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

You must Believe

GMAT Quant Tutor

How to start GMAT preparations?

How to Improve Quant Score?

Gmatclub Topic Tags

Check out my GMAT debrief

Quant Formula Sheet

How to Solve :

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