Olympiad Mathematics - Integers
Exam Duration: 45 Mins Total Questions : 30
What is the set of negative numbers and whole numbers called?
- (a)
The set of natural numbers
- (b)
The set of integers
- (c)
The set of positive numbers
- (d)
The set of negative numbers
The set of integers comprises negative numbers and whole numbers.
Which of the following is the greatest negative integer?
- (a)
-100
- (b)
Does not exist.
- (c)
-1
- (d)
-9
The greatest negative integer is - 1.
The opposite of -36 is 36. Which is the only integer that does not have an opposite?
- (a)
-100
- (b)
0
- (c)
No such number exists in Z.
- (d)
476
Which of these is the smallest positive integer?
- (a)
0
- (b)
100
- (c)
1
- (d)
9
To which side of 0 on a horizontal number line are the negative integers located?
- (a)
Right
- (b)
Left
- (c)
Above
- (d)
Below
Which symbol should be placed in the box to make -56 \(\Box\) -64 true?
- (a)
<
- (b)
=
- (c)
>
- (d)
Either (A) or (B).
Smaller number with a negative sign is larger.
Match the following:
Column -I | Column-II | |||
(i) | 36 + 14 | ( ) | (a) | 26 |
(ii) | 38 + (-12) | ( ) | (b) | 12 |
(iii) | (-18) + (30) | ( ) | (c) | -16 |
(iv) | (-7) + (-9) | ( ) | (d) | 50 |
- (a)
(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
- (b)
(i)-(d),(ii)-(a), (iii)-(b), (iv)-(c)
- (c)
(i)-(b), (ii)-(d), (iii)-(a), (iv)-(c)
- (d)
(i)-(c), (ii)-(d), (iii)-(a), (iv)-(b)
A thermometer that records a winter day's temperature at 5: 30 a.m.
If the temperature starts at -4°C, rises by 4°C, falls by 3 °C and then rises again by 6°C then what would be the final temperature?
- (a)
6 °C
- (b)
0 °C
- (c)
2 °C
- (d)
3 °C
(-4°C) + (4°C) + (-3°C) + (6°C)
= 3°C
A thermometer that records a winter day's temperature at 5: 30 a.m.
By how much will the temperature have risen if it registers 4 °C?
- (a)
12°C
- (b)
0°
- (c)
16 °C
- (d)
14°C
4 °C- (-12°C) = 4 °C + 12°C = 16 °C
What are the integers between -3 and 3?
- (a)
-4, -5, 4 and 5
- (b)
-2, - 1, 0, 1 and 2
- (c)
3, 4, 5, 6 and 7
- (d)
-3, -2, -1, 2 and -15
Between which two integers does -6 lie?
- (a)
-6 and 6
- (b)
7 and 5
- (c)
-7and-10
- (d)
-7and-5
In 0___,___(-3). what are the numbers that fill the blanks?
- (a)
-1 and -5
- (b)
-5 and -12
- (c)
-1 and -2
- (d)
1 and 2
Numbers between 0 & -3 are -1 and -2.
The following is an account of a shopkeeper that shows profit & loss from the sale of certain items.
Name of the item | Profit | Loss | Representation with sign |
Rice | ' 150 | ____ | A |
Wheat | ____ | 250 | B |
Sugar | ' 225 | ____ | ' 225 |
Groundnut oil | ____ | 330 | C |
Jowar | ' 200 | ____ | ' 200 |
What is the increasing order of the profit on different items?
- (a)
Rs 225, Rs 150, Rs 200
- (b)
Rs 150, Rs 200, Rs 225
- (c)
Rs 150, Rs 225, Rs 200
- (d)
Rs225,Rs 150, Rs 330
The ascending order of profit values =Rs 150, Rs 200, Rs 225
The following is an account of a shopkeeper that shows profit & loss from the sale of certain items.
Name of the item | Profit | Loss | Representation with sign |
Rice | ' 150 | ____ | A |
Wheat | ____ | 250 | B |
Sugar | ' 225 | ____ | ' 225 |
Groundnut oil | ____ | 330 | C |
Jowar | ' 200 | ____ | ' 200 |
What is the total profit or loss?
- (a)
Rs 5 loss
- (b)
No profit
- (c)
Rs 86 profit
- (d)
No loss
Total profit (or loss)
= Rs (150 + 200 + 225) -Rs(250 + 330)
= Rs 575 - Rs 580 = - Rs 5 = Rs 5 loss
Which is the largest of the integers -3, -10, -236, -15 ?
- (a)
-15
- (b)
-3
- (c)
-10
- (d)
-236
Which of the following lies between the integers -603 and -317?
- (a)
-450
- (b)
-680
- (c)
-315
- (d)
-630
The temperature of city A is -34 °C.lt falls by 18°C. What is the temperature after the fall?
- (a)
-34°C+ 18°C
- (b)
-34°C - 18°C
- (c)
18 °C - 34°C
- (d)
34 °C - 18°C
Ajay lives 3 km north of his school and Ajit lives 5 km south of school. How are distances of their houses from their school denoted?
- (a)
3 km, 5 km
- (b)
3 km, -5 km
- (c)
-3 km, 5 km
- (d)
-3 km, -5km
Which of the following statements is true? (If N, W and I represents Natural number, Whole number and Integer respectively.)
- (a)
N⊂W⊂I
- (b)
I⊂N⊂W
- (c)
W⊂N⊂I
- (d)
I⊂W⊂N
Select the CORRECT statement.
- (a)
If the dividend and divisor have opposite signs, then the quotient will be negative.
- (b)
If the two factors of a number are of same sign, then their product is positive.
- (c)
If the addends are of same sign, then sign of their sum is same as the sign of the addends.
- (d)
All of these
The value of (-172) + (-40) + 5 + (-425) + (-275) + 600 -(-15) is_____________.
- (a)
315
- (b)
-201
- (c)
400
- (d)
-292
We have,
(-172) + (-40) + 5 + (-425) + (-275) + 600 -(-15) = (-172 - 40 - 425 - 275) + (5 + 600 + 15) = -912 + 620 = -292
Arnav travelled to the school 10 km West from his house. He then travelled to the central library 35 km East from the school. Find the distance between the house and the central library.
- (a)
24 km
- (b)
25 km
- (c)
22 km
- (d)
23 km
Distance between the house and the central library = (35 - 10) km = 25 km
State 'T' for true and 'F' for false.
(i) Since 5 > 3, therefore -5 > -3.
(ii) The difference between an integer and its additive inverse is always even.
(iii) The sum of three different integers can never be zero.
(iv) All whole numbers are integers
- (a)
(i) (ii) (iii) (iv)
T F T F - (b)
(i) (ii) (iii) (iv)
F F T T - (c)
(i) (ii) (iii) (iv)
F T F T - (d)
(i) (ii) (iii) (iv)
T T F F
Find the value of
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 ... + 19 - 20
- (a)
- 10
- (b)
110
- (c)
20
- (d)
-30
We have
1- 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 + 17 - 18 + 19 - 20
= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) + [(-2) + (-4) + (-6) + (-8) + (-10) + (-12) + (-14) + (-16) + (-18) + (-20)]
= 100 + (-110)
= 100 - 110 = -10.
What is the correct option for the value in between O and R.
- (a)
negative and positive integer
- (b)
8 more than - 2
- (c)
8 less than 6
- (d)
All of above
O is a negative integer and R is a positive integer.
8 more than - 2 \(\longrightarrow\) R.
8 less than 6 \(\longrightarrow\) O.
The successor of integer -200 is ________.
- (a)
-199
- (b)
-201
- (c)
200
- (d)
none of above
The successor of - 200 is - 199.
Which of the following is false?
- (a)
(4 + 2) = (4) + (2)
- (b)
(2 - 4) = (2) + (4)
- (c)
(4 - 2) = (4) - (2)
- (d)
[(-2) + (-4)] = (-2) + (-4)
Choose the correct Statement:
- (a)
a. - 8 is to the right of - lOon a number line
- (b)
-100 is to the right of -50 on a number line
- (c)
-26 is greater than -25
- (d)
Smallest negative integer is - 1
- 8 is to the right of - 10 on a number line.
Choose the correct option for placing the following integers in increasing order.
-106, 107, -286, 235, -320, 18, -96, 78, -7
- (a)
-7, 18, 78, -96, -106, 107, 235, -286, -320
- (b)
-320, -286, -106, -96, -7, 18, 78, 107, 235
- (c)
-320, -286, 233, 107, -106, -96, 78, 18, -7
- (d)
-7, -79, -106, -286, -320, 18, 78, 107, 235
When placed in increasing order, the integers are
-320, -286, -106, -96, -7, 18, 78, 107, 235
The value of -10 + 10 - 7 + 17 - 5 + (- 5) is ___________.
- (a)
Whole Number
- (b)
Positive integer
- (c)
Negative integer
- (d)
None of above
The of -10 + 10 - 7+ 17 - 5 + (-5)
0 - 7 - 5 + 17
-17 + 17 = 0
0 which is a whole number and it is neither a positive nor negative integer.