Data Sufficiency

Q: If the no. ABCD, where A,B,C and D are the thousand, Hundred, tens and Unit digit, is
subtracted from DCBA. What could be the largest value?
1: 8640
2: 8840
3: 8642
4: 9999
5: 8888

I can' remember the exact values but all the choices are above 8500

I THINK WE CAN'T DO 9900-99 BECAUSE IN THAT CASE DCBA WILL BE 0099. THIS IS NOT A FOUR DIGIT INTEGER

Its not mentioned that DCBA is 4 digit.
anyway,

9901 - 1099 = 8802 is one option.

I am assuming A,B, C and D are all distinct digits and the number has to be a four digit number.
We have to substract ABCD from DCBA
In order to get maximum difference, Each number should have an maximum net effective weight.


D should be 9 - (9 gives me 9000 in DCBA against 9 it gives me in ABCD)- Difference is max when D is biggest.
C Should be 8 - (8 gives me 800 in DCBA as against 80 it gives be in ABCD)- Difference is max when C is biggest.
B should be 0 - (Best choice is 0, 0 adds nothing to ABCD or DCBA. If you choose something like 7, you add 70 in DCBA and 700 in ABCD, which will reduce the difference and we do not want that.

A should be 1 - (Same logic as that above.)

So the result is

9801
-1089
======
8712

[email protected] wrote:Q: If the no. ABCD, where A,B,C and D are the thousand, Hundred, tens and Unit digit, is
subtracted from DCBA. What could be the largest value?
1: 8640
2: 8840
3: 8642
4: 9999
5: 8888

I can' remember the exact values but all the choices are above 8500

I THINK WE CAN'T DO 9900-99 BECAUSE IN THAT CASE DCBA WILL BE 0099. THIS IS NOT A FOUR DIGIT INTEGER

The way I approach this type of questions is following>>>

DCBA = 1000xD + 100xC + 10xB + A
ABCD = 1000xA + 100xB + 10xC + D

DCBA - ABCD = 1000xD + 100xC + 10xB + A - (1000xA + 100xB + 10xC + D)
= 999xD + 90xC - 90xB - 999xA
= 9(111xD + 10xC - 10xB - 111xA)

So the final number must be divisible by 9. Therefore, the only possible right options are 1. 8640 and 4. 9999.

However, to have two 4 digit numbers A can't be equal zero. So the final number must starts with thousand digit below or equal 8.

The right answer is 1 - 8640.

It is not mentioned that the numbers are distinct and moreover asking for the largest subtracted value.

Example

ABCD=9999

DCBA=1111
-------
8888

Hence E

Looks like the largest among the options.

This ques is little awkward , from where did you get it?

prateek_guy2004 wrote:It is not mentioned that the numbers are distinct and moreover asking for the largest subtracted value.

Example

ABCD=9999

DCBA=1111
-------
8888

Hence E

Looks like the largest among the options.

This ques is little awkward , from where did you get it?

Yes, it isn't mentioned that DCBA>ABCD, but all the answers are positive so it must be true.

The other error you have, D in one number must be equal D in the other, same for the rest of the letters.