Olympiad Mathematics - Knowing Our Numbers
Exam Duration: 45 Mins Total Questions : 30
Observe the following pattern for obtaining the sums, and find the sum of numbers from 781 to 790.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + 13+ ........ + 19 + 20 = 155
21 + 22 + 23 + ....... + 29 + 30 = 255
51 + 52 + 53 + ....... + 59 + 60 = 555
- (a)
7055
- (b)
7855
- (c)
7955
- (d)
8155
Observing the pattern, we see that the last two digits are 55 and the left-most digits is/are the two left-most digits of the number in the given sums. Thus, 781 + 782 + ....+ 789 + 790 = 7855.
How many numbers are there containing 2 digits?
- (a)
90
- (b)
99
- (c)
100
- (d)
89
Number of two digit numbers
= (The greatest two digit number - The smallest two digit number) + 1
= (99 - 10) + 1 = 90
Which of the following is the greatest?
- (a)
7212
- (b)
7122
- (c)
7211
- (d)
7221
The smallest 4-digit number formed by using the digits 5,0, 3, 1 and 7 only once contains
- (a)
0 in thousands place
- (b)
5 in tens place
- (c)
3 in tens place
- (d)
7 in units place
Write the greatest 4-digit number using different digits with 6 in the tens place.
- (a)
9876
- (b)
9867
- (c)
9687
- (d)
6987
Round 3500 to the nearest thousand.
- (a)
3000
- (b)
3600
- (c)
4000
- (d)
4500
Which of the following is the largest 8-digit number?
- (a)
888999
- (b)
99999999
- (c)
999999
- (d)
8999999
Take '9' in all 8-digits to write the largest 8-digit number.
What is the place value of 8 in the number 86,93,04,600?
- (a)
Eight crores
- (b)
Eighty crores
- (c)
Crores
- (d)
Eighty six crores
8 \(\times\) 10,00,00,000= 80,00,00,000= Eightycrores
Which is the place that comes on the immediate right of the hundreds place in the place value chart?
- (a)
Thousands
- (b)
Tens
- (c)
Ones
- (d)
Ten thousands
How many millions are there in 10 crores?
- (a)
100
- (b)
10
- (c)
1
- (d)
100
What is the difference between the place values of the two 3s in 3116365?
- (a)
2999700
- (b)
3000700
- (c)
2990700
- (d)
3000005
3000000 - 300 = 2999700
What are the numerals that cannot be subtracted in Roman System?
- (a)
V, L and D
- (b)
I.X and V
- (c)
C and X
- (d)
M and C
Bobby's date of birth is 19th September. How is Bobby's date of birth represented in Roman System?
- (a)
XXI
- (b)
XIXX
- (c)
IIX
- (d)
XIX
What is the Hindu-Arabic numeral for CCCXLVII?
- (a)
357
- (b)
347
- (c)
367
- (d)
387
CCCXLVIl= 100 + 100 + 100 + (50 -10) + 5 + 1 + 1 = 347
What is the Roman numeral for the number obtained when 144 is divided by 16?
- (a)
X
- (b)
VII
- (c)
VIII
- (d)
IX
144 \(\div \)16 = 9 = IX
How is the product obtained when 28 is multiplied by 2 represented in Roman System?
- (a)
LlV
- (b)
LlI
- (c)
LVI
- (d)
LVII
What is the Roman numeral for 2143?
- (a)
MMCXLlIl
- (b)
MMCLlIl
- (c)
MMCXLlI
- (d)
VIIVIII
2143 = 1000 + 1000 + 100 + (50 - 10) + 1 + 1 + 1 = MMCXLlIl
Which of the following is/are meaningless?
- (a)
VX
- (b)
IXIV
- (c)
XlIV
- (d)
All the above
How many 8-digit numbers are there?
- (a)
99999999
- (b)
89999999
- (c)
90000000
- (d)
100000000
(7268 - 2427) estimated to the nearest hundred is_________
- (a)
4800
- (b)
4900
- (c)
4841
- (d)
5000
We have, 7268 - 2427 = 4841
Rounded off 4841 to the nearest hundred = 4800
When a Roman numeral of smaller value is put between two numerals of greater value, it is subtracted from the numeral on its__________.
- (a)
Left
- (b)
Right
- (c)
Both sides
- (d)
Next numeral from left
The difference of the greatest 6-digit number and the smallest 4-digit number is______________
- (a)
988999
- (b)
998999
- (c)
99899
- (d)
998099
Greatest 6-digit number = 999999
Smallest 4-digit number = 1000
\(\therefore \) Required difference = 999999 - 1000
= 998999
Commas are inserted in a number after each________
- (a)
Place
- (b)
Digit
- (c)
Period
- (d)
None of these
The difference between the smallest 3-digitnumber and the greatest 2-digit number is_____________
- (a)
I
- (b)
XX
- (c)
XC
- (d)
C
Smallest 3-digit number = 100
Greatest 2-digit number = 99
\(\therefore \)Required difference = 100 - 99 = 1 i.e., I
Identify the place value for the underlined digit of the number given below.
8, 523,615
- (a)
Millions
- (b)
Thousands
- (c)
Hundreds
- (d)
Tens
8 | 5 | 2 | 3 | 6 | 1 | 5 |
M | HTh | TTh | Th | H | T | 0 |
Place value of a digit decreases by ____________times as it moves place by place from left to right
- (a)
100
- (b)
\(\cfrac { 1 }{ 10 } \)
- (c)
10
- (d)
1000
Millions period consists of the place___________
- (a)
M, TM
- (b)
M, TM, HM
- (c)
TTH, HTH, M
- (d)
O, T, M
Millions period consists of the places M, TM, HM
Place value and face value are always equal at which place?
- (a)
Hundreds
- (b)
Ones
- (c)
housands
- (d)
Ten
The distance between Akash's school and home is 2 km 385 m. Every day, he walks to and from the school. Calculate the total distance covered by him from Monday to Friday
- (a)
23 km 870 m
- (b)
23 km 850 m
- (c)
21 km 860 m
- (d)
20 km 850 m
Total distance between Akash's schooland home = 2 km 385 m
Distance covered by him in one day = (2 km 385 m) x 2 = 4km 770 m
Number of days from Monday to Friday = 5
\(\therefore \) Total distance covered by Akash in 5 days = (4 km 770 m) x 5 = 23 km 850 m
If a new number is formed by interchanging the tens and thousands place digits of 8727, then what is the relation between them?
- (a)
New number is greater than original number
- (b)
New number is smaller than original number
- (c)
New number is equal to the original number.
- (d)
Can't be determined
Original number = 8727
After interchanging the tens and thousands place digits, we get 2787.
So, new number is smaller than original number.