PS-Comb

Question

How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6 
B.) 9*9*8*8*8 
C.) 9^5
D.) 9*8^4 
E.) 10*9^4

FN · Answer

i get C as well

first integer is 9 ways, second integer 9 also, includes 0, so now the next we can continue the same 9^5

vivektripathi · Answer

The first place has 9 possibilities, since 0 is not to be counted. All others have 9 each, since you cannot have the digit, which is same as the preceding one.
Hence 9^5

scthakur · Answer

Oh, my silly analysis!

Thanks Vivek.

sudhanshu_arora · Answer

Whats the OA. i would think the answer would be since it is 5 digits .

first digit is going to be from 0..9
second digit is going to be one option less then 0..9 
third .. (same as first two ) and so forth.

10*9*8*7*6

Curious to know the OA and explanation.

mrsmarthi · Answer

I guess the answer would be D - 9 * 8^4 And here is the explanation

Let _ _ _ _ _ be five digits  positive integers  (Means they can range from 1 to 9. I call them as first digit, second digit etc starting from Left side.

So the first digit can be picked from  9 positive integers  =  9  
Since no two consecutive digits should be same, second digit can be picked from 8 different numbers(eliminating the number picked from first digit =  8 
Similary third, fourth and fifth digits can be picked from 8 different numbers each(eliminating the number picked from previous digit ).

So the answer is 9 * 8 * 8 * 8 * 8 = 9 * 8^4.

GMAT TIGER · Answer

First digit from 1 to 9 = 9 ways
Second digit from 0 to 9 but exclude one that is already in first digit = 9 ways
Third digit from 0 to 9 but exclude one that is already in second digit = 9 ways
Fourth digit is also from 0 to 9 but exclude one that is already in third digit = 9 ways
Fifth (final) digit is also from 0 to 9 but exclude one that is already in fourth digit = 9 ways

So the possibilities are 9x9x9x9x9 = 9^5 ways..

mrsmarthi · Answer

I have given my guess based on the fact that it is 5 digit positive integers. So my understanding is all the 5 digits can be positive integers in other words 1 to 9. O is neither positive or negative.

Any official answer???

Any official answer???

GMAT TIGER · Answer

You are talking about a single digit where as the question is about 5 digit integer.
Suppose if 10,101 is a 5 digit +ve integer, -10,101 is a 5 digit -ve integer.

This is what meant by the +ve and -ve integer in the question.

PS-Comb

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards