Find the sum of all the 4 digit numbers which are formed by the digits 1,2,5,6.

a) 933510

b) 93324

c) 65120

d) 8400

A 4 digit number abcd is written as 1000*a + 100*b + 10*c + d

Possible 4digit numbers starting with 1 in thousdands digit are

1256

1265

1526

1562

1625

1652

As, you will notice the pattern in the hundred's ten's and unit's digit then 2,5 and 6 each occur twice in hundred's ten's and unit's digit

So Sum of all the numbers in which 1 is in the thousand's digit is given by

1000*6*1 + 100*2*(2+5+6) + 10*2*(2+5+6) + 1*2*(2+5+6)

= 6000 + (2+5+6)*2*(100+10+1)

= 6000 + 13*2*111

= 8886

Similarly when 2 is in the thousand's digit then the sum of all the numbers will be

1000*6*2 + 100*2*(1+5+6) + 10*2*(1+5+6) + 1*2*(1+5+6)

= 12,000 + 12*2*111

=> Sum = 14664

Similarly when 5 is in the thousand's digit then the sum of all the numbers will be

1000*6*5 + 100*2*(1+2+6) + 10*2*(1+2+6) + 1*2*(1+2+6)

= 30,000 + 111*2*9

=> Sum =31,998

Similarly when 6 is in the thousand's digit then the sum of all the numbers will be

1000*6*6 + 100*2*(1+2+5) + 10*2*(1+2+5) + 1*2*(1+2+5)

= 36,000 + 111*2*8

=> Sum = 37,776

Total Sum = 8886 + 14664 + 31,998 + 37,776 = 93,324

ONe MOre way of doing this is taking all the sums together then we have

1000*6*(1+2+5+6) + 100*2*3*(1+2+5+6) + 10*2*3*(1+2+5+6) + 1*2*3*(1+2+5+6)

= (1+2+5+6) * (6000+600+60+6)

= 14 * 6666

= 93,324

So, Answer is B

Hope it helps!

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor

How to start GMAT preparations?

How to Improve Quant Score?

Gmatclub Topic Tags

Check out my GMAT debrief

How to Solve :

Statistics || Reflection of a line || Remainder Problems || Inequalities