Olympiad Mathematics - Algebra
Exam Duration: 45 Mins Total Questions : 30
What do literals usually represent?
- (a)
Known quantities
- (b)
Variables
- (c)
Constants
- (d)
Depends on the problem.
Literals usually represent variables.
What is the number of sides of an equation?
- (a)
2
- (b)
3
- (c)
4
- (d)
0
Find the value of p if \(\frac { p }{ 4 } \) =12
- (a)
48
- (b)
-48
- (c)
-24
- (d)
24
Choose a value of 'a' that satisfies the equation 6a = -30.
- (a)
5
- (b)
30
- (c)
-5
- (d)
10
6a = - 30
⇒ a =\(\frac { -30 }{ 6 } \)= -5
For what value of 'a' is 6(2a -1) + 8 = 14 true?
- (a)
-1
- (b)
3\(\frac { 1 }{ 2 } \)
- (c)
1\(\frac { 3 }{ 12 } \)
- (d)
1
Determine the value of x given 6x-1 = 2x + 9
- (a)
1\(\frac { 1 }{ 2 } \)
- (b)
-2\(\frac { 1 }{ 2 } \)
- (c)
\(\frac { 4 }{ 10 } \)
- (d)
2\(\frac { 1 }{ 2 } \)
In the given figure, what are the magnitudes of the angles shown?
- (a)
40o,135o
- (b)
45o,130o
- (c)
45o,135o
- (d)
180o
From the figure,
xo+ 3xo = 180o (straight angle)
⇒ 4xo = 180o
⇒ xo= 45o
:. 3xo = 3\(\times\)45° = 135°
Which of the following is the perimeter of a regular hexagon of side's' units?
- (a)
6 s units
- (b)
12 s units
- (c)
6 s2 sq units
- (d)
-6 s units
A reqular hexagon has 6 equal sides.
Hence perimeter = 6s units.
In a piggy bank the number of 25 pa!se coins is five times the number of 50 parse coins.If there are 120 coins, find the amount in the bank
- (a)
Rs.25
- (b)
Rs.10
- (c)
Rs.35
- (d)
Rs.40
Let the number of 50 paise coins be x.
⇒ 25 paise coins = 5x
Given that total coins = 120
⇒ 6x =120
⇒ x=\(\frac { 120 }{ 6 } \) =20
∴ 50 paise coins = 20
⇒ Amount = 20\(\times\)50 P = Rs.10
Value of 25 paise coins
=25p\(\times\)5\(\times\)20
=25p\(\times\)100 =Rs.25
∴ Total amount Rs(25+10) =Rs.35
If half of a number is added to 18, the sum is 46. What is the number?
- (a)
92
- (b)
56
- (c)
65
- (d)
0
Determine the coefficient of x in \(4y-\frac { x }{ y } \)
- (a)
-\(\frac { 1 }{ 7 } \)
- (b)
\(\frac { 1 }{ 7 } \)
- (c)
4
- (d)
-4
Karan is x years old. His brother is twice his age.What is the sum of their ages?
- (a)
\(\frac { 3 }{ 2 } \) x years
- (b)
x years
- (c)
3x years
- (d)
2x years
Which is the correct expression for '-p multiplied by 5' ?
- (a)
-(-5p)
- (b)
-p+5
- (c)
-5p
- (d)
5-p
Madhu buys 'p' oranges at 50 paise each and 'q' mangoes at Rs.0.60 each. How much does he pay for the fruits?
- (a)
(0.5 P + 0.6 q) paise
- (b)
Rs (50 P + 6q) paise
- (c)
Rs (50 P + 60q) paise
- (d)
(0.5 P + 60 q) paise
The table shows the values of m + 7 for different values of m.By inspection, find the solution of m + 7 = 12
m | 1 | 2 | 3 | 4 | 5 |
m+7 | 8 | 9 | 10 | 11 | 12 |
- (a)
m =4
- (b)
m =5
- (c)
m =2
- (d)
m =3
Identify the equation with one variable from the following
- (a)
x+12>24
- (b)
20-(10-5)= (3\(\times\)5)
- (c)
2n+1 =11
- (d)
\(\frac { 3q }{ 2 } \)< 0
An equation with one variable has equality sign (=) and a variable (n in this case).
Choose the set that has the solution for the equation n + 8 = 20
- (a)
(12,8,20,0)
- (b)
(-2,0,2,4)
- (c)
(7,2,10,14)
- (d)
(4,-4,2,0)
n + 8 = 20 ⇒ n = 12
By trial and error method, substitute values from each set and find the solution.
In a party room, 20 workers decorate 70 tables. Each table is decorated with 10 silver balloons and 15 gold balloons. Which equation could be used to find x, the total number of silver and gold balloons needed to decorate all the tables?
- (a)
x = 70 (10 + 15)
- (b)
x = 15 (70 + 10)
- (c)
x = 70 + (10\(\times\)15)
- (d)
x = 20 (70 + 10 + 15)
Number of tables = 70
Total number of silver and gold balloons
used to decorate each table = 10 + 15
∴ The required equation isx = 70 (10 + 15)
P\(\times\)1000ml=7.65l What is the value of P?
- (a)
7.65
- (b)
76.5
- (c)
765
- (d)
7650
1000 ml = 1 litre
∴ 7.65\(\times\)1000ml=7.65 l
A paper file costs Rs.80 and a plastic file costs Rs.1.50.Suman bought x paper files and y plastic files. How many rupees should she pay the shopkeeper?
- (a)
8y+15x
- (b)
8x+15y
- (c)
80x+1500y
- (d)
0.8x+1.5y
Cost of a paper file Rs.0.80
∴ Cost of x paper files = Rs.0.80x
cost of a plastic file= Rs.150
∴ Cost of y plastic files =Rs.1.50y
Total amount to be paid to the shopkeeper =Rs.(0.80x+1.50y)
When Raju multiplies a certain number by 17 and adds 4 to the product, he gets 225. Find the number.
- (a)
13
- (b)
14
- (c)
15
- (d)
16
Let the number be x.
According to question,
17x + 4 = 225
\(\Rightarrow\)17x = 225 - 4 = 221 \(\Rightarrow\) x = \(\frac{221}{17}\) = 13
Which of the following equations justify the given statement? "Perimeter of an equilateral triangle is three times its side l".
- (a)
l x l x l
- (b)
3 x 3 x 3
- (c)
3 x l
- (d)
3 + l
If twelve less than 3 times a number is 27, then the number is______________.
- (a)
29
- (b)
39
- (c)
65
- (d)
13
Let the number be x.
According to question,
3x - 12 = 27 \(\Rightarrow\) 3x = 39
\(\Rightarrow\)x=\(\frac{39}{13}\)=13
The number of girls in a class is 3 times the number of boys. Which of the following cannot be the total number of students in the class?
- (a)
24
- (b)
32
- (c)
36
- (d)
41
Let the number of boys be x.
\(\therefore\)Number of girls = 3x
If x + 3x = 41
\(\Rightarrow\)4x = 41 \(\Rightarrow\) x = \(\frac{41}{4}\)
And we know that the number of students can't be in fraction.
The algebraic expression for the statement 'Thrice of x is added to y multiplied by itself' is____________.
- (a)
3x+ 2y
- (b)
3x + y2
- (c)
3(x + y2)
- (d)
3x+ Y
3(x) + y x y = 3x + y2
Preeti travelled 3x km distance by walk, 9y km by cycle and 5 km by bus. The total distance covered by Preeti is____________.
- (a)
(3x - 9y + 5) km
- (b)
(3x + 9y + 5) km
- (c)
(3x - 9y- 5) km
- (d)
(9x + 3y- 5) km
Total distance covered by Preeti = (3x + 9y + 5) km
Meera bought packs of trading cards that contain 10 cards each. She gave 7 cards to her friend.
x = Number of packs of trading cards
Which expression shows the number of cards left with Meera?
- (a)
10x-7
- (b)
7x-8
- (c)
5-10x
- (d)
8-5x
Number of cards in one pack = 10
\(\therefore\)Number of cards in x packs = 10x
\(\therefore\)Number of cards left with Meera = 10x- 7
Ashima bought 23 things from the market. She bought five more jeans than shirts and two fewer watches than jeans. If x ~ represents the number of shirts in total, then which mathematical statement can be used to find how many of each thing are bought?
- (a)
x + (x + 5) + (x + 3) = 23
- (b)
x + (x - 5) + (x - 3) = 23
- (c)
(x + 5) + (x + 3) = 23
- (d)
x + (x + 3) = 23
Number of shirts bought by Ashima = x
\(\therefore\)Number of jeans bought by her = x + 5
\(\therefore\)Number of watches bought by her
= (x + 5) - 2 = x + 3
\(\therefore\)Total number of things bought by her
= x + (x + 5) + (x + 3) = 23
Which of the following equations does not have a solution in integers?
- (a)
x + 1 = 1
- (b)
x - 1 = 3
- (c)
2x + 1 = 6
- (d)
1 - x = 5
(A) x + 1 = 1
\(\Rightarrow\)x+1-1=1-1
[Subtracting 1 from both sides]
\(\Rightarrow\)x = 0, which is an integer
(8) x - 1 = 3
\(\Rightarrow\)x-1+1=3+1
[Adding 1 to both sides]
\(\Rightarrow\) x = 4, which is an integer.
(C) 2x + 1 = 6
\(\Rightarrow\)2x + 1 - 1 = 6 - 1
[Subtracting 1 from both sides]
\(\Rightarrow\)\(\frac{2x}{2}\) = \(\frac{5}{2}\)
\(\Rightarrow\)x =\(\frac{5}{2}\), which is not an integer.
(D) 1 - x = 5
\(\Rightarrow\) 1-x-1=5-1
[Subtracting 1 from both sides]
\(\Rightarrow\) -x = 4
\(\Rightarrow\) -(-x) =-4
[Multiplying both sides by (-1)]
\(\Rightarrow\) x = -4, which is an integer.
Thus, the above conditions show that equation 2x + 1 = 6 does not have a solution in integers.
State 'T' for true and 'F' for false.
P. x = 15 is the solution of the equation 41 -x= 25.
Q. An equation is an algebraic expression which involves an "equal to" sign.
R. 'x exceeds y by 7' can be expressed as x = y + 7.
- (a)
P Q R
F T T - (b)
P Q R
F T F - (c)
P Q R
T F T - (d)
P Q R
T T T
P. 41 - x = 25 ~ 41 - x - 41 = 25 - 41
[Subtracting 41 from both sides]
\(\Rightarrow\)-x = -16
[Multiplying both sides by (-1)]
\(\Rightarrow\) -(-x) = -(-16)\(\Rightarrow\) x = 16