Olympiad Mathematics - Integers
Exam Duration: 45 Mins Total Questions : 30
What do we call the set of negative numbers and whole numbers?
- (a)
Natural numbers
- (b)
Integers
- (c)
Positive numbers
- (d)
The set of whole numbers.
The set of negative numbers and whole numbers is called integers. Z = (,..........-2, -1,0,1,2, ..........)
Which of the following is the smallest positive integer?
- (a)
0
- (b)
100
- (c)
1
- (d)
9
1 is the smallest positive integer.
Where are the negative numbers located on a horizontal number line?
- (a)
On the right of 0
- (b)
On the left of 0
- (c)
Above 0
- (d)
Below 0
All the other positve numbers to its right are greater than, the negative numbers are located on the leftside of 0.
What is the opposite of earning Rs 100?
- (a)
+ Rs 100
- (b)
Profit of Rs 100
- (c)
Gain of Rs 100
- (d)
Spending Rs 100
The required opposite is spending Rs 100.
How is the withdrawal of Rs 200 represented?
- (a)
Depositing Rs 200
- (b)
- Rs 200
- (c)
Rs 200
- (d)
-200
Calculate (-32) \(\times\) (-4) \(\times\) (-3) \(\times\) 0 \(\times\) (-6).
- (a)
27648
- (b)
276480
- (c)
0
- (d)
-27648
(-32) \(\times\) (-4) \(\times\) (-3) \(\times\) 0 \(\times\) (-6) = 0 as the product of any number and 0 is 0.
If the dividend and divisor have unlike signs, what is the sign of the quotient?
- (a)
Positive
- (b)
Negative
- (c)
Zero
- (d)
Indeterminate
Match the following.
Column ·1 | Column -II | |||
---|---|---|---|---|
(i) | (132)\(\div \)(-12) | ( ) | (a) | 49 |
(ii) | (-144) \(\div \) (+16) | ( ) | (b) | 8 |
(iii) | (-32) \(\div \) (-4) | ( ) | (c) | (-9) |
(iv) | (196)\(\div \)(4) | ( ) | (d) | (-11) |
- (a)
(i)-(b), (ii)-(a), (iii)-(c), (iv)-(d)
- (b)
(i)-(a), (ii)-(b), (iii)-(d), (iv)-(c)
- (c)
(i)-(d), (ii)-(c), (iii)-(b), (iv)-(a)
- (d)
(i)-(c), (ii)-(d), (iii)-(a), (iv)-(b)
What is the additive identity for the set of integers?
- (a)
0
- (b)
(-1)
- (c)
1
- (d)
+10
0 is identity element with respect to addition of integers. e.g., (-5) + 0 = + 0 + (-5) = (-5).
Which of the following orders is used while evaluating an expression?
- (a)
[]. (), {}
- (b)
{}, (), []
- (c)
(), {}, []
- (d)
(), [], {}
( ), { }, [ ] is the correct order of evaluation of brackets.
What is the value of the expression 7 - [13 - {-2 - 6 (6 of -5)}]?
- (a)
-172
- (b)
180
- (c)
172
- (d)
0
Use of the order of removal of brackets and simplifY.
7 - [13 - {-2 -6 (6 of -5)}]
= 7 - [13 - {-2 -6 \(\times\) -30)] = 172
Over which of the following operations is multiplication distributed in the set of integers?
- (a)
-, \(\div \)
- (b)
-, \(\times\)
- (c)
+, -
- (d)
\(\times\), \(\div \)
The sum of two integers is 62. If one of the integers is -48, what is the other?
- (a)
14
- (b)
-14
- (c)
-110
- (d)
110
x + (-48) = 62, where x is the unknown integer.
\(\Rightarrow\) x = 62-(-48)
= 62 + 48 = 110
The product of two integers is -48. If one of the integers is -6, what is the value of the other?
- (a)
1
- (b)
288
- (c)
0
- (d)
8
P \(\times\) -6 = -48, where P is the unknown integer.
\(\Rightarrow\) P = -48 \(\div \) -6 = 8
A man walked 3 km towards North then 8 km towards South. What is his final position with respect to his initial position?
- (a)
5 km towards East
- (b)
3 km towards South
- (c)
8 km towards North
- (d)
5 km towards South
In a quiz, positive marks were given for correct answers and negative marks for incorrect answers. If Guru's scores in five successive rounds were 35, - 10, -15, 20 and 5, what is his total score at the end?
- (a)
25
- (b)
35
- (c)
45
- (d)
55
35 + (-10) + (-15) + 20 + 5
= 35 - 10 - 15 + 20 + 5
= 35 - 25 + 25 = 35
In a class test containing 10 questions, 3 marks are awarded for every correct answer and (-1) mark is awarded for every incorrect answer and 0 for the questions not attempted. Srinu gets two correct and six incorrect answers out of eight questions he attempts. What is his total score?
- (a)
0
- (b)
2
- (c)
-2
- (d)
6
Of the 10 questions in the test, 2 are correct and 6 are incorrect 2 are not attempted. So, the total score
= 2 \(\times\) (+3) + 6 \(\times\) (-1) + 2 \(\times\) (0)
=6 - 6 + 0 = 0
What should be multiplied by (-12) in order to get 180?
- (a)
15
- (b)
-15
- (c)
16
- (d)
-16
Let the unknown number be x. Then x \(\times\) (-12) = 180
\(\Rightarrow \quad x=\frac { 180 }{ -12 } =-\frac { 180 }{ 12 } =-15\)
Which of the following statements holds correct?
- (a)
N \(\subset \) W \(\subset \) Z
- (b)
Z\(\subset \) N \(\subset \)W
- (c)
W\(\subset \) N \(\subset \)Z
- (d)
Z\(\subset \) W\(\subset \) N
The quotient of two numbers is (-17). If one of the numbers is (-340), what is the other number?
- (a)
20
- (b)
17
- (c)
(-20)
- (d)
(-30)
Evaluate: \(\frac { (-16)\div [(-13)+(-3)] }{ (-60)\div (-60) } \)
- (a)
2
- (b)
-1
- (c)
1
- (d)
-2
Which of the following statements is INCORRECT?
- (a)
The multiplicative identity for integers is 1.
- (b)
Subtraction does not obey commutative law in integers.
- (c)
Multiplication of two integers with unlike signs is always positive.
- (d)
Multiplicative inverse of integer a is \(\frac { 1 }{ a } \)
Multiplication of two integers with unlike signs is always negative.
The value of (- 5) \(\times\) (- 4) \(\times\) (- 3) \(\times\) (- 2) \(\times\) (-1) \(\times\) 0 + 0 \(\times\) (1) \(\times\) (2) \(\times\) (3) \(\times\) (4) \(\times\) (5) is ______________
- (a)
120
- (b)
- 120
- (c)
240
- (d)
0
We have, (-5) \(\times\) (-4) \(\times\) (-3) \(\times\) (-2) \(\times\) (-1) \(\times\)0 + 0 \(\times\)1\(\times\) 2 \(\times\) 3 \(\times\) 4 \(\times\) 5 = 0 + 0 = 0
Which of the following statements is CORRECT?
Statement-1 : When a positive integer and a negative integer are added, we always get a negative integer.
Statement-2 : When two negative integers are added, we get a positive integer.
- (a)
Only Statement-1
- (b)
Only Statement-2
- (c)
Both Statement-1 and Statement-2
- (d)
Neither Statement-1 nor Statement-2
When a positive integer and a negative integer are added, we can get a positive or negative integer. \(\therefore\) Statement 1 is false. And when two negative integers are added, we get a negative integer. \(\therefore\) Statement 2 is false
The value of [(- 4) \(\times\) (-9) \(\times\) (-25)] \(\div \) [(-2) \(\times\)(-3) \(\times\)(-5)] is ______________
- (a)
10
- (b)
20
- (c)
30
- (d)
40
Find the value of the given expression (- 45) - (-39) + 42 - 28 - (-152) - 85 + (-9).
- (a)
- 78
- (b)
- 32
- (c)
- 550
- (d)
66
In my accounts book, I write positive numbers for profits and negative numbers for losses that I make in my business. Following are the entries in the book for the last seven days: 21, -19, 11, -20, 17, 25 and -13. How much profit did I make in the last week?
- (a)
32
- (b)
22
- (c)
34
- (d)
24
Profit made by me = 21 + 11 + 17 + 25 = 74
Loss made by me = -19 - 20 - 13 = - 52
Net profit made by me = 74 + (-52) = 74 - 52 = 22
An elevator descends into a mine shaft at the rate of 8 m/min. If the descend starts from 12 m above the ground level, how long will it take to reach -468 m?
- (a)
60 mins
- (b)
30 mins
- (c)
50 mins
- (d)
10 mins
Total distance covered from A to C
= ( 12 + 468)m = 480 m
Speed = 8 m/min
\(\therefore\) Time
\(=\frac { Total\quad distance\quad covered }{ Speed } \)
\(=\frac { 480 }{ 8 } =60\quad minutes\)
Pooja makes a profit of Rs 9 on every large basket she sells and a loss of Rs 4 on every small basket. She cannot make only large baskets as buyers require baskets of both sizes.
(i) If she gets an order to supply 7200 large baskets and 11,200 small baskets, what is the profit or loss she will be making from this order?
(ii) If in the next order she has to supply 8100 small baskets, then how many large baskets does she need to sell so that she will make neither profit nor loss?
- (a)
(i) (ii) Loss of Rs 20000 3000 - (b)
(i) (ii) Profit of Rs 20000 3600 - (c)
(i) (ii) Loss of Rs 25000 3600 - (d)
(i) (ii) Profit of Rs 30000 2000
(i) Profit on large baskets
= Rs (7200 \(\times\) 9) = Rs 64800
Loss on small baskets = Rs (11200 \(\times\) 4) = Rs 44800
Profit = Rs (64800 - 44800) = Rs 20000
(ii) Number of small baskets = 8100
Loss on 8100 small baskets = Rs (8100 \(\times\) 4)
= Rs 32400
Let number of large baskets be \(\times\)
\(\therefore\) Profit on large baskets = Rs 32400
\(\Rightarrow \quad 9x=32400\Rightarrow x=\frac { 32400 }{ 9 } \Rightarrow x=3600\)
Match the following.
(i) For any two integers a and b, \(\times\)a b is also an integer. Thus, integers are | (a) Distributive under addition and multiplication |
(ii) a \(\times\) b = b \(\times\) a; this denotes that integers are | (b) Positive quotient |
(iii) a \(\times\) (b + c) = a \(\times\) b + a \(\times\) c; this denotes that | (c) Closed under multiplication |
(iv) The division of a negative integer by another negative integer results in | (d) Commutative under multiplication |
- (a)
(i) \(\rightarrow\) (b), (ii) \(\rightarrow\) (c), (iii) \(\rightarrow\) (d), (iv) \(\rightarrow\) (a)
- (b)
(i) \(\rightarrow\) (c), (ii) \(\rightarrow\) (d), (iii) \(\rightarrow\) (a), (iv) \(\rightarrow\) (b)
- (c)
(i) \(\rightarrow\) (d), (ii) \(\rightarrow\) (c), (iii) \(\rightarrow\) (a), (iv) \(\rightarrow\) (b)
- (d)
(i) \(\rightarrow\) (c), (ii) \(\rightarrow\) (d), (iii) \(\rightarrow\) (b), (iv) \(\rightarrow\) (a)