1
What are the solutions to |x| + 6 = 34?
Medium
A
x = 6 only
B
x = -30 or x = 30
C
x = -28 or x = 28
D
x = 34 only
Explanation |x| + 6 = 34 means |x| = 28, so x = 28 or x = -28.
2
How many distinct prime factors does 320 have?
Medium
A
3
B
4
C
2
Explanation The prime factorization of 320 is 2^6 × 5^1, which includes 2 distinct prime(s).
3
What is the remainder when 261 is divided by 10?
Medium
A
6
B
1
C
3
Explanation 261 = 10 × 26 + 1, so the remainder is 1.
4
How many solutions does |x + 28| = −6 have?
Medium
A
No solution
B
Infinitely many solutions
C
Exactly 2 solutions
D
Exactly 1 solution
Explanation An absolute value can never equal a negative number, so |x + 28| = −6 has no solution.
5
A shop offers successive discounts of 10% and 30% on an item marked at Rs. 1900. What is the final selling price?
Medium
A
1197
B
1239
C
1130
D
1122
Explanation Final price = 1900 × (1 − 10/100) × (1 − 30/100) = Rs. 1197.
6
Three warning lights flash every 20, 14, and 4 seconds respectively. If they all flash together at the same instant, after how many seconds will they next flash together?
Medium
A
140
B
131
C
141
D
153
Explanation They will next flash together after LCM(20, 14, 4) = 140 seconds.
7
If 11 workers can complete a task in 33 days, how many days would 3 workers take to complete the same task (assuming the same work rate per worker)?
Medium
A
121
B
111
C
107
D
127
Explanation Total work = 11 × 33 = 363 worker-days. With 3 workers, days = 363/3 = 121.
8
What is 7/4 − 1?
Medium
A
1
B
2
C
11/4
D
3/4
Explanation Using a common denominator, 7/4 − 1 = 3/4.
9
What is the simple interest on Rs. 2812 at 12% per annum for 2 years?
Medium
A
674.88
B
661.88
C
666.88
D
652.88
Explanation Simple Interest = (P × R × T) / 100 = (2812 × 12 × 2) / 100 = Rs. 674.88.
10
What is 8/7 ÷ 8/5?
Medium
A
32/35
B
64/35
C
1
D
5/7
Explanation Dividing by a fraction means multiplying by its reciprocal: 8/7 × 5/8 = 5/7.
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11
If two positive integers are 18 and 7, what is the product of their LCM and GCD?
Medium
A
115
B
126
C
128
D
133
Explanation For any two positive integers, LCM × GCD = product of the numbers = 18 × 7 = 126.
12
What is the distance between 39 and -100 on the number line?
Medium
A
142
B
-139
C
139
D
-61
Explanation The distance between two points on a number line is |39 − (-100)| = 139.
13
How many integers satisfy |x − 21| < 20?
Medium
A
39
B
38
C
37
D
40
Explanation |x − 21| < 20 means 1 < x < 41. The integers strictly between 1 and 41 number 39.
14
Rs. 15057 is invested at 7% simple interest per annum for 8 years. What is the total amount after 8 years?
Medium
A
23488.92
B
23420.92
C
23567.92
D
23561.92
Explanation Amount = Principal + Interest = 15057 + 8431.92 = Rs. 23488.92.
15
A trader buys an item for Rs. 1600 and wants to make a profit of 24%. At what price should the item be sold?
Medium
A
2047
B
1979
C
1984
D
1986
Explanation Selling price = CP × (1 + 24/100) = 1600 × 1.2400 = Rs. 1984.
16
Among 87, -29, -30, and -82, which is closest to 0 on the number line?
Medium
A
-82
B
-30
C
-29
D
87
Explanation The number closest to 0 has the smallest absolute value. |-29| = 29, which is the smallest among the options.
17
What is the smallest number that must be subtracted from 3554 so that the result is exactly divisible by 39?
Medium
A
5
B
16
C
12
D
7
Explanation 3554 divided by 39 leaves remainder 5, so subtracting 5 makes it exactly divisible by 39.
18
Which is farther from -16 on the number line: -72 or 55?
Medium
A
55
B
They are equally far
C
Cannot be determined
D
-72
Explanation Distance from -16: |-72 − (-16)| = 56, and |55 − (-16)| = 71. So 55 is farther.
19
Are 24 and 36 relatively prime (i.e., is their greatest common divisor 1)?
Medium
A
Only if both are odd
B
Cannot be determined
C
Yes
D
No
Explanation GCD(24, 36) = 12, so they are not relatively prime, since they share the common factor 12.
20
What is 16.2 × 12.6?
Medium
A
28.8
B
204.12
C
205.12
D
203.12
Explanation 16.2 × 12.6 = 204.12.
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21
If A:B = 12:11 and B:C = 10:7, what is A:B:C?
Medium
A
120:110:77
B
12:11:7
C
121:110:77
D
120:110:78
Explanation Scale both ratios so B matches: A:B = 120:110 and B:C = 110:77, giving A:B:C = 120:110:77.
22
What single discount is equivalent to two successive discounts of 55% and 25%?
Medium
A
80%
B
66.25%
C
64.25%
D
69.25%
Explanation Equivalent discount = 100 − (100−55)(100−25)/100 = 66.25%.
23
Does the fraction 27/499 terminate as a decimal, or does it repeat?
Medium
A
It equals exactly 0
B
Repeats (does not terminate)
C
Terminates
D
Cannot be determined without long division
Explanation In lowest terms, 27/499 = 27/499. 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).
24
Which is greater: 7/3 or 5/6?
Medium
A
Cannot be determined
B
They are equal
C
5/6
D
7/3
Explanation 7/3 = 2.3333 and 5/6 = 0.8333, so 7/3 is greater.
25
What single discount is equivalent to two successive discounts of 8% and 12%?
Medium
A
19.04%
B
22.04%
C
20%
D
17.04%
Explanation Equivalent discount = 100 − (100−8)(100−12)/100 = 19.04%.
26
Convert 82/7 to a mixed number.
Medium
A
11 6/7
B
12 5/7
C
11 5/7
D
10 5/7
Explanation 82 ÷ 7 = 11 remainder 5, so 82/7 = 11 5/7.
27
A shopkeeper marks up an item costing Rs. 1056 by 3%. What is the markup amount (in Rs.)?
Medium
A
26.68
B
25.68
C
31.68
D
34.68
Explanation Markup amount = CP × 3/100 = 1056 × 0.0300 = Rs. 31.68.
28
A value is first increased by 25% and then increased by 50%. What is the overall net percentage change?
Medium
A
-87.5%
B
+82.5%
C
+92.5%
D
+87.5%
Explanation Starting with 100: after the first change it becomes 125.00, and after the second change it becomes 187.50 — a net change of +87.5% from the original 100.
29
What is |-17|?
Medium
A
20
B
17
C
-19
D
-17
Explanation Absolute value gives the distance from 0, which is always non-negative, so |-17| = 17.
30
Convert 43/3 to a mixed number.
Medium
A
13 1/3
B
14 2/3
C
14 1/3
D
15 1/3
Explanation 43 ÷ 3 = 14 remainder 1, so 43/3 = 14 1/3.
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31
What is 70% of 75% of 1208?
Medium
A
665.2
B
558.2
C
551.2
D
634.2
Explanation 70% of 75% of 1208 = (70/100) × (75/100) × 1208 = 634.2.
32
What is the distance between -11 and 36 on the number line?
Medium
A
48
B
47
C
-47
D
25
Explanation The distance between two points on a number line is |-11 − 36| = 47.
33
What is the smallest positive number that must be added to 2586 so that the sum is exactly divisible by 15?
Medium
A
10
B
11
C
9
D
6
Explanation 2586 divided by 15 leaves remainder 6, so adding 15 − 6 = 9 makes it exactly divisible by 15.
34
Rs. 10170 is invested at 16% simple interest per annum for 6 years. What is the total amount after 6 years?
Medium
A
19851.2
B
19933.2
C
19943.2
D
19977.2
Explanation Amount = Principal + Interest = 10170 + 9763.2 = Rs. 19933.2.
35
The ratio of boys to girls in a class is 1:1. If there are 18 boys, how many girls are there?
Medium
A
20
B
18
C
14
D
15
Explanation Since boys:girls = 1:1 and there are 18 boys, each 'part' = 18/1 = 18, so girls = 1 × 18 = 18.
36
If 36 workers can complete a task in 9 days, how many days would 27 workers take to complete the same task (assuming the same work rate per worker)?
Medium
A
15
B
8
C
13
D
12
Explanation Total work = 36 × 9 = 324 worker-days. With 27 workers, days = 324/27 = 12.
37
What single discount is equivalent to two successive discounts of 50% and 10%?
Medium
A
58%
B
60%
C
53%
D
55%
Explanation Equivalent discount = 100 − (100−50)(100−10)/100 = 55%.
38
Which of the following numbers lies between -7 and 20?
Medium
A
23
B
-26
C
19
D
-14
Explanation 19 lies strictly between -7 and 20, while the other options fall outside that range.
39
What are the solutions to |x| + 20 = 32?
Medium
A
x = -12 or x = 12
B
x = 32 only
C
x = -14 or x = 14
D
x = 20 only
Explanation |x| + 20 = 32 means |x| = 12, so x = 12 or x = -12.
40
Two buses leave a station together. One returns to the station every 17 minutes and the other every 32 minutes. After how many minutes will both buses be at the station together again?
Medium
A
547
B
544
C
529
D
506
Explanation Both buses will be at the station together again after LCM(17, 32) = 544 minutes.
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41
A sum of Rs. 672 is divided between two people in the ratio 5:9. What is the larger share?
Medium
A
443
B
432
C
422
D
466
Explanation Total parts = 5 + 9 = 14. Each part = Rs. 672 / 14 = Rs. 48. So the shares are Rs. 240 and Rs. 432; the larger share is Rs. 432.
42
For a = -13 and b = 13, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
A
Strictly less than
B
Equal
C
Cannot be determined
D
Strictly greater than
Explanation |a + b| = 0 and |a| + |b| = 26. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
43
What is the highest power of 13 that divides 24! (24 factorial) exactly?
Medium
A
3
B
1
C
4
D
2
Explanation Using Legendre's formula, the exponent of 13 in 24! is floor(24/13) + floor(24/169) + ... = 1.
44
What is 79.56 ÷ 15.6?
Medium
A
5.1
B
10.5
C
6.1
D
4.1
Explanation 79.56 ÷ 15.6 = 5.1.
45
If an integer n leaves a remainder of 2 when divided by 13, what is the remainder when n^2 is divided by 13?
Medium
A
7
B
12
C
4
Explanation n = 13q + 2 for some integer q, so n^2 ≡ 2^2 = 4 (mod 13), which leaves remainder 4 when divided by 13.
46
35^2 = 1225. How many positive divisors does 1225 have?
Medium
A
6
B
5
C
13
D
9
Explanation 1225 = 5^2 × 7^2, giving 9 divisors — always an odd count for a perfect square, since every divisor pairs with another except the square root.
47
A shopkeeper marks up an item costing Rs. 906 by 36%. What is the markup amount (in Rs.)?
Medium
A
318.16
B
333.16
C
326.16
D
309.16
Explanation Markup amount = CP × 36/100 = 906 × 0.3600 = Rs. 326.16.
48
What is the remainder when 893 is divided by 12?
Medium
A
1
B
10
C
2
D
5
Explanation 893 = 12 × 74 + 5, so the remainder is 5.
49
What are the solutions to |x − 10| = 1?
Medium
A
x = 10 only
B
x = 9 or x = 11
C
x = 8 or x = 12
D
x = -9 or x = -11
Explanation |x − 10| = 1 means x is 1 away from 10, so x = 10 + 1 = 11 or x = 10 − 1 = 9.
50
Which of the following numbers lies between -48 and -19?
Medium
A
-67
B
-49
C
-12
D
-23
Explanation -23 lies strictly between -48 and -19, while the other options fall outside that range.
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51
Which is greater: 1/2 or 7/10?
Medium
A
1/2
B
7/10
C
Cannot be determined
D
They are equal
Explanation 1/2 = 0.5000 and 7/10 = 0.7000, so 7/10 is greater.
52
How many multiples of 4 are there between 125 and 206, inclusive?
Medium
A
16
B
18
C
20
D
22
Explanation The multiples of 4 in this range run from 128 to 204, giving 20 multiples.
53
What is 1/12 of 456?
Medium
A
44
B
36
C
38
D
33
Explanation 1/12 of 456 = (1 × 456) / 12 = 38.
54
A sum of Rs. 14615 earns Rs. 23384 in simple interest over 8 years. What is the annual interest rate?
Medium
A
20%
B
17%
C
19%
D
15%
Explanation Rate = (SI × 100) / (P × T) = (23384 × 100) / (14615 × 8) = 20%.
55
A shop offers successive discounts of 20% and 25% on an item marked at Rs. 135. What is the final selling price?
Medium
A
86
B
84
C
81
D
76
Explanation Final price = 135 × (1 − 20/100) × (1 − 25/100) = Rs. 81.
56
What is the ratio of 242 to 220, expressed in lowest terms?
Medium
A
12:10
B
11:10
C
10:11
D
11:11
Explanation 242:220 reduces by dividing both terms by their GCD (22), giving 11:10.
57
What is 30.61 + 86.44?
Medium
A
116.05
B
-55.83
C
117.05
D
118.05
Explanation 30.61 + 86.44 = 117.05.
58
What is 75% of 48% of 270?
Medium
A
76.2
B
103.2
C
97.2
D
100.2
Explanation 75% of 48% of 270 = (75/100) × (48/100) × 270 = 97.2.
59
What is 270.43 − 146.06?
Medium
A
416.49
B
124.37
C
125.37
D
123.37
Explanation 270.43 − 146.06 = 124.37.
60
A sum of Rs. 3372 at 20% simple interest per annum earns Rs. 6744 in interest. For how many years was it invested?
Medium
A
12
B
13
C
10
D
14
Explanation Time = (SI × 100) / (P × R) = (6744 × 100) / (3372 × 20) = 10 years.
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61
What is the midpoint between 6 and 30 on the number line?
Medium
A
18
B
-12
C
17
D
19
Explanation The midpoint of 6 and 30 is (6 + 30) / 2 = 36/2 = 18.
62
How many digits does 8^23 have?
Medium
A
18
B
20
C
21
D
24
Explanation The number of digits of 8^23 is floor(23 × log10(8)) + 1 = 21.
63
Which is greater: |-38| or |-65|?
Medium
A
They are equal
B
|-38|
C
Cannot be determined
D
|-65|
Explanation |-38| = 38 and |-65| = 65, so |-65| is greater.
64
Are 44 and 47 relatively prime (i.e., is their greatest common divisor 1)?
Medium
A
Cannot be determined
B
Only if both are odd
C
Yes
D
No
Explanation GCD(44, 47) = 1, so they are relatively prime.
65
How many multiples of 7 are there between 38 and 288, inclusive?
Medium
A
39
B
36
C
40
D
32
Explanation The multiples of 7 in this range run from 42 to 287, giving 36 multiples.
66
If 3:2 = 36:x, what is the value of x?
Medium
A
21
B
28
C
24
D
22
Explanation Since 36/3 = 12, x = 2 × 12 = 24.
67
What is 160.68 + 175.8?
Medium
A
336.48
B
335.48
C
337.48
D
-15.12
Explanation 160.68 + 175.8 = 336.48.
68
Is 7276 divisible by 11?
Medium
A
No
B
Yes
C
Cannot be determined
D
Only if n is even
Explanation Using the alternating digit-sum rule for 11, the result is -6, which is not a multiple of 11, so the answer is No.
69
What is the distance between -69 and 98 on the number line?
Medium
A
-167
B
171
C
167
D
29
Explanation The distance between two points on a number line is |-69 − 98| = 167.
70
If 40 workers can complete a task in 2 days, how many days would 20 workers take to complete the same task (assuming the same work rate per worker)?
Medium
A
4
B
2
C
5
D
7
Explanation Total work = 40 × 2 = 80 worker-days. With 20 workers, days = 80/20 = 4.
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71
A sum of Rs. 3330 at 20% simple interest per annum earns Rs. 1998 in interest. For how many years was it invested?
Medium
A
5
B
2
C
6
D
3
Explanation Time = (SI × 100) / (P × R) = (1998 × 100) / (3330 × 20) = 3 years.
72
What is |11 × 9|?
Medium
A
103
B
99
C
95
D
101
Explanation |11 × 9| = |11| × |9| = 11 × 9 = 99.
73
Round 458.0553 to the nearest hundredth.
Medium
A
458.07
B
458.06
C
458.0
D
458.05
Explanation Rounding 458.0553 to the nearest hundredth gives 458.06.
74
What is the difference between the compound interest and simple interest on Rs. 11250 at 16% per annum for 2 years?
Medium
A
276
B
288
C
270
D
277
Explanation For 2 years, the difference between CI and SI is always P × (R/100)^2 = 11250 × (16/100)^2 = Rs. 288.
75
Among -58, -27, -85, and 29, which is closest to 0 on the number line?
Medium
A
-58
B
29
C
-85
D
-27
Explanation The number closest to 0 has the smallest absolute value. |-27| = 27, which is the smallest among the options.
76
What is the units digit of 5^20?
Medium
A
2
B
5
C
7
D
4
Explanation Units digits of powers of 5 repeat in a cycle of length 1. Using 20 mod 1, the units digit is 5.
77
What is the smallest number that must be subtracted from 7408 so that the result is exactly divisible by 6?
Medium
A
2
B
3
C
4
D
5
Explanation 7408 divided by 6 leaves remainder 4, so subtracting 4 makes it exactly divisible by 6.
78
An interest rate rises from 52% to 68%. By how many percentage points did it increase?
Medium
A
16 points
B
18 points
C
11 points
D
20 points
Explanation A percentage-point increase is a simple subtraction: 68% − 52% = 16 percentage points.
79
Convert the mixed number 7 10/11 to an improper fraction.
Medium
A
98/11
B
88/11
C
87/11
D
17/11
Explanation 7 10/11 = ((7 × 11) + 10) / 11 = 87/11.
80
Which is greater: 38.6 or 48.4?
Medium
A
48.4
B
They are equal
C
Cannot be determined
D
38.6
Explanation Comparing digit by digit, 48.4 is greater than 38.6.
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81
What is |-48 ÷ 6|?
Medium
A
8
B
13
C
4
D
6
Explanation |-48 ÷ 6| = |-48| ÷ |6| = 48 ÷ 6 = 8.
82
Which is greater: 3/14 or 1/4?
Medium
A
1/4
B
Cannot be determined
C
3/14
D
They are equal
Explanation 3/14 = 0.2143 and 1/4 = 0.2500, so 1/4 is greater.
83
A value is first decreased by 70% and then increased by 2%. What is the overall net percentage change?
Medium
A
+69.4%
B
-69.4%
C
-74.4%
D
-64.4%
Explanation Starting with 100: after the first change it becomes 30.00, and after the second change it becomes 30.60 — a net change of -69.4% from the original 100.
84
What is the simple interest on Rs. 3690 at 10% per annum for 5 years?
Medium
A
1916
B
1785
C
1845
D
1770
Explanation Simple Interest = (P × R × T) / 100 = (3690 × 10 × 5) / 100 = Rs. 1845.
85
What is 9/2 + 1/5?
Medium
A
47/10
B
24/5
C
10/7
D
43/10
Explanation Using a common denominator, 9/2 + 1/5 = 47/10.
86
How many solutions does the equation |x + 14| = 0 have?
Medium
A
Infinitely many
B
1
C
2
Explanation |x + 14| = 0: since 0 is exactly zero, there is exactly one solution.
87
The ratio of boys to girls in a class is 14:9. If there are 154 boys, how many girls are there?
Medium
A
99
B
90
C
97
D
93
Explanation Since boys:girls = 14:9 and there are 154 boys, each 'part' = 154/14 = 11, so girls = 9 × 11 = 99.
88
Which of the following numbers lies between 11 and 45?
Medium
A
-4
B
1
C
53
D
43
Explanation 43 lies strictly between 11 and 45, while the other options fall outside that range.
89
A shopkeeper marks up an item costing Rs. 413 by 55%. What is the markup amount (in Rs.)?
Medium
A
227.15
B
219.15
C
218.15
D
220.15
Explanation Markup amount = CP × 55/100 = 413 × 0.5500 = Rs. 227.15.
90
Which is greater: 7/10 or 15/13?
Medium
A
They are equal
B
15/13
C
7/10
D
Cannot be determined
Explanation 7/10 = 0.7000 and 15/13 = 1.1538, so 15/13 is greater.
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91
A shopkeeper marks up an item costing Rs. 804 by 3%. What is the markup amount (in Rs.)?
Medium
A
23.12
B
30.12
C
24.12
D
25.12
Explanation Markup amount = CP × 3/100 = 804 × 0.0300 = Rs. 24.12.
92
What is the greatest common divisor of 132, 156, and 48?
Medium
A
15
B
12
C
11
D
18
Explanation The largest integer dividing all of 132, 156, and 48 evenly is 12.
93
Among 38, 62, 43, and 20, which is closest to 0 on the number line?
Medium
A
38
B
43
C
20
D
62
Explanation The number closest to 0 has the smallest absolute value. |20| = 20, which is the smallest among the options.
94
What is 10% of 30% of 1080?
Medium
A
28.4
B
24.4
C
36.4
D
32.4
Explanation 10% of 30% of 1080 = (10/100) × (30/100) × 1080 = 32.4.
95
Simplify 70/100 to its lowest terms.
Medium
A
70/99
B
7/10
C
7/20
D
69/100
Explanation 70 and 100 share a common factor of 10; dividing both by it gives 7/10.
96
What is the average (arithmetic mean) of the 3 consecutive integers from 59 to 61?
Medium
A
57
B
62
C
63
D
60
Explanation For consecutive integers, the average equals the middle value, which is 60.
97
What is the smallest positive number that must be added to 4322 so that the sum is exactly divisible by 25?
Medium
A
10
B
3
C
8
D
4
Explanation 4322 divided by 25 leaves remainder 22, so adding 25 − 22 = 3 makes it exactly divisible by 25.
98
34^2 − 25^2 is exactly divisible by which of the following?
Medium
A
19
B
5
C
10
D
9
Explanation 34^2 − 25^2 = (34 − 25)(34 + 25) = 9 × 59, so it is always divisible by 9 (and by 59).
99
What is the compound interest on Rs. 200 at 10% per annum, compounded annually, for 2 years?
Medium
A
45
B
49
C
42
D
40
Explanation Amount = P(1 + R/100)^2 = 200 × (1 + 10/100)^2 = Rs. 242, so CI = Rs. 242 − Rs. 200 = Rs. 42.
100
Is 79790 divisible by 11?
Medium
A
No
B
Yes
C
Only if n is even
D
Cannot be determined
Explanation Using the alternating digit-sum rule for 11, the result is -4, which is not a multiple of 11, so the answer is No.