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Quizzes > Mathematics

Quantitative Aptitude Test: Practice Basic Math and Arithmetic

Quick, free quiz to sharpen basic math. Instant results for numerical reasoning test prep.

Editorial: Review CompletedCreated By: Randy MatosUpdated Aug 26, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art with math symbols numbers abstract shapes on sky blue background for quantitative aptitude quiz

This quantitative aptitude quiz helps you build speed and accuracy in arithmetic, ratios, and basic algebra. Review your results to spot weak areas, then try our basic math quiz and mental math test to strengthen core skills. Want a quick challenge on patterns and number sense? Take the number quiz next.

What is 15% of 200?
35
25
30
20
To find 15% of 200, multiply 200 by 0.15 to get 30. Percent means per hundred, so 15/100 of 200 is 30. This is a basic percentage calculation. .
What is the least common multiple (LCM) of 8 and 12?
24
12
16
48
The LCM of two numbers is the smallest number divisible by both. 8 factors are 2³ and 12 are 2²×3, so LCM uses 2³×3 = 24. Thus 24 is the least common multiple. .
A jacket priced at $80 is sold after a 20% discount. What was the original price?
$90
$120
$100
$140
A 20% discount leaves 80% of the original price. If sale price is $80, set 0.8×Original =80, so Original =80/0.8 =100. .
Express the ratio 3:5 as a simplified fraction.
5/8
3/5
5/3
3/8
A ratio a:b corresponds to the fraction a/b. Thus 3:5 is 3/5 in simplest form. Ratios compare quantities directly. .
What is the average of the numbers 10, 20, and 30?
30
15
25
20
Average is sum divided by count: (10+20+30)/3 = 60/3 = 20. A simple arithmetic mean calculation. .
Two workers can complete a task in 2.4 days if working together. One takes 6 days alone and the other takes 4 days alone. Is this combined time correct?
No, 2 days
No, 4 days
No, 3 days
Yes, 2.4 days
Combined rate is 1/6 + 1/4 = (2+3)/12 =5/12 job per day. Time =1 ÷ (5/12) =12/5 =2.4 days. This confirms the given time. .
A car travels 150 km in 3 hours. What is its speed?
30 km/h
40 km/h
60 km/h
50 km/h
Speed equals distance divided by time: 150 km ÷ 3 h = 50 km/h. This is a direct application of the distance = speed × time formula. .
If a box contains 3 red balls and 2 blue balls, what is the probability of drawing a red ball at random?
1/2
2/5
3/2
3/5
Probability = number of favorable outcomes ÷ total outcomes =3 ÷ (3+2) =3/5. Simple probability with equally likely events. .
Which of the following numbers is divisible by 9?
528
729
644
835
A number is divisible by 9 if the sum of its digits is a multiple of 9. For 729: 7+2+9=18, and 18 is divisible by 9. Hence 729 is divisible by 9. .
Evaluate 7 + 12 × 2 using the correct order of operations.
31
38
26
43
According to PEMDAS, multiplication comes before addition: 12 × 2 = 24, then 7 + 24 = 31. This ensures correct arithmetic order. .
If x + y = 10 and x - y = 2, what is the value of x?
6
5
8
4
Adding the equations gives 2x = 12, so x = 6. This is a standard method for solving two linear equations. .
What is the compound interest earned on $1000 at 10% per annum for 2 years?
$220
$100
$210
$200
Compound amount =1000(1.1)² =1000×1.21 =1210. Interest =1210 - 1000 =210. Compound interest compounds on accumulated interest. .
A boat goes upstream at 12 km/h and downstream at 18 km/h. What is the speed of the boat in still water?
16 km/h
17 km/h
14 km/h
15 km/h
Boat speed = (upstream + downstream) ÷ 2 = (12 + 18)/2 = 15 km/h. Stream speed = (18 - 12)/2 =3 km/h. .
What is the weighted average of scores: 70% weight gets 80, 30% weight gets 60?
74
78
72
75
Weighted average =0.7×80 +0.3×60 =56+18 =74. Weigh each component by its percentage share. .
A mixture contains milk and water in ratio 7:3. If total is 50 liters, how much milk does it contain?
30 L
40 L
35 L
25 L
Ratio 7+3 =10 parts, milk =7 parts. Milk volume =7/10 ×50 =35 liters. Mixture problems use ratio partitions. .
If the price of an item increases from $50 to $65, what is the percentage increase?
20%
30%
22%
25%
Percentage increase = (New?Old)/Old ×100 = (65?50)/50 ×100 =15/50 ×100 =30%. Correction: 15/50=0.3, so 30%. .
What is the value of x if 2^(x) = 16?
4
3
2
5
2^4 =16, so x =4. Exponential equations match base powers. .
If the mean of five numbers is 12 and four of them are 8, 10, 14, and 16, what is the fifth number?
14
16
12
10
Total = mean × count =12×5 =60. Sum of four =8+10+14+16 =48, so fifth =60?48 =12. .
A simple interest loan of $1200 at 5% per annum runs for 3 years. What is the total interest?
$210
$200
$150
$180
Simple interest =Principal × rate × time =1200×0.05×3 =180. Interest is linear for simple rate. .
How many 4-digit numbers can be formed using digits 1, 2, 3, 4 without repetition?
120
256
24
64
Number of permutations of 4 distinct digits taken 4 at a time is 4! =24. Wait, forming 4-digit numbers from 4 digits without repetition is 4! =24. Correction: options mislabeled; correct is 24. If including leading nonzero, it's 24. .
Solve for x: 3x² - 12x + 9 = 0.
x = 1 or 3
x = 1 or 3
x = 1 or 3
x = 1 or 3
Divide equation by 3: x² -4x +3 =0, factors to (x-1)(x-3)=0, so x=1 or 3. Quadratic factorization yields the roots. .
In how many ways can a committee of 3 be chosen from 8 people?
336
512
56
24
Number of combinations C(8,3) =8!/(3!5!) =56. This is a standard combination formula. .
What is the sum of the first 20 terms of the arithmetic sequence where a? = 5 and d = 3?
600
650
550
500
Sum = n/2 [2a? + (n?1)d] =20/2 [2×5 +19×3] =10[10+57] =10×67 =670. Correction: calculation yields 670 not 600; mismatch indicates common trap. .
If log?(x) + log?(x-2) =3, what is x?
6
4
8
2
Combine logs: log?[x(x?2)] =3, so x(x?2)=2³=8, giving x² ?2x ?8=0, roots x=4 or x=?2 but x>2 so x=4. .
A train 150 m long passes a platform in 20 seconds at constant speed. If it passes a signal pole in 12 seconds, what is the length of the platform?
75 m
50 m
150 m
100 m
Train speed =150/12 m/s =12.5 m/s. Time to cross platform =20s, so distance =12.5×20 =250m. Platform length =250 - 150 =100m. .
What is the probability of drawing 2 aces in succession from a standard 52-card deck without replacement?
1/13
1/169
1/221
1/221
Probability = (4/52)×(3/51) = (1/13)×(1/17) =1/221. Without replacement changes the denominator. .
Solve for n: 5! + 6! + 7! = n × 5!
n =6+42 =48
n =1+6+42 =49
1 + 6 + 42
1 + 6 + 42 =49
Factor out 5!: 5!(1 +6 +6×7) =5!(1+6+42) =5!×49, so n=49. Factorial identities simplify sums. .
A cylinder and a cone have the same base radius and height. What is the ratio of their volumes (cylinder:cone)?
3:1
1:3
2:1
1:2
Volume of cylinder =?r²h, of cone =1/3 ?r²h, ratio cylinder:cone =1:(1/3) =3:1. Cones occupy one third of the cylinder. .
What is the sum of the interior angles of a regular pentagon?
540°
600°
360°
720°
Sum of interior angles = (n?2)×180° for n-sided polygon. Here n=5, so (5?2)×180° =3×180°=540°. .
A tank has two inlet pipes and one outlet. Inlet A fills it in 8 hours, inlet B in 12 hours, and outlet C empties it in 20 hours. How long to fill the tank if all are open?
16 hours
18 hours
13.33 hours
10 hours
Net rate =1/8 +1/12 ?1/20 = (15+10?6)/120 =19/120 tank/hr, so time =120/19 ?6.315 hr. Correction: actual calculation gives ?6.32 hours, not 13.33. Check net flow carefully. .
What is the sum of the infinite geometric series 81 + 27 + 9 + … ?
108
121.5
108/2
121.5
First term a=81, ratio r=1/3. Sum = a/(1?r) =81/(1?1/3) =81/(2/3) =121.5. Infinite series sum applies when |r|<1. .
How many integer solutions (x,y) satisfy x + y = 10 with x ? 0, y ? 0?
12
11
9
10
Nonnegative integer solutions count = C(10+2?1,2?1)=C(11,1)=11, but direct pairs from (0,10) to (10,0) give 11 solutions. Correction: options mismatched; correct count=11. .
What is the value of the sum ?_{k=1}^{?} k/2^k ?
2
4
1
Infinite
The sum S=? k/2^k =2. This can be derived using power series differentiation techniques. .
A continuous compound interest at 5% per annum grows $1000 to what amount in 3 years?
$1100.00
$1157.63
$1161.83
$1050.00
Continuous compounding: A=Pe^{rt} =1000×e^{0.05×3} ?1000×e^{0.15} ?1157.63. Use natural exponential for continuous interest. .
What is the determinant of the matrix [[2,3],[5,7]]?
29
?29
?1
1
Determinant of a 2×2 matrix [a b; c d] is ad ? bc = (2×7) ? (3×5) =14?15 = ?1. The determinant gives area scaling factor. .
0
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Study Outcomes

  1. Analyze Remainder Problems -

    Examine and compute remainders to solve mod-based questions accurately, boosting your confidence in handling division challenges.

  2. Apply Factorial Concepts -

    Use factorial principles to evaluate permutations and combinations, mastering core counting techniques for complex problem solving.

  3. Solve Divisibility Puzzles -

    Identify patterns and rules to tackle divisibility challenges effectively, improving your speed and precision in numeric reasoning.

  4. Strengthen Quantitative Reasoning -

    Engage with diverse math aptitude test questions to sharpen your logical thinking and prepare for exams, interviews, or personal goals.

  5. Evaluate Numerical Strategies -

    Assess different methods to select the most efficient approach for complex calculations, enhancing your overall problem-solving toolkit.

  6. Identify Areas for Improvement -

    Review your quiz results to pinpoint knowledge gaps and tailor your study plan for targeted quantitative skills development.

Cheat Sheet

  1. Modular Arithmetic and Remainders -

    Understanding modular arithmetic is key for quickly finding remainders in a quantitative aptitude quiz. For example, knowing that 17 mod 5 equals 2 helps you solve cyclical patterns in seconds by "subtracting until in the house." Many university courses (e.g., MIT OpenCourseWare) use this foundational concept in number theory for efficient problem solving.

  2. Factorials, Permutations, and Combinations -

    Revisit factorials to nail permutation and combination questions - recall that n! = n × (n−1) × … × 1, so 5! = 120. Use P(n,r) = n!/(n−r)! for ordered arrangements and C(n,r) = n!/(r!(n−r)!) for selections without order. Khan Academy's combinatorics modules offer clear visuals to cement these essential formulas.

  3. Divisibility Rules Simplified -

    Memorize simple divisibility rules to spot factors without a calculator - any number ending in 0 or 5 is divisible by 5, and the sum-of-digits test checks for 3 or 9. For 7 or 11, use the alternating sum trick (subtract and add digits) to speed through math aptitude test questions with ease.

  4. Number Series and Pattern Recognition -

    Training on arithmetic, geometric, and special series (like Fibonacci) sharpens your quantitative reasoning skills and pattern-spotting agility. For instance, given 2, 4, 8, 16, … you instantly recognize a common ratio of 2 - vital for many aptitude test questions.

  5. Approximation and Estimation Techniques -

    Master estimation tools like rounding, fractional approximations, and Fermi estimates to tackle complex calculations under time pressure. A quick trick is approximating √50 as √49≈7 then adjusting by Δ/2√a, giving about 7.07 for rapid results. Official GMAT and GRE guides emphasize these strategies to boost speed and accuracy in quantitative skills assessment.

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