annum for 3 years. What is the total amount after 3 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
A
22649.1
B
22607.1
C
22682.1
D
22679.1
Explanation Amount = Principal + Interest = 18516 + 4166.1 = Rs. 22682.1.
97
A population of 1248 grows by 50% each year. What will the population be after 5 years?
Algebra - Functions and Sequences (including word…
Medium
A
9484
B
9477
C
9457
D
9377
Explanation Population after 5 years = 1248 × (1 + 50/100)^5 = 9477.
98
If A:B = 5:11 and B:C = 5:8, what is A:B:C?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
A
26:55:88
B
25:55:88
C
5:11:8
D
25:55:89
Explanation Scale both ratios so B matches: A:B = 25:55 and B:C = 55:88, giving A:B:C = 25:55:88.
99
What is the nature of the roots of x^2 + 5x + 6 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
A
Two distinct real roots
B
Cannot be determined
C
No real roots
D
One repeated real root
Explanation The discriminant is b^2 − 4ac = (5)^2 − 4(1)(6) = 1, which is positive, so the equation has two distinct real roots.
100
What is the average (arithmetic mean) of the 9 consecutive integers from 8 to 16?
Arithmetic - Number Properties
Medium
A
21
B
11
C
17
D
12
Explanation For consecutive integers, the average equals the middle value, which is 12.