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GAT Qudrat Math

Provider · Qiyas — National Center for Assessment Section · Quantitative (الكمّي) Chapters · 8 Explorers · 3 interactive
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Test format & strategy

GAT Qudrat — Quantitative Format & Strategy No calculator

The General Aptitude Test (GAT — القدرات العامة, "Qudrat") is administered by Qiyas. Alongside a verbal section it has a quantitative section that measures reasoning with numbers rather than memorised content.

What to expect

Questions are multiple choice and are answered without a calculator, so speed and clean mental methods matter as much as the mathematics. The quantitative material draws on arithmetic, algebra, geometry and data — at roughly a middle- to early-secondary level — plus a distinctive quantitative-comparison question type covered in Chapter 5.

GAT Qudrat — Quantitative Section Map
Chapter Topics tested Typical share
1 — Arithmetic Operations, fractions, LCM/GCD, estimation ~20%
2 — Ratios & % Part:whole ratios, percentage change, proportions ~15%
3 — Algebra Linear equations, systems, expansion, substitution ~20%
4 — Geometry Perimeter, area, angles, triangles, circles ~15%
5 — QC Questions Compare Quantity A vs B; 4-choice response ~15%
6 — Sequences Arithmetic/geometric nth term, visual patterns ~10%
7 — Data & Probability Mean, median, mode; table reading; basic probability ~5%

Format: Multiple choice, no calculator. Questions are in Arabic. Key strategy: estimate first, test special values on QC questions.

Format
multiple choice
Calculator
not permitted
Skills
arithmetic · algebra · geometry · data
Signature
quantitative comparisons
▲ Three habits that save time

Estimate before computing; keep fractions instead of converting to decimals where possible; and on comparison questions, test convenient values (such as \( 0 \), \( 1 \), and a negative) before committing to an answer.

Practice Problem

A student answers 36 out of 45 questions correctly. What percentage is that?

Show solution
\(\dfrac{36}{45}\times100=80\%.\)

📝 Chapter Quiz
1

Arithmetic & Number Sense

GAT Qudrat — Quantitative Ch.1 Arithmetic No calculator

The foundation: order of operations, fractions, factors and multiples, and quick estimation.

▲ Reference — Number facts

Follow order of operations (brackets, powers, ×÷, +−). To compare fractions, cross-multiply or use a common denominator. A number's prime factorisation reveals its factors, GCD and LCM.

Order
brackets → powers → ×÷ → +−
Compare
\( \tfrac{a}{b}\ \text{vs}\ \tfrac{c}{d}\Rightarrow ad\ \text{vs}\ bc \)
Percent
\( p\%\ \text{of}\ N=\tfrac{p}{100}N \)
Average
\( \dfrac{\text{sum}}{\text{count}} \)
Worked example 1.A

Which is larger, \( \tfrac23 \) or \( \tfrac35 \)? Cross-multiply: \( 2\times5=10 \) versus \( 3\times3=9 \). Since \( 10>9 \), \[ \tfrac23>\tfrac35. \]

Worked example 1.B

Find \( 15\% \) of \( 200 \). \[ \tfrac{15}{100}\times200=30. \]

Practice Problem

What is \(\dfrac{5}{6}+\dfrac{7}{9}-\dfrac{1}{3}\)?

Show solution
LCD\(=18:\quad\dfrac{15}{18}+\dfrac{14}{18}-\dfrac{6}{18}=\dfrac{23}{18}=1\dfrac{5}{18}.\)

📝 Chapter Quiz
2

Ratios, Proportion & Percentages

GAT Qudrat — Quantitative Ch.2 Ratios & % No calculator

Ratios share a quantity in parts; percentages express change. Both appear constantly on the test, often disguised in word problems.

▲ Reference — Ratio & percent

To split a total in ratio \( a:b \), there are \( a+b \) equal parts. Percentage change is \( \dfrac{\text{new}-\text{old}}{\text{old}}\times100\% \). A rise of \( p\% \) then a fall of \( p\% \) does not return to the start.

Adjust the two parts of the ratio below and watch how a total of 120 divides between them.

⊙ Explorer · Sharing in a ratiointeractive
first share
second share

Each part is \( \tfrac{120}{a+b} \); the shares are \( a \) and \( b \) of those parts.

Now fix an original value of 80 and slide the new value to read the percentage change directly.

⊙ Explorer · Percentage changeinteractive
percentage change

\( \dfrac{\text{new}-80}{80}\times100\% \). Equal bars mean \( 0\% \) change.

Share
\( \dfrac{\text{total}}{a+b} \) per part
% change
\( \dfrac{\text{new}-\text{old}}{\text{old}}\times100 \)
Increase
\( \times(1+\tfrac{p}{100}) \)
Decrease
\( \times(1-\tfrac{p}{100}) \)
Worked example 2.A

Share \( 150 \) in the ratio \( 2:3 \). Five parts, each \( 30 \): \[ 60\ \text{and}\ 90. \]

Worked example 2.B

A price of \( 100 \) rises \( 10\% \), then falls \( 10\% \). Find the final price. \[ 100\times1.1\times0.9=99. \]

Practice Problem

A class has boys to girls in the ratio 3:5. If there are 40 girls, how many students in total?

Show solution
\(5\text{ parts}=40\Rightarrow1\text{ part}=8.\) Total parts\(=3+5=8.\quad\)Total students\(=8\times8=64.\)

📝 Chapter Quiz
3

Algebra Essentials

GAT Qudrat — Quantitative Ch.3 Algebra No calculator

Linear equations, simple systems, expansion and substitution — the algebra that the quantitative section relies on.

▲ Reference — Working with unknowns

Solve a linear equation by isolating the variable. A system of two equations can be solved by elimination or substitution. Expand \( (x+a)(x+b)=x^2+(a+b)x+ab \).

Linear
\( ax+b=c \)
Expand
\( (x+a)(x+b) \)
System
eliminate or substitute
Powers
\( a^{m}a^{n}=a^{m+n} \)
Worked example 3.A

Solve \( 2x+5=17 \). \[ 2x=12,\qquad x=6. \]

Worked example 3.B

If \( x+y=10 \) and \( x-y=4 \), find \( x \). Add the equations: \( 2x=14 \). \[ x=7. \]

Practice Problem

Solve: \(2x+y=11\) and \(x-y=1.\)

Show solution
Add: \(3x=12\Rightarrow x=4.\)

\(4-y=1\Rightarrow y=3.\)

📝 Chapter Quiz
4

Geometry & Measurement

GAT Qudrat — Quantitative Ch.4 Geometry No calculator

Angles, triangles, area, perimeter and volume — applied quickly, usually without a calculator.

▲ Reference — Shapes & space

Triangle angles sum to \( 180^{\circ} \); a quadrilateral to \( 360^{\circ} \). Pythagoras: \( a^2+b^2=c^2 \). Circle area \( \pi r^2 \), circumference \( 2\pi r \).

Triangle
angles \( =180^{\circ} \)
Rectangle
\( A=bh \)
Circle
\( A=\pi r^{2} \)
Pythagoras
\( a^{2}+b^{2}=c^{2} \)
Worked example 4.A

A right triangle has legs \( 6 \) and \( 8 \). Find the hypotenuse. \[ \sqrt{6^{2}+8^{2}}=10. \]

Worked example 4.B

Find the area of a circle with \( r=7 \), taking \( \pi=\tfrac{22}{7} \). \[ \tfrac{22}{7}\times49=154. \]

Practice Problem

A rectangle has length \((2x+3)\) cm and width \((x+1)\) cm with perimeter 38 cm. Find the area.

Show solution
\(2[(2x+3)+(x+1)]=38\Rightarrow3x+4=19\Rightarrow x=5.\) Length\(=13\) cm, Width\(=6\) cm. Area\(=78\) cm\(^2.\)

📝 Chapter Quiz
5

Quantitative Comparisons

GAT Qudrat — Quantitative Ch.5 QC Questions No calculator

The question type most associated with Qudrat: two quantities, A and B, and a single decision to make.

● The four responses

Choose: A > B, A < B, A = B, or cannot be determined — the last when the relationship changes depending on unknown values. Always test convenient numbers before deciding.

Here \( A=2x \) and \( B=x+3 \). Slide \( x \): notice the order of A and B flips, so with \( x \) unknown the honest answer is "cannot be determined".

⊙ Explorer · A vs Binteractive
A = 2x
B = x + 3
relationship

They are equal at \( x=3 \); to the left \( B \) leads, to the right \( A \) leads.

Worked example 5.A

A: \( 25\% \) of \( 80 \).   B: \( 20 \). Compare. \( 25\% \) of \( 80=20 \), so \[ A=B. \]

Worked example 5.B

A: \( x \).   B: \( x^{2} \), for a real number \( x \). Compare. If \( x=\tfrac12 \) then \( B<A \); if \( x=2 \) then \( B>A \). Therefore \[ \text{cannot be determined.} \]

▲ Quantitative comparison strategy

Each QC question gives two quantities, A and B. You choose: A>B, B>A, A=B, or cannot be determined. Plug in special values (0, 1, −1, fractions) to test.

Strategy 1
Simplify both columns algebraically before comparing
Strategy 2
Plug in 0, 1, −1, ½ to check if relationship is constant
Strategy 3
If a variable could make either column larger: "cannot determine"
Geometry tip
Draw a diagram; do not assume figures are to scale
Worked example

Column A: \( x^2 \). Column B: \( x \). Compare. If \( x=2 \): \( 4>2 \). If \( x=\frac{1}{2} \): \( \frac{1}{4}<\frac{1}{2} \). If \( x=0 \): equal. → Cannot be determined.

Practice Problem

Quantity A: \((x-3)^2\)   Quantity B: \(x^2-6x+9\) for any real \(x\). Compare.

Show solution
Expand A: \((x-3)^2=x^2-6x+9.\) A = B (always).

📝 Chapter Quiz
6

Sequences & Patterns

GAT Qudrat — Quantitative Ch.6 Sequences No calculator

Spotting the rule behind a list of numbers — arithmetic, geometric, or a quick visual pattern.

▲ Reference — Two key sequences

Arithmetic adds a constant difference \( d \): the \( n \)th term is \( a+(n-1)d \). Geometric multiplies by a constant ratio \( r \): the \( n \)th term is \( ar^{\,n-1} \).

Arithmetic
\( a+(n-1)d \)
Geometric
\( ar^{\,n-1} \)
First n integers
\( \tfrac{n(n+1)}{2} \)
Look for
difference or ratio
Worked example 6.A

Find the next term: \( 2,\,4,\,8,\,16,\ldots \) Geometric, ratio \( 2 \): \[ 32. \]

Worked example 6.B

Find the \( 10 \)th term of \( 5,\,8,\,11,\ldots \) \[ 5+9\times3=32. \]

Worked example 6.C

The sequence \(1,4,9,16,25,\ldots\) What is the 8th term? These are perfect squares: \(n^2.\) So the 8th term is \(8^2=64.\)

Practice Problem

An arithmetic sequence has first term 7 and common difference 5. Which term equals 82?

Show solution
\(7+(n-1)\cdot5=82\Rightarrow n-1=15\Rightarrow n=16.\) The 16th term.

📝 Chapter Quiz
7

Data Analysis & Probability

GAT Qudrat — Quantitative Ch.7 Data No calculator

Reading values from tables and charts, summarising with mean, median and mode, and computing simple probabilities.

▲ Reference — Summaries & chance

Mean is the total divided by the count; the median is the middle of the ordered list; the mode is the most frequent value. Probability of an event is \( \dfrac{\text{favourable}}{\text{total}} \).

Mean
\( \dfrac{\text{sum}}{\text{count}} \)
Median
middle (ordered)
Mode
most frequent
Probability
\( \dfrac{\text{favourable}}{\text{total}} \)
Worked example 7.A

Find the mean of \( 4,\,6,\,8,\,10,\,12 \). \[ \frac{40}{5}=8. \]

Worked example 7.B

A bag holds 2 red and 3 green balls. Find \( P(\text{red}) \). \[ \frac{2}{5}. \]

Practice Problem

Ages of 7 students: 14, 16, 14, 17, 15, 14, 18. Find mean, median, and mode.

Show solution
Ordered: 14,14,14,15,16,17,18. Mean\(=108/7\approx15.4.\) Median\(=15\) (4th value). Mode\(=14.\)

📝 Chapter Quiz
8

Word Problems & Reasoning

GAT Qudrat — Quantitative Ch.8 Word Problems No calculator

Many Qudrat items are short word problems testing translation into arithmetic or algebra and logical deduction.

▲ Reference — Strategy

Translate the words into an equation, work backwards from the answer choices, and estimate to eliminate. Always check units and whether the answer is reasonable.

Translate
to an equation
Backsolve
test the choices
Estimate
& eliminate
Check
units & sense
Worked example 8.A

A number increased by \( 6 \) equals \( 20 \). Find the number. \[ x+6=20\Rightarrow x=14. \]

Worked example 8.B

A car travels 240 km in 3 hours. At the same speed, how far in 5 hours? Speed \(=240/3=80\) km/h. Distance \(=80\times5=400\) km.

Practice Problem

Ahmad earns 1200 SAR/month and saves \(\frac{1}{4}\) of it. After 8 months he buys a device for 1800 SAR. How much remains?

Show solution
Monthly savings\(=1200\times\frac{1}{4}=300\) SAR. Total saved\(=300\times8=2400\) SAR. Remaining\(=2400-1800=600\) SAR.

📝 Chapter Quiz
§

Practice set

Fifty exam-style problems across all chapters — including a block of quantitative comparisons — tagged by difficulty. Click any problem for a full worked solution.

1

Find \( 15\% \) of \( 200 \).

Basic
\[ \tfrac{15}{100}\times200=30. \]
2

Find \( \tfrac35 \) of \( 60 \).

Basic
\[ \tfrac35\times60=36. \]
3

Compute \( 0.25\times80 \).

Basic
\[ \tfrac14\times80=20. \]
4

Which is larger, \( \tfrac23 \) or \( \tfrac35 \)?

Intermediate

Cross-multiply: \( 2\cdot5=10>3\cdot3=9 \).

\[ \tfrac23>\tfrac35. \]
5

Find the remainder when \( 47 \) is divided by \( 6 \).

Intermediate

\( 6\times7=42 \), remainder \( 47-42 \):

\[ 5. \]
6

Find the average of \( 12,\,18,\,30 \).

Intermediate
\[ \frac{60}{3}=20. \]
7

Evaluate \( 7^{2}-3^{2} \).

Intermediate
\[ 49-9=40. \]
8

If \( 5x=35 \), find \( x^{2} \).

Advanced

\( x=7 \), so \( x^{2}=49 \):

\[ 49. \]
9

Simplify the ratio \( 8:12 \).

Basic
\[ 8:12=2:3. \]
10

Increase \( 50 \) by \( 20\% \).

Intermediate
\[ 50\times1.2=60. \]
11

Decrease \( 90 \) by \( 10\% \).

Intermediate
\[ 90\times0.9=81. \]
12

Share \( 150 \) in the ratio \( 2:3 \).

Intermediate

Five parts, each \( 30 \):

\[ 60\ \text{and}\ 90. \]
13

If \( 3 \) pens cost \( 12 \), what do \( 5 \) pens cost?

Intermediate

One pen costs \( 4 \):

\[ 5\times4=20. \]
14

What percentage is \( 18 \) of \( 72 \)?

Intermediate
\[ \frac{18}{72}=\tfrac14=25\%. \]
15

A price of \( 100 \) rises \( 10\% \), then falls \( 10\% \). Find the net percentage change.

Advanced

\( 100\to110\to99 \):

\[ -1\%. \]
16

\( 40\% \) of a number is \( 32 \). Find the number.

Intermediate
\[ \frac{32}{0.4}=80. \]
17

Solve \( 2x+5=17 \).

Basic
\[ 2x=12,\qquad x=6. \]
18

Simplify \( 3a+2a-a \).

Basic
\[ 4a. \]
19

If \( x+y=10 \) and \( x-y=4 \), find \( x \).

Intermediate

Add: \( 2x=14 \):

\[ x=7. \]
20

Solve \( \tfrac{x}{3}=9 \).

Intermediate
\[ x=27. \]
21

Find the value of \( 3x-2 \) when \( x=4 \).

Intermediate
\[ 12-2=10. \]
22

Solve \( 2(x-3)=8 \).

Intermediate

\( x-3=4 \):

\[ x=7. \]
23

If \( a^{2}=49 \) and \( a<0 \), find \( a \).

Advanced
\[ a=-7. \]
24

Expand \( (x+2)(x+3) \).

Intermediate
\[ x^{2}+5x+6. \]
25

Solve the inequality \( x+4>9 \).

Intermediate
\[ x>5. \]
26

If \( 2^{x}=16 \), find \( x \).

Advanced
\[ 2^{4}=16\Rightarrow x=4. \]
27

Two angles of a triangle are \( 50^{\circ} \) and \( 60^{\circ} \). Find the third.

Basic
\[ 180^{\circ}-110^{\circ}=70^{\circ}. \]
28

Find the area of a rectangle \( 7\times6 \).

Intermediate
\[ 7\times6=42. \]
29

Find the perimeter of a square of side \( 9 \).

Intermediate
\[ 4\times9=36. \]
30

Find the area of a circle with \( r=7 \), taking \( \pi=\tfrac{22}{7} \).

Intermediate
\[ \tfrac{22}{7}\times49=154. \]
31

A right triangle has legs \( 6 \) and \( 8 \). Find the hypotenuse.

Intermediate
\[ \sqrt{36+64}=10. \]
32

Find the sum of the interior angles of a quadrilateral.

Intermediate
\[ 360^{\circ}. \]
33

Find the volume of a cube of side \( 5 \).

Advanced
\[ 5^{3}=125. \]
34

Two angles lie on a straight line; one is \( 130^{\circ} \). Find the other.

Intermediate
\[ 180^{\circ}-130^{\circ}=50^{\circ}. \]
35

Comparison. A: \( 25\% \) of \( 80 \).   B: \( 20 \).

Intermediate

\( 25\% \) of \( 80=20 \):

\[ A=B. \]
36

Comparison. A: \( 3^{2} \).   B: \( 2^{3} \).

Intermediate

\( 9 \) versus \( 8 \):

\[ A>B. \]
37

Comparison. A: the average of \( 10 \) and \( 20 \).   B: \( 15 \).

Intermediate

\( \tfrac{10+20}{2}=15 \):

\[ A=B. \]
38

Comparison. A: \( x \).   B: \( x^{2} \), for a real number \( x \).

Advanced

\( x=\tfrac12\Rightarrow B<A \); \( x=2\Rightarrow B>A \):

\[ \text{cannot be determined.} \]
39

Comparison. A: \( \tfrac12 \).   B: \( 0.4 \).

Intermediate

\( 0.5>0.4 \):

\[ A>B. \]
40

Comparison. A: perimeter of a square of side \( 4 \).   B: perimeter of a \( 3\times5 \) rectangle.

Advanced

\( 16 \) versus \( 2(3+5)=16 \):

\[ A=B. \]
41

Comparison. A: \( 2x+1 \).   B: \( 2x+3 \).

Advanced

B exceeds A by \( 2 \) for every \( x \):

\[ A<B. \]
42

Comparison. A: \( (-3)^{2} \).   B: \( -(3^{2}) \).

Advanced

\( 9 \) versus \( -9 \):

\[ A>B. \]
43

Find the next term: \( 2,\,4,\,8,\,16,\ldots \)

Basic
\[ 32. \]
44

Find the next term: \( 3,\,7,\,11,\,15,\ldots \)

Intermediate

Add \( 4 \):

\[ 19. \]
45

Find the \( 10 \)th term of \( 5,\,8,\,11,\ldots \)

Intermediate
\[ 5+9\times3=32. \]
46

Find \( 1+2+3+\cdots+10 \).

Advanced
\[ \frac{10\times11}{2}=55. \]
47

Find the mean of \( 4,\,6,\,8,\,10,\,12 \).

Basic
\[ \frac{40}{5}=8. \]
48

Find the median of \( 3,\,9,\,5,\,1,\,7 \).

Intermediate

Ordered \( 1,3,5,7,9 \); middle:

\[ 5. \]
49

A fair die is rolled. Find \( P(\text{result} > 4) \).

Intermediate

Favourable: \( 5,6 \):

\[ \frac{2}{6}=\tfrac13. \]
50

A bag holds 2 red and 3 green balls. Find \( P(\text{red}) \).

Advanced
\[ \frac{2}{5}. \]

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Full official exam paper

Based on the Saudi GAT Qudrat exam: 52 quantitative questions in 52 minutes. Includes standard MCQ and Quantitative Comparison items (Arabic/English bilingual). No calculator.

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