1
Which is farther from -3 on the number line: -42 or 38?
Medium
A
-42
B
They are equally far
C
Cannot be determined
D
38
Explanation Distance from -3: |-42 − (-3)| = 39, and |38 − (-3)| = 41. So 38 is farther.
2
Simplify 7/28 to its lowest terms.
Medium
A
1/4
B
3/14
C
7/27
D
1/8
Explanation 7 and 28 share a common factor of 7; dividing both by it gives 1/4.
3
Round 47.0212 to the nearest hundredth.
Medium
A
47.0
B
47.01
C
47.03
D
47.02
Explanation Rounding 47.0212 to the nearest hundredth gives 47.02.
4
A shopkeeper marks up an item costing Rs. 785 by 24%. What is the markup amount (in Rs.)?
Medium
A
188.4
B
199.4
C
200.4
D
179.4
Explanation Markup amount = CP × 24/100 = 785 × 0.2400 = Rs. 188.4.
5
Round 496.5753 to the nearest hundredth.
Medium
A
496.58
B
496.59
C
496.57
D
497.0
Explanation Rounding 496.5753 to the nearest hundredth gives 496.58.
6
How many integers satisfy |x + 16| < 15?
Medium
A
27
B
29
C
25
D
26
Explanation |x + 16| < 15 means -31 < x < -1. The integers strictly between -31 and -1 number 29.
7
What is |49| − |-17|?
Medium
A
26
B
32
C
33
D
31
Explanation |49| − |-17| = 49 − 17 = 32. (Note this is generally different from |49 − (-17)|.)
8
Which is greater: 2/3 or 13/14?
Medium
A
13/14
B
They are equal
C
2/3
D
Cannot be determined
Explanation 2/3 = 0.6667 and 13/14 = 0.9286, so 13/14 is greater.
9
Simplify 8/12 to its lowest terms.
Medium
A
2/3
B
8/11
C
1/3
D
7/12
Explanation 8 and 12 share a common factor of 4; dividing both by it gives 2/3.
10
What is 12/5 × 9/2?
Medium
A
8/15
B
69/10
C
329/30
D
54/5
Explanation Multiply numerators and denominators: (12×9)/(5×2) = 54/5.
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11
An interest rate rises from 51% to 67%. By how many percentage points did it increase?
Medium
A
20 points
B
21 points
C
16 points
D
17 points
Explanation A percentage-point increase is a simple subtraction: 67% − 51% = 16 percentage points.
12
A shop offers successive discounts of 50% and 30% on an item marked at Rs. 400. What is the final selling price?
Medium
A
147
B
140
C
144
D
136
Explanation Final price = 400 × (1 − 50/100) × (1 − 30/100) = Rs. 140.
13
If an integer n leaves a remainder of 2 when divided by 4, what is the remainder when (n + 13) is divided by 4?
Medium
A
2
B
1
C
3
Explanation (n + 13) ≡ (2 + 13) = 15 (mod 4), which leaves remainder 3 when divided by 4.
14
For a = -1 and b = -13, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
A
Strictly less than
B
Cannot be determined
C
Strictly greater than
D
Equal
Explanation |a + b| = 14 and |a| + |b| = 14. Since a and b have the same sign, the two are equal.
15
A value is first increased by 95% and then decreased by 65%. What is the overall net percentage change?
Medium
A
-31.75%
B
-36.75%
C
-26.75%
D
+31.75%
Explanation Starting with 100: after the first change it becomes 195.00, and after the second change it becomes 68.25 — a net change of -31.75% from the original 100.
16
How many solutions does the equation |x − 1| = 21 have?
Medium
A
Infinitely many
B
2
C
1
Explanation |x − 1| = 21: since 21 is positive, there are two solutions.
17
If 22 workers can complete a task in 9 days, how many days would 2 workers take to complete the same task (assuming the same work rate per worker)?
Medium
A
107
B
99
C
102
D
100
Explanation Total work = 22 × 9 = 198 worker-days. With 2 workers, days = 198/2 = 99.
18
What is the units digit of 6^51?
Medium
A
6
B
5
C
2
D
8
Explanation Units digits of powers of 6 repeat in a cycle of length 1. Using 51 mod 1, the units digit is 6.
19
What is the smallest positive integer that is divisible by all of 11, 19, and 12?
Medium
A
2783
B
2687
C
2414
D
2508
Explanation The smallest such number is LCM(11, 19, 12) = 2508.
20
How many prime numbers are there between 36 and 57, inclusive?
Medium
A
5
B
2
C
7
D
3
Explanation The primes between 36 and 57 are [37, 41, 43, 47, 53], totaling 5.
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21
Simplify 9/54 to its lowest terms.
Medium
A
1/6
B
9/53
C
1/12
D
4/27
Explanation 9 and 54 share a common factor of 9; dividing both by it gives 1/6.
22
An item marked at Rs. 2704 is sold at a discount of 25%. What is the selling price?
Medium
A
2028
B
2012
C
1969
D
2076
Explanation Selling price = Marked price × (1 − 25/100) = 2704 × 0.7500 = Rs. 2028.
23
What is 6.6 × 9.7?
Medium
A
63.02
B
65.02
C
64.02
D
16.3
Explanation 6.6 × 9.7 = 64.02.
24
Simplify 20/4 to its lowest terms.
Medium
A
20/3
B
19/4
C
5
D
5/2
Explanation 20 and 4 share a common factor of 4; dividing both by it gives 5.
25
What is the highest power of 7 that divides 53! (53 factorial) exactly?
Medium
A
8
B
6
C
10
D
9
Explanation Using Legendre's formula, the exponent of 7 in 53! is floor(53/7) + floor(53/49) + ... = 8.
26
What is the simple interest on Rs. 6618 at 18% per annum for 7 years?
Medium
A
8434.68
B
8338.68
C
8370.68
D
8310.68
Explanation Simple Interest = (P × R × T) / 100 = (6618 × 18 × 7) / 100 = Rs. 8338.68.
27
What single discount is equivalent to two successive discounts of 18% and 6%?
Medium
A
25.92%
B
20.92%
C
24%
D
22.92%
Explanation Equivalent discount = 100 − (100−18)(100−6)/100 = 22.92%.
28
How many integers satisfy |x − 4| < 2?
Medium
A
7
B
2
C
1
D
3
Explanation |x − 4| < 2 means 2 < x < 6. The integers strictly between 2 and 6 number 3.
29
What is 4 + 2/3?
Medium
A
10/3
B
14/3
C
5
D
3/2
Explanation Using a common denominator, 4 + 2/3 = 14/3.
30
What are the solutions to |8x + 8| = 80?
Medium
A
x = 11 or x = -9
B
x = -13 or x = 11
C
x = 9 only
D
x = -11 or x = 9
Explanation 8x + 8 = 80 or 8x + 8 = −80, which solve to x = 9 and x = -11.
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31
The digits of 3794 sum to 23. Based on this, is 3794 divisible by 3?
Medium
A
Only if n is even
B
Yes
C
Cannot be determined
D
No
Explanation A number is divisible by 3 if and only if its digit sum is divisible by 3. Here the digit sum is 23, which is not divisible by 3.
32
What single discount is equivalent to two successive discounts of 4% and 40%?
Medium
A
42.4%
B
40.4%
C
45.4%
D
44%
Explanation Equivalent discount = 100 − (100−4)(100−40)/100 = 42.4%.
33
What is 11/3 + 1/4?
Medium
A
47/12
B
41/12
C
4
D
12/7
Explanation Using a common denominator, 11/3 + 1/4 = 47/12.
34
What is the smallest positive integer that leaves a remainder of 4 when divided by 6 and a remainder of 5 when divided by 7?
Medium
A
42
B
40
C
37
D
43
Explanation Since both remainders are exactly 2 less than their divisors, the answer is LCM(6, 7) − 2 = 42 − 2 = 40.
35
If 15 pens cost Rs. 330, how much would 10 pens cost?
Medium
A
220
B
216
C
241
D
223
Explanation Cost per pen = Rs. 330/15 = Rs. 22. So 10 pens cost 10 × Rs. 22 = Rs. 220.
36
What is the smallest positive number that must be added to 6230 so that the sum is exactly divisible by 42?
Medium
A
21
B
28
C
25
D
20
Explanation 6230 divided by 42 leaves remainder 14, so adding 42 − 14 = 28 makes it exactly divisible by 42.
37
6198 is exactly divisible by which of the following numbers?
Medium
A
10
B
12
C
9
D
2
Explanation 6198 ÷ 2 = 3099, a whole number, so 2 divides 6198 exactly.
38
What is the least common multiple (LCM) of 25 and 14?
Medium
A
318
B
324
C
350
D
378
Explanation LCM(25, 14) = 350, the smallest number divisible by both 25 and 14.
39
What is the sum of 5 consecutive even integers starting from 46?
Medium
A
250
B
259
C
251
D
241
Explanation The 5 consecutive even integers are [46, 48, 50, 52, 54]; their sum is 250.
40
What is 173.17 − 118.21?
Medium
A
291.38
B
53.96
C
55.96
D
54.96
Explanation 173.17 − 118.21 = 54.96.
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41
A shopkeeper marks up an item costing Rs. 1375 by 45%. What is the markup amount (in Rs.)?
Medium
A
597.75
B
618.75
C
617.75
D
593.75
Explanation Markup amount = CP × 45/100 = 1375 × 0.4500 = Rs. 618.75.
42
How many prime numbers are there between 69 and 97, inclusive?
Medium
A
3
B
8
C
5
D
6
Explanation The primes between 69 and 97 are [71, 73, 79, 83, 89, 97], totaling 6.
43
What are the solutions to |x + 35| = 25?
Medium
A
x = -60 or x = -10
B
x = -35 only
C
x = -61 or x = -9
D
x = 60 or x = 10
Explanation |x + 35| = 25 means x is 25 away from -35, so x = -35 + 25 = -10 or x = -35 − 25 = -60.
44
Which is greater: 7/2 or 3/2?
Medium
A
7/2
B
Cannot be determined
C
They are equal
D
3/2
Explanation 7/2 = 3.5000 and 3/2 = 1.5000, so 7/2 is greater.
45
What is the distance between 92 and 16 on the number line?
Medium
A
77
B
108
C
-76
D
76
Explanation The distance between two points on a number line is |92 − 16| = 76.
46
Which is farther from 17 on the number line: -23 or 4?
Medium
A
4
B
They are equally far
C
Cannot be determined
D
-23
Explanation Distance from 17: |-23 − 17| = 40, and |4 − 17| = 13. So -23 is farther.
47
What is 85% of 227?
Medium
A
195.95
B
192.95
C
185.95
D
183.95
Explanation 85% of 227 = (85/100) × 227 = 192.95.
48
The digits of 8581 sum to 22. Based on this, is 8581 divisible by 3?
Medium
A
Yes
B
Only if n is even
C
Cannot be determined
D
No
Explanation A number is divisible by 3 if and only if its digit sum is divisible by 3. Here the digit sum is 22, which is not divisible by 3.
49
What is 2/5 + 11/7?
Medium
A
69/35
B
-41/35
C
13/12
D
2
Explanation Using a common denominator, 2/5 + 11/7 = 69/35.
50
If 24 workers can complete a task in 19 days, how many days would 6 workers take to complete the same task (assuming the same work rate per worker)?
Medium
A
72
B
85
C
74
D
76
Explanation Total work = 24 × 19 = 456 worker-days. With 6 workers, days = 456/6 = 76.
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51
What single discount is equivalent to two successive discounts of 35% and 5%?
Medium
A
41.25%
B
40%
C
38.25%
D
36.25%
Explanation Equivalent discount = 100 − (100−35)(100−5)/100 = 38.25%.
52
What are the solutions to |x| + 21 = 45?
Medium
A
x = -26 or x = 26
B
x = 45 only
C
x = -24 or x = 24
D
x = 21 only
Explanation |x| + 21 = 45 means |x| = 24, so x = 24 or x = -24.
53
What is 1.1 × 10.7?
Medium
A
10.77
B
11.77
C
11.8
D
12.77
Explanation 1.1 × 10.7 = 11.77.
54
The ratio of boys to girls in a class is 1:14. If there are 14 boys, how many girls are there?
Medium
A
177
B
192
C
196
D
215
Explanation Since boys:girls = 1:14 and there are 14 boys, each 'part' = 14/1 = 14, so girls = 14 × 14 = 196.
55
How many positive factors (divisors) does 58 have?
Medium
A
4
B
2
C
6
D
7
Explanation 58 = 2^1 × 29^1. The number of divisors is the product of (exponent+1) for each prime factor = 4.
56
What is the simple interest on Rs. 1278 at 13% per annum for 5 years?
Medium
A
830.7
B
808.7
C
874.7
D
862.7
Explanation Simple Interest = (P × R × T) / 100 = (1278 × 13 × 5) / 100 = Rs. 830.7.
57
Round 405.3043 to the nearest hundredth.
Medium
A
405.3
B
405.31
C
405.29
D
405.0
Explanation Rounding 405.3043 to the nearest hundredth gives 405.3.
58
Rs. 10170 is invested at 16% simple interest per annum for 6 years. What is the total amount after 6 years?
Medium
A
19977.2
B
19943.2
C
19933.2
D
19851.2
Explanation Amount = Principal + Interest = 10170 + 9763.2 = Rs. 19933.2.
59
What is |-20 × 10|?
Medium
A
206
B
194
C
200
D
204
Explanation |-20 × 10| = |-20| × |10| = 20 × 10 = 200.
60
After a 90% increase, a quantity became 38. What was the original quantity?
Medium
A
25
B
24
C
26
D
20
Explanation Original × (1 + 90/100) = 38, so original = 38 / 1.9000 = 20.
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61
How many integers satisfy |x + 17| < 12?
Medium
A
24
B
23
C
21
D
27
Explanation |x + 17| < 12 means -29 < x < -5. The integers strictly between -29 and -5 number 23.
62
What is 4/3 ÷ 5/2?
Medium
A
5/4
B
11/15
C
8/15
D
10/3
Explanation Dividing by a fraction means multiplying by its reciprocal: 4/3 × 2/5 = 8/15.
63
What is the smallest number that must be subtracted from 5618 so that the result is exactly divisible by 44?
Medium
A
32
B
18
C
37
D
30
Explanation 5618 divided by 44 leaves remainder 30, so subtracting 30 makes it exactly divisible by 44.
64
An interest rate rises from 38% to 45%. By how many percentage points did it increase?
Medium
A
4 points
B
10 points
C
7 points
D
5 points
Explanation A percentage-point increase is a simple subtraction: 45% − 38% = 7 percentage points.
65
Which of the following numbers lies between 27 and 53?
Medium
A
54
B
12
C
17
D
46
Explanation 46 lies strictly between 27 and 53, while the other options fall outside that range.
66
What is the sum of 6 consecutive even integers starting from 6?
Medium
A
66
B
51
C
81
D
58
Explanation The 6 consecutive even integers are [6, 8, 10, 12, 14, 16]; their sum is 66.
67
What is the smallest positive number that must be added to 3518 so that the sum is exactly divisible by 31?
Medium
A
14
B
16
C
7
D
25
Explanation 3518 divided by 31 leaves remainder 15, so adding 31 − 15 = 16 makes it exactly divisible by 31.
68
Which of the following numbers lies between -7 and 22?
Medium
A
-6
B
30
C
-18
D
-14
Explanation -6 lies strictly between -7 and 22, while the other options fall outside that range.
69
What is 3/4 ÷ 1/2?
Medium
A
3/2
B
1/3
C
3/8
D
17/10
Explanation Dividing by a fraction means multiplying by its reciprocal: 3/4 × 2 = 3/2.
70
What is the sum of 8 consecutive integers starting from 39?
Medium
A
340
B
351
C
342
D
332
Explanation The integers are 39 through 46; their sum is 340.
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71
Does the fraction 26/31 terminate as a decimal, or does it repeat?
Medium
A
Repeats (does not terminate)
B
Cannot be determined without long division
C
Terminates
D
It equals exactly 0
Explanation In lowest terms, 26/31 = 26/31. 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).
72
What is |2 × 15|?
Medium
A
30
B
36
C
32
D
31
Explanation |2 × 15| = |2| × |15| = 2 × 15 = 30.
73
Convert the mixed number 8 7/12 to an improper fraction.
Medium
A
15/12
B
103/12
C
104/12
D
115/12
Explanation 8 7/12 = ((8 × 12) + 7) / 12 = 103/12.
74
A shopkeeper buys an item for Rs. 700 and sells it for Rs. 1050. What is the profit percentage?
Medium
A
45%
B
20%
C
50%
D
44%
Explanation Profit % = ((SP − CP) / CP) × 100 = ((1050 − 700) / 700) × 100 = 50%.
75
What is 4.4 × 18.5?
Medium
A
80.4
B
82.4
C
81.4
D
22.9
Explanation 4.4 × 18.5 = 81.4.
76
The ratio of boys to girls in a class is 9:5. If there are 288 boys, how many girls are there?
Medium
A
158
B
159
C
154
D
160
Explanation Since boys:girls = 9:5 and there are 288 boys, each 'part' = 288/9 = 32, so girls = 5 × 32 = 160.
77
Solve for x: 9/20 = 63/x
Medium
A
148
B
140
C
153
D
130
Explanation Cross-multiplying: 9 × x = 20 × 63, so x = 1260/9 = 140.
78
Which is greater: 1/3 or 1/4?
Medium
A
1/3
B
Cannot be determined
C
1/4
D
They are equal
Explanation 1/3 = 0.3333 and 1/4 = 0.2500, so 1/3 is greater.
79
The digits of 1427 sum to 14. Based on this, is 1427 divisible by 3?
Medium
A
Only if n is even
B
Cannot be determined
C
Yes
D
No
Explanation A number is divisible by 3 if and only if its digit sum is divisible by 3. Here the digit sum is 14, which is not divisible by 3.
80
Simplify 6/10 to its lowest terms.
Medium
A
3/10
B
3/5
C
1/2
D
2/3
Explanation 6 and 10 share a common factor of 2; dividing both by it gives 3/5.
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81
What is the smallest number that must be subtracted from 2039 so that the result is exactly divisible by 21?
Medium
A
2
B
5
C
4
D
7
Explanation 2039 divided by 21 leaves remainder 2, so subtracting 2 makes it exactly divisible by 21.
82
If A:B = 11:4 and B:C = 10:4, what is A:B:C?
Medium
A
55:20:8
B
56:20:8
C
11:4:4
D
55:20:9
Explanation Scale both ratios so B matches: A:B = 55:20 and B:C = 20:8, giving A:B:C = 55:20:8.
83
How many digits does 8^25 have?
Medium
A
20
B
26
C
23
D
24
Explanation The number of digits of 8^25 is floor(25 × log10(8)) + 1 = 23.
84
How many distinct prime factors does 596 have?
Medium
A
3
B
2
C
1
D
4
Explanation The prime factorization of 596 is 2^2 × 149^1, which includes 2 distinct prime(s).
85
What is 97.53 + 98.84?
Medium
A
195.37
B
-1.31
C
197.37
D
196.37
Explanation 97.53 + 98.84 = 196.37.
86
Convert the mixed number 2 7/10 to an improper fraction.
Medium
A
37/10
B
9/10
C
27/10
D
28/10
Explanation 2 7/10 = ((2 × 10) + 7) / 10 = 27/10.
87
How many multiples of 14 are there between 57 and 141, inclusive?
Medium
A
8
B
2
C
6
D
5
Explanation The multiples of 14 in this range run from 70 to 140, giving 6 multiples.
88
What is the smallest positive number that must be added to 2968 so that the sum is exactly divisible by 35?
Medium
A
10
B
18
C
7
D
11
Explanation 2968 divided by 35 leaves remainder 28, so adding 35 − 28 = 7 makes it exactly divisible by 35.
89
What is the simple interest on Rs. 3686 at 10% per annum for 5 years?
Medium
A
1914
B
1884
C
1843
D
1890
Explanation Simple Interest = (P × R × T) / 100 = (3686 × 10 × 5) / 100 = Rs. 1843.
90
What is |-49 ÷ -7|?
Medium
A
5
B
7
C
3
D
2
Explanation |-49 ÷ -7| = |-49| ÷ |-7| = 49 ÷ 7 = 7.
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91
An interest rate rises from 8% to 22%. What is the percent increase relative to the original rate?
Medium
A
170%
B
14%
C
175%
D
185%
Explanation Relative percent increase = (((22 − 8) / 8) × 100 = 175%. (Note this differs from the 14-percentage-point change.)
92
What is |90 ÷ -15|?
Medium
A
7
B
1
C
6
D
9
Explanation |90 ÷ -15| = |90| ÷ |-15| = 90 ÷ 15 = 6.
93
What are the solutions to |4x − 8| = 20?
Medium
A
x = 7 only
B
x = -3 or x = 7
C
x = -5 or x = 9
D
x = 3 or x = -7
Explanation 4x − 8 = 20 or 4x − 8 = −20, which solve to x = 7 and x = -3.
94
Among 22, 2, 16, and -66, which is closest to 0 on the number line?
Medium
A
22
B
-66
C
2
D
16
Explanation The number closest to 0 has the smallest absolute value. |2| = 2, which is the smallest among the options.
95
What is the distance between 48 and 28 on the number line?
Medium
A
20
B
76
C
21
D
-20
Explanation The distance between two points on a number line is |48 − 28| = 20.
96
What is the ratio of 540 to 30, expressed in lowest terms?
Medium
A
18:2
B
19:1
C
18:1
D
1:18
Explanation 540:30 reduces by dividing both terms by their GCD (30), giving 18:1.
97
What is 44% of 874?
Medium
A
383.56
B
406.56
C
384.56
D
395.56
Explanation 44% of 874 = (44/100) × 874 = 384.56.
98
What is 104.12 − 7.13?
Medium
A
96.99
B
97.99
C
95.99
D
111.25
Explanation 104.12 − 7.13 = 96.99.
99
6040 is exactly divisible by which of the following numbers?
Medium
A
7
B
6
C
4
D
9
Explanation 6040 ÷ 4 = 1510, a whole number, so 4 divides 6040 exactly.
100
What is 80% of 805?
Medium
A
643
B
644
C
638
D
626
Explanation 80% of 805 = (80/100) × 805 = 644.