(1)  Five apples and 6 bananas together cost as much as 8 bananas and 9 pears.  One apple costs as much as 2 pears.  For the same price as 1 pear, how many bananas could be bought?

(A)  1  (B)  2  (C)  3  (D)  4  (E)  6


(2)  Let R = 8 · 9 · 7 · 13 and S = 4 · 6 · 11 · 49.  The greatest common factor of R and S is

(A)  12  (B)  42  (C)  56  (D)  168  (E)  504


(3)  What is the value of 4|x – y| - 3|xy| if x = -5 and y = 2?

(A)  -42  (B)  -18  (C)  -2  (D)  42  (E)  58


(4)  In the following sequence of eight numbers, each number has one more “1” than the number before it:

2, 12, 112, 1112,. . . . , 11111112

What is the hundreds digit in the sum of all eight of these numbers?

(A)  0  (B)  6  (C)  7  (D)  8  (E)  9


(5)  In Ms. Hsiao’s class there are twice as many boys as there are girls.  Half of the boys are in the math club and all of the girls are in the math club.  What percent of Ms. Hsiao’s class is in the math club?

(A)  25%  (B)  33  (1/3)%  (C)  50%

(D)  66 (2/3)%  (E)  75%


(6)  (16 + 5x) – (8 – 2x) =

(A)  8 + 3x  (B)  8 - 3x (C)  8 - 7x

(D)  8 + 7x (E)  24 - 7x


(7)  The three lines shown intersect in a point.  The value of x

(A)  is 100.  (B)  is 80.  (C)  is 50.  (D)  is 20. 

(E)  cannot be determined from the given information


(8)  The straight line graph shows how many people are in a large cafeteria eating lunch at different times.  If the people leave at a steady rate, at what time will oly 150 people remain?

(A)  1:15 P.M.  (B)  1:30 P.M.  (C)  1:45 P.M. 

(D)  2:15 P.M.  (E)  3:30 P.M.


(9)  Two congruent circles have centers P and Q as shown.  What is the measure of angle PXQ?

(A)  30°  (B)  45°  (C)  55°  (D)  60°  (E)  75°


(10)  Andrew has d dollars.  He has one-third as many dollars as Bruce has.  Carlos has $80 less than half the total of Andrew’s and Bruce’s dollars.  In terms of d, how many dollars does Carlos have?

(A)  4d – 40  (B)  2d – 40  (C)  2d + 40 

(D)  2d + 80  (E)  2d – 80


(11)  The sum of 7 unequal positive integers is 61.  What is the largest possible value that any of those integers can have?

(A)  55  (B)  40  (C)  39  (D)  13  (E)  9


(12)  In the set {1, 5, x, 10, 15}, the integer x is the median.  The mean of the five numbers is one less than x.  The value of x is

(A)  6  (B)  7  (C)  8  (D)  9  (E)  none of these.


(13)  If 7/50 < 1/x < 8/51 where x is an integer, then x =

(A)  8  (B)  7  (C)  6  (D)  5  (E)  4


(14)  Half of 28 is

(A)  27 (B)  26 (C)  24 (D)  18  (E)  8


(15)  If x is greater than 1/2 but less than 1, which of the following has the largest value?

(A)  2x – 1  (B)  x2  (C)  1/x  (D)  1 – x  (E)  x3 


(16)  Maria, Anoki, and Boris are teenagers, and the sum of their ages now is 49.  The sum of their ages 8 years from now will be F, and the sum of their ages 10 years ago was P.  The value of F – P is

(A)  54  (B)  18  (C)  17  (D)  6  (E)  2


(17)  If (1/4) + (1/x) = 1, then x =

(A)  1/8  (B)  2/3  (C)  4/3  (D)  2  (E)  3


(18)  When the integer N is divided by 7,  the quotient is Q and the remainder is 5.  When N + 24 is divided by 7, the remainder is ‘

(A)  4  (B)  3  (C)  2  (D)  1  (E)  0


(19)  Point B is on line segment AD, and point E is on line segment BC.  The value of x is

(A)  20  (B)  40  (C)  50  (D)  60  (E)  70


(20)  Three-fourths of a number is equal to L.  What is three-halves of that original number, in terms of L?

(A)  4/3L  (B)  3/2L  (C)  2L  (D)  3L  (E)  4L


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Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power


Quantitative aptitude

Multiplication tricks


Aptitude test online


Test - I

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Horizontal translation

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Converting customary units worksheet

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Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet



Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem


Mensuration formulas

Area and perimeter



Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

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Construction of angles - II

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Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem


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Area of triangle

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Matrix Calculators

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Missing addend 

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Direct proportion and inverse proportion

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Unitary method direct variation

Unitary method inverse variation

Unitary method time and work


Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry


Converting metric units

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HCF and LCM  word problems

Word problems on simple equations 

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Algebra word problems

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Word problems on direct variation and inverse variation 

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Converting customary units word problems 

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Word problems on simple interest

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Complementary and supplementary angles word problems

Double facts word problems

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Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

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Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree


Profit and loss shortcuts

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Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

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