Latest GRe Aptitude Question SOLUTION: A four-digit number gets reversed when it is multiplied by 4. find the sum of the digits of the number.

• Placement Papers
• /
• GRe
• /
• Numerical Ability
• /
• Number System

GRe Question Papers:

(#M40034964) GRE Numerical Ability question number system Keep an EYE

A four-digit number gets reversed when it is multiplied by 4. find the sum of the digits of the number.

Asked In GRe uppala (10 years ago)

Solved Dr.Dipin Singh Read Solution (6)

Is this Puzzle helpful?   (2)   (3) Submit Your Solution Number System

Read Solution (6) :

RAKESH  (10 years ago)

let number is (1000x + 100 y + 10z + w)
so, x must be 2. if it's greater then 2 then no. will be of 5 digit
& x=1 is also not possible bcoz if no. is reversed then unit digit is 1 which can't be multiple of 4.

from given condn
4000x + 400y + 40z + 4w = 1000w + 100z + 10y + x
=> 3999x + 390y - 60z - 996w = 0
=> 1333x + 130y - 20z - 332w = 0-----(1)

now w can be 3 or 8 coz last digit of reversed no. is 2 [3*4 & 8*4 gives 2]

so, w=8, as 2yzw * 4 = wzy2

put x=2,w=8 in (1)
2666 + 130y - 20z - 2656 = 0
=> 10 + 130y - 20z = 0
=> 1 + 13y - 2z = 0
=> 2z = (13y +1)
only possible value of y = 1 [ for y > 1 , z is not single digit]
so, z=7

so, no. is 2178 & 2178 * 4 = 8712

sum of digits = x+y+z+w = 2+1+7+8 = 18

Is this solution Helpfull? Yes (8) | No (1)  

azharshahid01@gmail.com  (10 years ago)

Answer is 2+1+7+8= 18.
number is 2178.
2178*4= 8712

Is this solution Helpfull? Yes (4) | No (2)  

Dr.Dipin Singh  (10 years ago)

2178*4 = 8712

Is this solution Helpfull? Yes (3) | No (4)  

Ann Theressa  (10 years ago)

Let the 4-digit number be x = 1000a+100b+10c+d

4*(1000a+100b+10c+d) = 1000d+100c+10b+a ---(1)

a = 1 or 2 (because 4*x is a 4 digit number, so a < 3)

From equation (1)
4*a = d ---(2)
and
4*d = a ---(3)

To satisfy both (2) and (3)
a = 2 and d = 8

4*(2000+100b+10c+8) = 8000+100c+10b+2
8032 + 400b + 40c = 8002 + 100c + 10b
30 + 390b = 60c
1 + 13b = 2c ---(4)

From (4)
b = 1 (max possible value of c is 9 for which RHS = 18 so, LHS

Is this solution Helpfull? Yes (2) | No (2)  

Ann Theressa  (10 years ago)

b = 1 (max possible value of c is 9 for which RHS = 18 so, LHS < 18 and hence b=1)

2c = 13*1 + 1
= 14
c =14/2 = 7

a+b+c+d = 2+1+7+8 = 18

Is this solution Helpfull? Yes (1) | No (1)  

Raj Kumar Ray  (10 years ago)

@dipin bro please tell the solution...

Is this solution Helpfull? Yes | No (2)  

Please Login to Read Solution.