A 4 digit number, having all digits different and non odd, has sum of all digits equal to 12. The su

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05 Jun 2015 number

A 4 digit number, having all digits different and non odd, has sum of all digits equal to 12. The sum of middle two digits is equal to the first digit. Second digit is greater than third digit. The product of first 3 digits will be

OPtion

1) 64
2) 96
3) 48
4) 72
5) 32
6) 16
7) 8
8) 192
9) 216
10) 512

Solution

Let the number is 1000x + 100y + 10z + p
According to the given conditions
x + y + z + p = 12 ..................(1)
y + z = x ..................(2)
Using y + z from (2) into (1)
we get 2x + p = 12
Possible combinations for the values of x and p are given below
x = 2, p = 8 ...................(A)
x = 4, p = 4 ...................(B)
x = 6, p = 0 ...................(C)
If (A) is correct then by (2) either y or z will become equal to x
If (B) is correct then by (2) two cases arise
(1) either y or z will become equal to x
(2) or y will become equal to z
so x = 6, p = 0 will be the case
so y + z = 6
=> y = 4 and z = 2
so number is 6420.

Correct Option: 3 Best Solution (52)

viswambher   9 years AGO

sum of all numbers in the four digit number is given as twelve and since the digits are even, the digits must be 0,2,4,6 since any other combination doesn't work

and it is also given that the sum of middle two digits is equal to first digit and 2nd digit is greater than 1st

so the number is 6420
therefore product of first three digits is 48

Like? Yes (2) | No   

padmapriya   9 years AGO

Assign numbers as 6,4,2,0 so it satisfies all the three criterias. and their product is 48

Like? Yes (2) | No   

Supriya Mondal   9 years AGO

According to the question the number will be 6420
So, multiplication of first 3 digit is=6*4*2=48
So, option 3)48 is the right answer

Like? Yes (2) | No   

jalaj   9 years AGO

Acc to 1 condition that all numbers are different and even possible numbers are 2,4,6,8,0
Acc to 2 and 3 condition that sum of the numbers is 12 and 2nd and 3rd number sum must be equal to first can be 6,2,4,0 or 6,4,2,0.
Similarly acc to condition 4 u can analyze that the required number is 6,4,2,0 Hence the prod of first 3 numbers are 48

Like? Yes (3) | No (1)  

Yathiraj   9 years AGO

if a, b, c and d are the digits of a 4 digits number
then
a+b+c+d = 12
a = b+c
b>c
the only possibility is
a=6
b=4
c=2
d=0

Hence, a*b*c = 6*4*2 = 48

Option 3.

Like? Yes (3) | No (1)  

manikanta mitta   9 years AGO

Given all the digits are not odd then remaining are 0,4,2,6,8

For sum of digits of number is 12 and non repeating the required digits are 6 ,4,2,0

the only option 6420(given sum of middle two digits is equal to 1st digit and second digit is greater than first)

product of first three digits is 48

Like? Yes (1) | No   

MRITUNJAY   9 years AGO

after satisfying the condition digits will be

6 4 2 0

product will be 6*4*2=48

Like? Yes (1) | No   

Aashish gohel   9 years AGO

there is a 4 digit number and that should be from non odds and that are 0,2,4,6,8...
the sum of 2nd and 3rd is equal to 1st term,so 2nd term is 4 and 3rd term is 2 and it also satisfies the another condition that 2nd term is greater than 3rd term..
and sum of the all 4 terms is equal to 12 so answer is 6420...
multiplication of 1st 3 terms =6*4*2=48

Like? Yes (1) | No   

Karthick Raja   9 years AGO

4digit non repetive odd number is 6420
(sum of middle 2digit is equal to first digit 4+2=6 and 2nd digit is greater than 3rd digit ) .so the product of first three digit is 6*4*2=48
Note: here only say no odd digits are in four digit number '0' is not an odd or even number so I can use 0 in 4 digit number.

Like? Yes (1) | No   

Devendra Marghade   9 years AGO

The number is 6420
So product of first three digits=6*4*2=48
Answer is option (3)

Like? Yes (1) | No   

Venkatesh kadali   9 years AGO

the num shoulb be 6420
because first number sum of 2nd and 3rd digits s0 4+2=6
6+4+2=12 so 4th digit is zero so number is 6420,
then first threedigits multiplication is 48

Like? Yes (1) | No   

Pranati Kundu   9 years AGO

the number is 6420
therefore the product of 1st three digits is 48

Like? Yes (1) | No   

shabana banu shaik   9 years AGO

let the numbers be 6,4,2,0.......and the other pattern which satisfies the condition is 2,6,4,0.......the product of the numbers will be 48

Like? Yes (1) | No   

Mehul D Parmar   9 years AGO

here possible non odd no is 0,2,4,6,8

then we take 0,2,4,and 6

then sum of all digit is 0+2+4+6=12
and sum of middle two digit is equal to first digit : 6 =2+ 4

one more condition given here is second digit is greater than third digit. then 4 > 2


so four digit number is 6420

hence multiplication of first 3 digit is 6*4*2=48

then ans is 3 option 48

Like? Yes (1) | No   

akas   9 years AGO

the four digit no is 6420
the product of first 3 digit is 48

Like? Yes (1) | No   

amit   9 years AGO

only 4 digits are in the list 2, 4, 6,8
among that it is easy to check

Like? Yes (1) | No   

Dinni   9 years AGO

Considering last no. as 0
Then 2x+0=12, x=6
Then 6+4+2+0=12
The product is 6*4*2=48

Like? Yes (1) | No   

NESAB JAFAR   9 years AGO

number possibilities =6,4,2

Like? Yes (1) | No   

N.Dayanithi   9 years AGO

Numbers will be 6 4 2 0
The sum of middle two digits.. 4 + 2 = 6
Second digit is greater than third digit = 4 > 2
The product of first 3 digits = 6*4*2 = 48

Like? Yes (1) | No   

Nagarajan C S   9 years AGO

6420. total is 12, Sum of middle two is first digit 4+2=6.
4

Like? Yes (1) | No   

shivangi   9 years AGO

even nos. are 0,2,4,6,8...
the perfect sum can be 2,4,6 and 8,4,0
but 2+4=6
hence 6 is first digit ,4 is d second no.and 2 be third digit

Like? Yes (1) | No   

Priyanka   9 years AGO

6+4+2+0=12
4+2=6
4>2
6*4*2=48

Like? Yes (1) | No   

kumari jyoti   9 years AGO

digits allowed are only non odd and non repeating. so,largest digit that can be used can be 6. hence the consecutive even nos. 4& 2 and 0 fit in the criteria given.

Like? Yes (1) | No   

naina shukla    9 years AGO

WE CAN TAKE ALL THE DIGITS EVEN FOR THIS TYPE OF 4 DIGIT NO.
EX- 6420
HERE, 4+2=6 , AND 4>2 AND 6+4+2=12
SATISFIES ALL THE CONDITIONS

Like? Yes (1) | No   

niyati Shastri   9 years AGO

Let the 4 digit number be abcd.
so a+b+c+d=12 and b+c=a and b>c
therefore 2a+d=12
if d=1, a=5.5 which is not possible
if d=2,a=5 which is also not possible as it is given in question that all digits are non odd.
so for any value of d the equation is not satisfied.
So the value of d is 0.
d=0 , a= 6, therefore b=4 nd c=2 as b>c
so the number will be 6420
and so product of 1st three terms will be 6×4×2=48

Like? Yes (1) | No   

Jotshnesh Patel   9 years AGO

ANSWER: OPTION : - 3) 48
NUMBER IS 6420......

Like? Yes (2) | No (1)  

Rahul Varshney   9 years AGO

according to the question number should be 6420. so the product of first 3 digits will be 48.

Like? Yes (1) | No   

Yogesh Kumawat   9 years AGO

Let first digit is x...likewise second digit is y...third is z....fourth is K..possible non odd digits are 0,2,4,6,8....
According to question
x+y+z+k =12
from this we conclude that only possible of digits are 0,2,4,6
x= y+z.....y>z
from this we conclude...x=6...y = 4...z=2,..
remaining digit k=0
number is 6420 and product of first three digit is 6*4*2 = 48 :)

Like? Yes (1) | No   

shashank verma   9 years AGO

4 digit no is 6420 so the sum of 2nd and 3rd digit is 6 and product of 1st 3 digit is 48
so the answer is 48.

Like? Yes (1) | No   

siddharth prakash singh   9 years AGO

required no will be 6420 and req ans will be 48.

Like? Yes (1) | No   

kamal   9 years AGO

possible digit-8,4,6,2,0
9 not possible ,bcus it will cause sum to be more than 12
than 6=4+2
4>2

Like? Yes (1) | No   

anuanwesh   9 years AGO

6240 nonodd, 2+4=6,2 greater than4 so 6•2•4= 48

Like? Yes (1) | No   

vini   9 years AGO

4 digit number, all are different and non odd numbers, so only possible is even numbers 0,2,4,6,8
It is 4 digit number so zero is not possible in first place
The sum of all four digit number is 12
The sum of two middle number is equal to first number
so the possible number is 6420
6+4+2+0=12(satisfy all the conditions)
so the product of first three numbers is 6*4*2=48

Like? Yes (1) | No   

ramakrishna velaga   9 years AGO

x1,x2,x3 are in a.p.and x4=0 as per given conditions.

Like? Yes (1) | No   

Samkit Jain   9 years AGO

As numbers are even, and second digit is greater than third digit, So, possibilities are for second and third number are 2 and 4 respectively, First digit is 6
So, Number is 6420

Like? Yes (1) | No   

Parvathi.R   9 years AGO

6420
1) 6+4+2+0=12
2)4+2=6
3) 4>2

therefore.. 6*4*2= 48

Like? Yes (1) | No   

Nitish Kumar Dubey   9 years AGO

6+4+2+0=12

4>2

4+2=6

all condition verified

Like? Yes (1) | No   

POSHRAJ SHARMA   9 years AGO

all even and total 12 and all distinct
so possible 4 digitcombinations
using 2, 4, 6, 0
2+4+6+0 = 12
first = second + third
first = 6
second > third
4 > 2
second = 4
third = 2
fouth has to be 0 then
4 digit number : 6420

6*4*2 = 48

Like? Yes (1) | No   

DEEPIKA REDDY GUNUKULA   9 years AGO

by given condition the numbers are 0,2,4,6(sum condition and it should not be odd)
first digit is = sum of next two=>6=4+2
so the number might be 6420,6240
without going for the next condition we can go for the question directly
here we dnt need exact number.
6*4*2=6*2*4=48

Like? Yes (1) | No   

keerthi   9 years AGO

non odd terms means 0, 2, 4, 6, 8
digits in the number must be different
we have an conditions
i) sum of total digits are 12
a+b+c+d=12
ii)Sum of middle digits are equal to 1st digit
b+c=a
iii)2nd digit is greater than 3rd digit
b>c
By using these conditions and trail and error method
number should be 6420
The product of first three digits is 6*4*2=48
the ans is 48

Like? Yes (1) | No   

Sravanthi Aasa   9 years AGO

All digits are different and non odd implies it can take all even numbers including zero(i.e., 0,2,4,6,8)
here sum of 4 digits=12--> digits are 0,2,4,6
sum of middle 2 digits = first digit-->2+4=6
second digit is greater then third digit-->4>2
so complete four digit no. is 6420
and product of first 3 digits is 6*4*2=48

Like? Yes (1) | No   

RAVAL   9 years AGO

because if we follow the condition as mention in question then;
four nos. are,
2,4,6,0
product = 2*4*6=48

Like? Yes (1) | No   

shivesh kumar   9 years AGO

here sum of middle no is equal to first no

then if we can't take 2,2 in middle because repeatiosion of disit is not allowedand also we can not take 0 in first three digit. hence we have to take 4, 2 in middle
then first digit will be 6

and product of first 3 digits will be 6*4*2=48

Like? Yes (1) | No   

W J Krishna Teja   9 years AGO

since the digits are not odd they must be 0,2,4,6,8
we must select the 4 digits such that sum is 12 with non repeating digits.
so the possible combination is (0,2,6,4)
according to given conditions the number must be 6420
therefore product of first three digits is 6*4*2=48

Like? Yes (1) | No   

vinuvardhini   9 years AGO

The four digit number is 6420. The sum of the single digits gives 12.The sum of middle two digits is equal to first digit.So the product of first 3 digits(6*4*2) is 48.

Like? Yes (1) | No   

krishna chandrika   9 years AGO

four digit number is 6420
product of first 3digits is 6x4x2=48

Like? Yes (1) | No   

RAMYA   9 years AGO

the digit is 6420
i) even digits
ii)4+2=6
iii)4>2
iv)product of first three digit =48

Like? Yes (1) | No   

ammar   9 years AGO

Let the four digit number be abcd.
Given that a+b+c+d=12 and a=b+c
Therefore 2a+d=12
Since all the digits are non odd and different,therefore only possible digits are 0,2,4 and 6. Now the digits satisfying the condition a=b+c are 6,4 and 2. Therefore units digits is 0 and thousands digit is 6. Also it is given that b>c therefore hundreds digit is 4. Hence number is 6420. And product of first three digits = 6*4*2=48.

Like? Yes (1) | No   

vamsi   9 years AGO

even numbers are 0,2,4,6,8
let four digits as x+y x y z 6 428

Like? Yes (1) | No   

Prasad Bagauli   9 years AGO

the no. is 6420. so the ind sum is 12, 4>2, 4+2 = 6 and thus 6*4*2 = 48

Like? Yes (1) | No   

PRASHANT KUMAR   9 years AGO

probable digits are 0,2,4,6,8.............
NOW SUM =12 SO THE SET IS{2,4,6,0)..........SO THE NO. IS 0246........PRODUCT=2*4*6=48

Like? Yes (1) | No   

Mohit   9 years AGO

on solving the answer is found to be 48

Like? Yes (1) | No (1)