0

Formation of greatest and smallest numbers

Description: formation of greatest and smallest numbers
Number of Questions: 30
Created by:
Tags: whole numbers and operations with whole numbers numbers : revision maths large numbers knowing our numbers play with numbers numbers and place value numbers
Attempted 0/30 Correct 0 Score 0

The smallest $7$ digit number is

  1. $1000000$

  2. $1:+$ greatest $6$ digit number

  3. either A or B

  4. none of these


Correct Option: C
Explanation:

(C) Smallest 7-digit number
$=1000000$
also $1+999999$
$=1000000$
So, answer is either A or B.

Smallest 6-digit number that can be formed by the digits 9, 6, 0, 5, 8, 1 is

  1. $015,689$

  2. $1,05,689$

  3. $5,01,689$

  4. $9,86,510$


Correct Option: B
Explanation:

$\Rightarrow$  The given numbers are $9,\,6,\,0,\,5,\,8,\,1$

$\Rightarrow$  To form smallest 6-digit number, we have to start number with smallest digit and end with largest digit.
$\Rightarrow$  Here, we can not use $0$ as first digit because then number will becomes 5 digit.
$\therefore$   The smallest 6-digit number = $1,05,689$.

Smallest 6-digit number that can be formed by the digits 9, 6, 0, 5, 8, 1 is 

  1. 0,15,689

  2. 1,05,689

  3. 5,01,689

  4. 9,86,510


Correct Option: B
Explanation:

Smallest  6  digit number that can be formed by the digits 9,6,0,5,8,1 is  1,05,689.  

 0 cannot  in the first place . Then it will become 5 digit number.

Which of the following are the three digit numbers that can be formed by using $0, 1$ and $2$ only once.

  1. $102$

  2. $201$

  3. $012$

  4. None of the above


Correct Option: A,B
Explanation:

Three digit numbers that can be formed from 0, 1 and 2 are $102$ and $201$.
So, (c) is not a three digit number.

So, options A and B are correct.

The greatest number formed by $9, 8$ and $7$ is

  1. $987$

  2. $789$

  3. $897$

  4. None of the above


Correct Option: A
Explanation:
The 3 digit numbers formed by $9, 8$ and $7$ are $987, 978, 897, 879, 798$ and $789$.
The greatest number is $987$.
So. option A is correct.

The smallest three digit number formed by the digits $2, 0$ and $3$.

  1. $203$

  2. $032$

  3. $302$

  4. None of the above


Correct Option: A
Explanation:

The numbers formed by $2, 0$ and $3$ are $203, 302, 023, 320, 230$ and $032$.

The smallest 3 digit number formed is $203$.
So, option A is correct.

Find the correct option such that the formation of $3$ numbers, using three digit number $128$? (Without repeating the numbers)

  1. $281, 221$ and $182$

  2. $281, 851$ and $182$

  3. $681, 821$ and $182$

  4. $281, 821$ and $182$


Correct Option: D
Explanation:

$128$ can be written using the general form $abc = 100 \times  a + 10 \times  b + c$
By changing the alphabetic orders of $a, b, c$, we get $3$ more numbers from $3$ digit number.
Here, $281, 821$ and $182$ are formed from the $3$ digit number $128$.

Which of the following fractions is the largest?

  1. $\dfrac { 7 }{ 8 } $

  2. $\dfrac { 13 }{ 16 } $

  3. $\dfrac { 31 }{ 40 } $

  4. $\dfrac { 63 }{ 80 } $


Correct Option: A
Explanation:

L.C.M. of $8$, $16$, $40$ and $80 = 80$.
$\dfrac { 7 }{ 8 } =\dfrac { 70 }{ 80 }$; $\dfrac { 13 }{ 16 } =\dfrac { 65 }{ 80 }$; $\dfrac { 31 }{ 40 } =\dfrac { 62 }{ 80 } $


Since, $\dfrac { 70 }{ 80 } > \dfrac { 65 }{ 80 } > \dfrac { 63 }{ 80 } > \dfrac { 62 }{ 80 } $

       So $\dfrac { 7 }{ 8 } > \dfrac { 13 }{ 16 } > \dfrac { 63 }{ 80 } > \dfrac { 31 }{ 40 } $
      $\therefore$ $\dfrac { 7 }{ 8 } $ is the largest.

Which of the following fractions is greater than $\dfrac { 3 }{ 4 } $ and less than $\dfrac { 5 }{ 6 } $?

  1. $\dfrac { 1 }{ 2 } $

  2. $\dfrac { 2 }{ 3 } $

  3. $\dfrac { 4 }{ 5 } $

  4. $\dfrac { 9 }{ 10 } $


Correct Option: C
Explanation:

$\dfrac { 3 }{ 4 } =0.75,\quad \dfrac { 5 }{ 6 } =0.833,\quad \dfrac { 1 }{ 2 } =0.5,\quad \dfrac { 2 }{ 3 } =0.66,\quad \dfrac { 4 }{ 5 } =0.8,\quad \dfrac { 9 }{ 10 } =0.9$.


Clearly, $0.8$ lies between $0.75$ and $0.833$.

$\therefore \dfrac { 4 }{ 5 } $ lies between $\dfrac { 3 }{ 4 } $ and $\dfrac { 5 }{ 6 } $.

The smallest three-digit number using the digits $3, 9, 7, 8, 6$ (repetition not allowed) is

  1. $387$

  2. $367$

  3. $389$

  4. $386$


Correct Option: B
Explanation:

$3,9,7,8,6$

Smallest three digit number will be formed my smallest of the three digits from the given ones, i.e. $3,6,7$

Smallest three digits number possible $= 367$

A three digit number from the given digits $2, 5, 7,9$ which divisible by 2.

  1. $257$

  2. $925$

  3. $527$

  4. $752$


Correct Option: D
Explanation:

Consider the given digits.

$2, 5, 7, 9$

If a number which is divided by $2$, then the units digit must be even.

So, from the given options there is only one option which has unit digit $2$.

Hence, the three digit number will be $752$.

Hence, this is the answer.

Let the given digits be $2, 3, 6,7$, find the greatest three digit number that can be formed with using the given digits only once.

  1. $763$

  2. $736$

  3. $723$

  4. $732$


Correct Option: A
Explanation:

$2,3,6,7$

Greatest three digit number will be formed my largest of the three digits from the given ones, i.e. $7,6,3$

Greatest three digits number possible $= 763$

Form a three digits even number using the digits $7, 6, 9.$

  1. $796$

  2. $769$

  3. $976$

  4. $967$


Correct Option: A,C
Explanation:

the number formed using given digits are

$769,796,976,967,679,697$
Even numbers are $796,976$

Find the greatest three-digit number using the digits $7, 6, 3$

  1. $763$

  2. $367$

  3. $637$

  4. $376$


Correct Option: A
Explanation:
The descending order of the given numbers $7,6,3$ is:

$7>6>3$ 

We observe that the smallest digit is $3$ and the largest digit is $7$, so the number should start with $7$ and end with $3$.
 
Thus, the largest number formed is $763$.

Hence, the greatest three digit number formed is $763$.

Find a smallest three digit number using the digits $4,7,9$

  1. $974$

  2. $497$

  3. $479$

  4. $794$


Correct Option: C
Explanation:

Smallest three digit number which can be formed is if we arrange them in ascending order, i.e. $479$


Hence $479$ is the smallest three digit number.

Mohit has five number cards with numbers $7,9,0,5$ and $2$. Raman asked him to from the greatest $5$-digit even number with his cards. From the number Mohit has to form.

  1. $97520$

  2. $97502$

  3. $27509$

  4. $75902$


Correct Option: A
Explanation:

According to given information
The $5$-digit number is even
$\therefore$ $5$th number will be $0$ or $2$ which are the only even numbers
So, the greatest $5$-digit even number that can be formed is $97520$

Which of the following will be the last digit of the second highest number after the positions of the digits in each number is reversed? 

$738, 429, 156, 273, 894$.

  1. $1$

  2. $2$

  3. $4$

  4. $7$


Correct Option: D
Explanation:
The given sequence is : $738,429,156,273,894$
After reversing the digits, the sequence becomes : $837, 924, 651, 372, 498$.
The second highest number is $837$ and it's last digit is $7$.
Hence, $7$ is the correct answer.

$a, b, c (a > c)$ are three digits from left to right, of a three digits number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digits 4 in its unit place. The other two digits from left to right are

  1. 5 and 4

  2. 5 and 9

  3. 4 and 5

  4. 9 and 5


Correct Option: B
Explanation:

$ Let\quad the\quad number\quad be\quad written\quad as\quad follows\ Place\quad value\quad \longrightarrow Hundreds\quad \quad \quad Tens\quad \quad \quad Units\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a\quad \quad \quad \quad \quad \quad \quad \quad b\quad \quad \quad \quad \quad \quad c\ Reversing\quad \longrightarrow \quad \quad \quad \quad \quad c\quad \quad \quad \quad \quad \quad \quad \quad b\quad \quad \quad \quad \quad \quad a\ \ Units\quad place:-\quad Given\quad a>c\ \therefore \quad We\quad borrow\quad 10\quad and\quad the\quad result\quad is\quad \ \quad \quad c+10-a=4\ \Rightarrow a=c+6----(1)\ Tens\quad place:-\quad upper\quad row\quad b\quad has\quad become\quad b-1\ \therefore \quad We\quad borrow\quad 10\quad and\quad the\quad result\quad is\ \quad \quad (b-1+10)-b=9.\ Hundreds\quad place:-\quad a\quad has\quad become\quad a-1\ \therefore \quad (a-1)-c\quad is\quad the\quad result.\ Substituting\quad the\quad value\quad of\quad a\quad from\quad (1),\quad the\quad result\ will\quad be\quad c+6-1-c=5\ \therefore \quad The\quad other\quad two\quad numbers\quad are\quad 5,\quad 9\quad \quad (Ans)\ \quad \quad (i.e.\quad The\quad result\quad is\quad 594) $

How many positive integers less than $1000$ are $6$ times the sum of their digits ?

  1. $0$

  2. $1$

  3. $2$

  4. $4$


Correct Option: B

Find the greatest number that will divide $400$, $435$ and $541$ leaving $9$, $10$ and $14$ as remainders respectively

  1. $17$

  2. $4$

  3. $55$

  4. $11$


Correct Option: A
Explanation:

$400-9=391$


$435-10=425$


$541-14=527$

$391=17\times23$

$425=5\times5\times17$

$527=17\times31$

 HCF of $391,425$ and $527=17$ 

Required number$=17$ 

If + means $ \div$, $ \times $ means - , - means $ \times $ & $ \div $means +, then $ 38+ 19-16\times 17 \div 3 $ is equal to

  1. 16

  2. 19

  3. 18

  4. 12


Correct Option: C
Explanation:
$ 38+ 19-16\times 17 \div 3 $ converts to 

$38 ÷ 19 × 16 - 17 + 3$

$= \dfrac{38}{19} × 16 - 17 + 3$

$= 2 × 16 - 17 + 3$

$= 32 - 17 + 3$

$= 35 - 17$

$= 18$

The smallest $7$ digit number is

  1. $1000000$

  2. $1 +$ greatest 6 digit number

  3. either A or B

  4. none of these


Correct Option: C
Explanation:

Smallest 7-digit number
$= 1000000$

Greatest 6 digit number$=999999$
also $1 + 99999$
$= 1000000$

The three digit number formed by $4, 6$ and $2$ is/are

  1. $462$

  2. $264$

  3. $642$

  4. All of the above


Correct Option: D
Explanation:

The numbers formed by $4$,$6$ and $2$ are $462$ ,$264$ and $642$.

So, option D is correct.

'6 less than ten times a' is written as

  1. 6 - 10a

  2. 10a - 6

  3. 10ac

  4. $6\, <\, 10\, \times\, a\, $


Correct Option: D
Explanation:

    It is clear from options.It is just expressed in mathematical form.

Find a smallest four digit number using the digits $7,8,9,5$ such that the number thus formed has $9$ at its hundreds place and $8$ at its one's place.

  1. $5978$

  2. $7598$

  3. $7958$

  4. $7985$


Correct Option: A
Explanation:
The ascending order of the given numbers $7,8,9,5$ is:

$5 < 7 < 8 < 9$ 

We observe that the smallest digit is $5$ and the largest digit is $9$.
 
Therefore, the smallest number formed is $5789$.

But it is given that the number formed should have $9$ at its hundredth place and $8$ at its one's place, therfore, the required number is:

$5978$ where $8$ is at one's place, $7$ is at tens place, $9$ is at hundredth place and $5$ is at thousandth place. 

Hence, the smallest $4$ digit number formed is $5978$.

 Write the smallest $4$ digit number formed using the digits $8,3,0,1$.

  1. $1038$

  2. $1308$

  3. $1083$

  4. $0138$


Correct Option: A
Explanation:
The ascending order of the given numbers $8,3,0,1$ is:

$0 < 1 < 3 < 8$ 

A number cannot begin with $0$, so we will put it in the second place. 

The smallest digit (other than $0$) is $1$. 

Therefore, the number will begin with $1$.
 
Thus, the smallest number formed is $1038$.

Hence, the smallest $4$ digit number formed is $1038$.

Which among the following  is a four digit prime number using the digits $1,7,0,9$?

  1. $1790$

  2. $1709$

  3. $9710$

  4. $7910$


Correct Option: B
Explanation:
A prime number is a number which is only divisible by itself and $1$.

(a) $1790$ is divisible by $2$, so it is not a four digit prime number.

(b) $1709$ is only divisible by itself, so it is a four digit prime number.

(c) $9710$ is divisible by $2$, so it is not a four digit prime number.

(d) $7910$ is divisible by $2$, so it is not a four digit prime number.

Hence, $1709$ is a four digit prime number using the digits $1,7,0,9$.

Find the sum of smallest three digit even number and greatest three-digit odd number using the digits $6, 2, 3$

  1. $859$

  2. $958$

  3. $598$

  4. $985$


Correct Option: A
Explanation:
The three digit numbers that can be formed using the digits $6,2,3$ are $623,632,263,236,362,326$ in which the odd numbers are $623,263$ and the even numbers are $632,236,362,326$.

The smallest even number is $236$ and the greatest odd number is $623$ and their sum can be determined as:

$236+623=859$

Hence, the sum of smallest three digit even number and greatest three-digit odd number using the digits $6,2,3$ is $859$.

Find a three-digit number using the digits $6, 7, 4$ such that the resultant number is divisible by 4

  1. $746$

  2. $764$

  3. $467$

  4. $647$


Correct Option: B
Explanation:
(a) Let us take a number $746$ using the digits $6,7,4$ and divide it by $4$ as follows:

$\dfrac {746}{4}=\dfrac {373}{2}$

Therefore, $746$ is not divisible by $4$.

(b) Let us take a number $764$ using the digits $6,7,4$ and divide it by $4$ as follows:

$\dfrac {764}{4}=191$

Therefore, $764$ is divisible by $4$.

(c) Let us take a number $467$ using the digits $6,7,4$ and divide it by $4$ as follows:

$\dfrac {467}{4}$

Therefore, $467$ is not divisible by $4$.


(d) Let us take a number $647$ using the digits $6,7,4$ and divide it by $4$ as follows:

$\dfrac {647}{4}$

Therefore, $647$ is not divisible by $4$.

Hence, only $764$ is divisible by $4$.

Find an even $4$ digit number using $2, 7, 5,1$.

  1. $7512$

  2. $5217$

  3. $7125$

  4. $1275$


Correct Option: A
Explanation:
An even number is an integer which is "evenly divisible" by two. This means that if the integer is divided by $2$, it yields no remainder.

(a) $7512$ is divisible by $2$ as $\dfrac {7512}{2}=3756$, so it is a four digit even number.

(b) $5217$ is not divisible by $2$, so it is not a four digit even number.

(c) $7125$ is not divisible by $2$, so it is not a four digit even number.

(d) $1275$ is not divisible by $2$, so it is not a four digit even number.

Hence, $7512$ is a four digit even number using the digits $2,7,5,1$.
- Hide questions