Free GAT Quantitative Practice Questions with Full Solutions

GAT Practice Question

Arithmetic Word Problems Easy Multiple Choice Translate a word problem into two simple equations

Ahmed is 8 cm longer than Ali, Saad is shorter than Ali by 9 cm. If Saad is 142 cm long, what is the height of Ahmed?

A. 143

B. 152

C. 146

D. 159

Correct answer: Choice D

159

Full solution Saad is 9 cm shorter than Ali, so Ali = 142 + 9 = 151. Ahmed is 8 cm longer than Ali, so Ahmed = 151 + 8 = 159.

Common mistake A common mistake is adding 8 and 9 directly to Saad, even though the problem first asks you to move from Saad to Ali, then from Ali to Ahmed.

Trap to watch Do not combine the 8 and 9 until you know which direction each comparison goes.

Method note Move step by step: Saad → Ali → Ahmed.

Qudurat note Qudurat note: This is a basic relation question. Read who is taller and who is shorter before doing any arithmetic.

Speed note This should be solved in a few seconds if you track the relationships in order.

GAT Practice Question

Arithmetic Number Sense Easy Multiple Choice Count terms in an arithmetic pattern

How many even numbers are there from 3 to 99?

A. 47

B. 49

C. 50

D. 48

Correct answer: Choice D

48

Full solution The even numbers from 3 to 99 are 4, 6, 8, ..., 98. This is an arithmetic sequence with first term 4, last term 98, and common difference 2. The number of terms is (98 − 4) ÷ 2 + 1 = 48.

Common mistake A common mistake is forgetting that the count starts at 4, not 2, and ends at 98, not 100.

Trap to watch Watch the endpoints. The range says from 3 to 99, so only 4 through 98 matter.

Method note When the numbers follow a steady step, use the arithmetic-sequence count formula.

Qudurat note Qudurat note: On questions like this, do not list all the terms. Count smartly.

Speed note Faster route: first even is 4, last even is 98, then count by difference.

GAT Practice Question

Arithmetic Radicals and Fractions Medium Multiple Choice Simplify radicals involving fractions

Evaluate √(14) × √(1636).

A. 23

B. 32

C. √23

D. 13

Correct answer: Choice D

13

Full solution First, √(14) = 12. Next, √(1636) = 46 = 23. Multiply: (12) × (23) = 13.

Common mistake A common mistake is multiplying inside the radicals incorrectly or forgetting to simplify 46 to 23.

Trap to watch Do not rush the second radical. √(1636) is 46, then simplify.

Method note Simplify each radical first, then multiply.

Qudurat note Qudurat note: In radical-fraction questions, simplify in small pieces instead of all at once.

Speed note Fast route: take square roots separately, then multiply.

GAT Practice Question

Arithmetic Nested Radicals Medium Multiple Choice Evaluate a nested radical from the inside out

Evaluate √(4 + √(16 + √81)).

A. 1

B. 2

C. 3

D. 8

Correct answer: Choice C

3

Full solution Start from the innermost radical. √81 = 9. Then √(16 + 9) = √25 = 5. Finally, √(4 + 5) = √9 = 3.

Common mistake A common mistake is trying to combine everything at once instead of working from the innermost radical outward.

Trap to watch Do not skip the middle radical.

Method note For nested radicals, always simplify from inside to outside.

Qudurat note Qudurat note: Order matters more than speed here. If you go inside-out, the question becomes simple.

Speed note Fast route: 81 → 9, then 25 → 5, then 9 → 3.

GAT Practice Question

Arithmetic Series and Patterns Easy Multiple Choice Use the sum of the first n integers

Find the sum 1 + 2 + 3 + 4 + 5 + ... + 100.

A. 4050

B. 5050

C. 5000

D. 6500

Correct answer: Choice B

5050

Full solution The sum of the first n integers is n(n + 1) ÷ 2. Here n = 100, so the sum is 100 × 101 ÷ 2 = 5050.

Common mistake A common mistake is using 100 × 100 ÷ 2 instead of 100 × 101 ÷ 2.

Trap to watch Do not forget the +1 in n(n + 1)/2.

Method note Remember the formula n(n + 1) ÷ 2.

Qudurat note Qudurat note: This is a classic pattern question. Use the formula, do not add term by term.

Speed note This should be almost instant if you remember the formula.

GAT Practice Question

Arithmetic Word Problems Easy Multiple Choice Translate a ratio statement and use unit facts

In a farm, the number of chickens is twice the number of cows. If the total number of cow legs is 52, find the number of chickens.

A. 13

B. 35

C. 27

D. 26

Correct answer: Choice D

26

Full solution Each cow has 4 legs, so the number of cows is 52 ÷ 4 = 13. The number of chickens is twice the number of cows, so chickens = 2 × 13 = 26.

Common mistake A common mistake is dividing 52 by 2 because of the word twice, before first finding the number of cows.

Trap to watch Find the cows first. The question does not say 52 animals; it says 52 cow legs.

Method note Use the real-life fact first: 4 legs per cow. Then apply the ratio.

Qudurat note Qudurat note: In mixed word problems, separate the counting step from the ratio step.

Speed note Quick route: 52 legs means 13 cows, then double it.

GAT Practice Question

Arithmetic LCM and Cycles Medium Multiple Choice Use least common multiple to find repeated coincidence

A person has 3 friends. He meets the first one every 3 days, the second every 2 days, and the third every 5 days. How often do they all meet in 60 days?

A. 1

B. 3

C. 2

D. 10

Correct answer: Choice C

2

Full solution They all meet together every LCM(3, 2, 5) = 30 days. In 60 days, that happens 60 ÷ 30 = 2 times.

Common mistake A common mistake is adding the intervals instead of taking the least common multiple.

Trap to watch Do not add 3 + 2 + 5. Meeting together depends on common multiples.

Method note When several repeating schedules line up together, use LCM.

Qudurat note Qudurat note: This is a cycle question, not a sum question.

Speed note Find the LCM directly. Once you get 30, the rest is immediate.

GAT Practice Question

Arithmetic Sequences and Patterns Medium Multiple Choice Identify an alternating pattern

Find the missing number: 13, 11, 15, 9, 17, 7, 19, ?

A. 19

B. 9

C. 5

D. 18

Correct answer: Choice C

5

Full solution The sequence alternates between two patterns. Odd positions are 13, 15, 17, 19, which increase by 2. Even positions are 11, 9, 7, ?, which decrease by 2. So the missing number is 5.

Common mistake A common mistake is trying to use one rule for the whole sequence instead of noticing the alternating structure.

Trap to watch Do not force one pattern across all terms if the jumps keep changing.

Method note If one pattern fails, check whether the terms split into two interleaved sequences.

Qudurat note Qudurat note: Many Qudurat sequence questions alternate two simple rules.

Speed note Fast route: separate odd-position terms from even-position terms.

GAT Practice Question

Arithmetic Work and Rate Medium Multiple Choice Use inverse proportion in work problems

If 9 men can do a piece of work in 8 hours, in how many hours will 12 men do it?

A. 4

B. 5

C. 6

D. 8

Correct answer: Choice C

6

Full solution The total work is constant. If 9 men take 8 hours, then the total work is 9 × 8 = 72 man-hours. With 12 men, the time is 72 ÷ 12 = 6 hours.

Common mistake A common mistake is thinking more men means more hours, instead of fewer hours.

Trap to watch Do not treat this as direct proportion.

Method note For fixed work, men × time stays constant.

Qudurat note Qudurat note: This is an inverse relationship. When the number of workers goes up, the time goes down.

Speed note Fast route: use man-hours. 9 × 8 = 72, then divide by 12.

GAT Practice Question

Arithmetic Exponents and Radicals Medium Multiple Choice Rewrite radicals as fractional exponents

Evaluate ¹⁰√(2⁸).

A. 2^0.4

B. 2^0.6

C. 2^0.8

D. 2⁸⁰

Correct answer: Choice C

2^0.8

Full solution The 10th root means power 110. So ¹⁰√(2⁸) = (2⁸)^1/10 = 2^8/10 = 2^0.8.

Common mistake A common mistake is multiplying 10 and 8 instead of dividing the exponent by the root index.

Trap to watch Do not turn 10th root into multiplication.

Method note Use the rule ⁿ√(a^m) = a^m/n.

Qudurat note Qudurat note: Root-exponent conversion is one of the most useful quick rules in the exam.

Speed note Fast route: root 10 means divide the exponent 8 by 10.

GAT Practice Question

Arithmetic Rates and Arithmetic Easy Multiple Choice Find the difference between two constant rates over time

Two cars consume fuel at rates of 35 liters per hour and 40 liters per hour. Find the difference after 10 hours.

A. 120

B. 40

C. 90

D. 50 liters

Correct answer: Choice D

50 liters

Full solution The difference in fuel consumption per hour is 40 − 35 = 5 liters. Over 10 hours, the total difference is 5 × 10 = 50 liters.

Common mistake A common mistake is adding the two rates instead of subtracting them.

Trap to watch The question asks for difference, not total fuel consumed.

Method note Difference after time = difference per unit × time.

Qudurat note Qudurat note: This is a direct rate-difference question.

Speed note Find the hourly gap first, then multiply once.

GAT Practice Question

Algebra Algebra Easy Multiple Choice Substitute a value into a linear equation

If 3x − y = 15, find y where x = 3.

A. −3

B. 6

C. 7

D. −6

Correct answer: Choice D

−6

Full solution Substitute x = 3 into 3x − y = 15. Then 3(3) − y = 15, so 9 − y = 15. Subtract 9 from both sides to get −y = 6, which means y = −6.

Common mistake A common mistake is moving terms too quickly and missing the negative sign on y.

Trap to watch When you get −y = 6, the answer is y = −6, not 6.

Method note Substitute first, then solve carefully for the remaining variable.

Qudurat note Qudurat note: This is a standard substitution question. The sign is the only real trap.

Speed note Quick route: plug in x immediately, then isolate y.

GAT Practice Question

Algebra Algebra Easy Multiple Choice Solve a simple rational equation

Find the value of x where 12x + 1 = 1x + 2.

A. 4

B. −1

C. 1

D. 3

Correct answer: Choice C

1

Full solution Since both fractions have the same numerator 1, their denominators must be equal. So 2x + 1 = x + 2. Solving gives x = 1.

Common mistake A common mistake is cross-multiplying correctly but making an arithmetic mistake when isolating x.

Trap to watch Do not overcomplicate this with long cross-multiplication.

Method note When two fractions with numerator 1 are equal, compare denominators directly if both are defined.

Qudurat note Qudurat note: This is simpler than it looks. Equal unit fractions mean equal denominators here.

Speed note Fast route: set 2x + 1 = x + 2 immediately.

GAT Practice Question

Geometry Geometry Medium Multiple Choice Use rhombus diagonals and the Pythagorean theorem

Find the perimeter of a rhombus whose diagonals are 8 cm and 6 cm.

A. 40 cm

B. 42 cm

C. 50 cm

D. 20 cm

Correct answer: Choice D

20 cm

Full solution In a rhombus, the diagonals bisect each other at right angles. So half the diagonals are 4 cm and 3 cm. One side of the rhombus is the hypotenuse of a right triangle with legs 4 and 3, so side = √(4² + 3²) = 5. Perimeter = 4 × 5 = 20 cm.

Common mistake A common mistake is adding the diagonals directly or forgetting to halve them first.

Trap to watch The given diagonals are full diagonals, not side lengths.

Method note Use half-diagonals to form a right triangle.

Qudurat note Qudurat note: In rhombus questions, diagonals usually lead to a right triangle.

Speed note Think 3-4-5 triangle immediately.

GAT Practice Question

Geometry Geometry with Figures Medium Multiple Choice Use the square area to infer circle radius from a figure

If the area of a square is 64 cm², find the area of the circle shown.

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A. 25π

B. 36π

C. 49π

D. 16π

Correct answer: Choice D

16π

Full solution The square area is 64, so the side length is √64 = 8. From the figure, the circle diameter matches that side length, so the radius is 4. Area of the circle = πr² = π(4²) = 16π.

Common mistake A common mistake is using side length 8 as the radius instead of the diameter.

Trap to watch Do not confuse diameter with radius.

Method note From a square area, find the side first. Then connect the side to the circle diameter.

Qudurat note Qudurat note: On figure questions, first extract the side length. The rest usually becomes direct.

Speed note Fast route: square area 64 means side 8, so the circle radius is 4.

GAT Practice Question

Geometry Geometry with Figures Hard Multiple Choice Find shaded area by subtracting four circle areas from the square

If the area of the square is 400 cm², find the area of the shaded region.

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A. 56 cm²

B. 20 cm²

C. 60 cm²

D. 86 cm²

Correct answer: Choice D

86 cm²

Full solution Square area = 400, so side length = 20. Since the 4 equal circles fit in a 2 by 2 arrangement, each circle has diameter 10 and radius 5. Total area of the 4 circles = 4 × π × 5² = 100π. The shaded area is 400 − 100π ≈ 400 − 314 = 86 cm².

Common mistake A common mistake is using radius 10 instead of diameter 10, or forgetting that there are 4 circles.

Trap to watch The hardest trap is misreading the circle diameter.

Method note Area of shaded region = total area − area of white circles.

Qudurat note Qudurat note: This is a subtraction-area question. Find the square first, then the circles.

Speed note Fast route: side 20 → circle diameter 10 → radius 5 → subtract 100π from 400.

GAT Practice Question

Data Analysis and Statistics Averages Easy Multiple Choice Use the average formula

The average of 2, 8, 10, x is 6. Find the value of x.

A. 2

B. 3

C. 4

D. 6

Correct answer: Choice C

4

Full solution Average = sum ÷ number of values. So (2 + 8 + 10 + x) ÷ 4 = 6. That gives 20 + x = 24, so x = 4.

Common mistake A common mistake is dividing too early or forgetting that there are 4 numbers in the average.

Trap to watch Do not average the known numbers first and then guess the missing value.

Method note Use average = total ÷ count, then solve for the missing value.

Qudurat note Qudurat note: Average questions are direct if you write the equation first.

Speed note This should be very quick once you write the average equation.

Hospital Pie Chart Set

Data Analysis and Statistics Charts and Percentages Shared Diagram

Use the same hospital pie chart for the following 3 questions.

GAT Practice Question

Data Analysis and Statistics Charts and Percentages Medium Multiple Choice Use a percentage from a pie chart to find a sector angle

Use the hospital pie chart. If the number of men is 38 and the number of women is 19, find the angle of the women sector.

hospital

men: 25%

women: 19 people

children: ?

A. 60°

B. 30°

C. 45°

D. 18°

Correct answer: Choice C

45°

Full solution Men represent 25% of the hospital chart, and the number of men is 38. So the total number of people is 38 ÷ 0.25 = 152. Women are 19 out of 152, so the women fraction is 19152 = 18. The sector angle is 18 × 360° = 45°.

Common mistake A common mistake is using 19 directly as a percent. It is a number of people, not a percentage.

Trap to watch Do not treat the women count as the women percentage.

Method note First find the total from the men data, then convert the women count into a fraction of the total.

Qudurat note Qudurat note: Pie-chart questions usually need you to move between count, percent, and angle.

Speed note Fast route: men are one quarter, so total is 38 × 4 = 152. Then women are 19/152 = 1/8.

GAT Practice Question

Data Analysis and Statistics Charts and Percentages Medium Multiple Choice Use a pie chart percentage to find a missing group count

Using the same hospital pie chart, if the number of men is 38 and the number of women is 19, find the number of children.

A. 95

B. 90

C. 88

D. 100

Correct answer: Choice A

95

Full solution Men are 25% of the total, and there are 38 men. Therefore, total people = 38 ÷ 0.25 = 152. Women are 19. So children = 152 − 38 − 19 = 95.

Common mistake A common mistake is subtracting only one group from the total. Children are what remains after removing both men and women.

Trap to watch Do not subtract women only or men only; children are the remaining group.

Method note Use the percentage group to find the total first, then subtract the known counts.

Qudurat note Qudurat note: This is a remainder question after finding the total.

Speed note Fast route: total is 38 × 4 = 152, then subtract 38 and 19.

GAT Practice Question

Data Analysis and Statistics Charts and Percentages Medium Multiple Choice Convert a group count into a pie-chart sector angle

Using the same hospital pie chart, if the number of men is 38 and the number of women is 19, find the angle of the children sector.

A. 150°

B. 210°

C. 225°

D. 245°

Correct answer: Choice C

225°

Full solution From the men data, total people = 38 ÷ 0.25 = 152. Children = 152 − 38 − 19 = 95. The children fraction is 95152 = 58. Therefore, the children sector angle is 58 × 360° = 225°.

Common mistake A common mistake is using the men angle or women angle instead of finding the children portion of the total.

Trap to watch Do not use the visible size of the chart only; calculate the sector from the count.

Method note Find the group fraction first, then multiply by 360°.

Qudurat note Qudurat note: Sector angle equals group fraction multiplied by 360°.

Speed note Fast route: children are 95 out of 152, which simplifies to 5/8. Then 5/8 × 360° = 225°.

GAT Practice Question

Comparison Comparison Medium Multiple Choice Compare two expressions with symmetric fractions

Compare:

A) 119 − 911
B) 911 − 119

A. A

B. B

C. equal

D. not enough information

Correct answer: Choice A

A

Full solution Compute each expression. A = 119 − 911 = (121 − 81)/99 = 4099. B = 911 − 119 = (81 − 121)/99 = −4099. Since 4099 is positive and −4099 is negative, A is greater.

Common mistake A common mistake is thinking the two expressions are equal because they use the same numbers. The order changes the sign.

Trap to watch Do not ignore order in subtraction. Reversing the terms changes the answer completely.

Method note If one expression is the negative of the other, compare the signs before doing anything else.

Qudurat note Qudurat note: Comparison questions are often faster with sign logic than with full calculation.

Speed note Fast route: B is just the reverse of A, so it must be the negative of A.

GAT Practice Question

Comparison Comparison Easy Multiple Choice Use sign reasoning in a comparison question

If x > 0 and y < 0, compare A) xy and B) x − y.

A. A

B. B

C. equal

D. not enough information

Correct answer: Choice B

B

Full solution Since x is positive and y is negative, xy is negative. Also, x − y = x − (negative number) = x + positive number, which is positive. A negative quantity is always less than a positive quantity, so B is greater.

Common mistake A common mistake is focusing on the actual values of x and y, even though the sign information alone is enough.

Trap to watch Do not waste time picking sample numbers unless the sign logic is already enough.

Method note Use signs first in comparison questions. Sometimes that alone solves the problem.

Qudurat note Qudurat note: Comparison questions often hide a very short sign argument.

Speed note Fast route: product of positive and negative is negative, but x − y becomes positive.